« General Election Cattle Call, July 21 | Main | Open Thread »

## Wednesday, July 21, 2004

### Electoral Vote Predictor

Posted by**DavidNYC**

Many, many sites have crystal balls telling them how the election will turn out. Of course, the General Election Cattle Call (track record: 0-for-0, perfect!) is the best of them all. But I've come across some other interesting methodologies as well. One of the simplest (and most visually appealing) is the Electoral Vote Predictor. The owner of that site uses the latest poll he (or she) can find for each state and plugs `em into an electoral map. Good spreadsheets and charts abound.

David Wissing does something similar, albeit without the fancy maps. The two sites come to slightly different conclusions as of this precise moment, but I think it's because Wissing doesn't use Zogby's "interactive" polls, while the EVP does. Apparently, using Zogby favors Kerry, because he has a bigger lead on EVP.

Do you know of any other good sites which attempt to predict the outcome of the election, particularly those which use a state-by-state approach? Let us know in the comments.

Posted at 03:19 PM in General | Technorati

## Comments

Hi,

This is exactly what we do at www.Race2004.net. We in fact have three big maps.

1 - The ongoing campaign, allows for states to be undecided. Also discerns between strong and weak candidate support within states.

2 - If the election were held today (assumes Nader is on the ballot unless he has officially failed to qualify).

3 - If the election were held today (assumes Nader is not on the ballot unless he made it via teh Reform party or turned in enough signatures).

Our methodology is a little complex to decide, as it varies slightly depending on which of the above three options you're considering. But generally speaking, we look at an average of the last three polls for the state.

Best of all, the site is extremely fast and has no tacky ads on the site. I run the site as a hobby and have no problem that it doesn't make a dime.

--Stephen

Posted by: Stephen at July 21, 2004 04:38 PM | Permalink | Edit Comment | Delete Comment

Check out 2.004k.com, which has links to all polls, a "What's New" page, and many different ways to view data in spreadsheet-like formats.

Posted by: PollFan at July 21, 2004 04:51 PM | Permalink | Edit Comment | Delete Comment

Projections with a map can be found at http://www.electionprojection.com/elections2004.html

Also the LA Times has a fun map that you can click on a state and turn it red, blue or white and the tally is automatic. When you get to 270 the presidential anthem is played.

Posted by: Steven M at July 21, 2004 04:52 PM | Permalink | Edit Comment | Delete Comment

There is always here...

http://www.mydd.com/outlook/president

and this fellow gives weekly updates on daily kos

http://www.dailykos.com/user/Wayne%20in%20Missouri/diary

Posted by: Keith Brekhus at July 21, 2004 06:00 PM | Permalink | Edit Comment | Delete Comment

*When you get to 270 the presidential anthem is played.*

If you get 270 red EVs, I hope it's something from Radiohead's "Hail to the Thief."

Posted by: DavidNYC at July 21, 2004 06:05 PM | Permalink | Edit Comment | Delete Comment

Intrade is a betting market with claims for the Presidential election including state-by-state outcomes. Currently, Bush and Kerry are neck-and-neck, with market odds of 51% that Bush will win the election.

Bush is the odds-on favorite in MO, OH and AR, while the opposition is narrowly favored in PA, IA, WI, OR, NH, NM. Florida is still a toss-up. My home state of WA isn't even close, with 3:1 odds against Bush. (Note: Most of the state-by-state claims are pretty thinly traded, so I'm not sure how well the current prices represent a genuine market consensus.)

If you think any of the claims are misvalued, you can take a position and make a profit if you're right...

Posted by: Matt Brubeck at July 21, 2004 06:14 PM | Permalink | Edit Comment | Delete Comment

here's one more if not here already...

http://www.geocities.com/samboni1342/state_polls.htm

Posted by: Scott Crawford at July 21, 2004 08:34 PM | Permalink | Edit Comment | Delete Comment

I've got a survey of 19 prediction/projection sites (20 including my own) here. It includes all the sites mentioned in this thread. I hope to update it regularly.

Posted by: Ed Fitzgerald (unfutz) at July 21, 2004 10:43 PM | Permalink | Edit Comment | Delete Comment

I've been tracking the values at intrade.com, they seem pretty reasonable. I've also been putting them into an excel sheet and calculating the expected number of electoral votes. Bush has held the lead until today. Currently Kerry leads 271-267. I like this method because it doesn't require you to pick swing states one way or another, but simply give a probability. Here are the most recent values (Bush's probability of winning) for the closest states:

ARKANSAS 59

MISSOURI 58.7

NEVADA 58

OH 56

FLORIDA 50.2

newhampshire 48

PENN 42.3

WISC. 41.1

newmexico 41

Posted by: Ben at July 21, 2004 10:47 PM | Permalink | Edit Comment | Delete Comment

I happened to have just finished counting votes on Intrade, in order to update my survey, and I got a different total.

The 22 states Kerry wins are:

CA, CT, DC, DE, HI, IL, IA, ME, MD, MA, MI, MN, NH, NJ, NM, NY, OR, PA, RI, VT, WA and WI

I put this into the LA Times tracker and checked the results on the dKos calculator and the one at Opinion Journal, and I get:

Kerry 264 - Bush 274

Did I miss something?

Posted by: Ed Fitzgerald (unfutz) at July 21, 2004 11:25 PM | Permalink | Edit Comment | Delete Comment

I was adding up expected values so let's take North Carolina as an example. Bush has a 77% chance of winning. Thus Bush can expect 11.55 electoral votes, Kerry 3.45. Adding them all up, you get Kerry 271, Bush 267.

Posted by: Ben at July 21, 2004 11:45 PM | Permalink | Edit Comment | Delete Comment

*I was adding up expected values so let's take North Carolina as an example. Bush has a 77% chance of winning. Thus Bush can expect 11.55 electoral votes, Kerry 3.45. Adding them all up, you get Kerry 271, Bush 267.*

Each state (except Nebraska and Maine) is a unit, its electoral votes indivisible, so if Bush is ahead in North Carolina with traders predicting a 77% chance of his winning there, he should be credited with all of North Carolina's 15 votes, not 77% of them. When you add things up that way (which I believe is the correct method), you get my count of Kerry 264 - Bush 274.

Posted by: Ed Fitzgerald (unfutz) at July 21, 2004 11:50 PM | Permalink | Edit Comment | Delete Comment

Ummm, yes, I'm familiar with that (though I ignore it in the cases of Nebraska and Maine). Shaq has career free throw percentage of 53.7% If he shoots 100 free throws, do you predict him to make 100 of them since his probability on each one is greater than 50%. Personally, I'd predict him to make 54.

Posted by: Ben at July 22, 2004 12:11 AM | Permalink | Edit Comment | Delete Comment

Shaq's past performance would lead me to predict that, on average (at least until his skill deteriorate) he would make 54 out of 100 free throws. However, unlike Shaq's free throws, electoral college votes (except in Nebraska and Maine) don't exist individually as seperate, discrete entities, they exist only in pre-determined packages, so if Shaq is trying to win North Carolinas electoral votes, he's either going to come away all 15 of them, or none at all. There's no real-world possibility that he's going to go home with 11.55 electoral votes in his pocket, because in the real world there ain't no such animal.

So, if we award Shaq North Carolina by virtue of making a free throw, then he has a 54% chance of walking away with 15 votes, and a 46% chance of walking away with nothing. On the basis that his chances of making the free throw are better than the chances of his missing it, I'd be willing to make a bet that he'll leave with 15 votes.

If you make a bet that he'll leave with 11.55 votes, you are going to be wrong 100% of the time.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:36 AM | Permalink | Edit Comment | Delete Comment

(Sigh) That's not the proper analogy, the analogy would be that every state's electoral votes are decided by a Shaq free throw. By your method, we would predict Bush 538, Kerry 0. I would probably be closer with my Kerry 289, Bush 249. This is basic probability, theory of expectations.

Posted by: Ben at July 22, 2004 12:43 AM | Permalink | Edit Comment | Delete Comment

I have to say, I'm loving this Shaq thread, but Ben, I don't understand your methodology. Can you try explaining once again?

Posted by: DavidNYC at July 22, 2004 01:10 AM | Permalink | Edit Comment | Delete Comment

OK, every state is dependent on the outcome of a free-throw, and Shaq's overall shooting percentage is 53.7%, but it turns out that when Shaq shoots free-throws in North Carolina, his percentage of success is 77%, and when he shoots them in Ohio, it's 56%, and when he shoots them in Hawaii, it's only 5% (he's obviously distracted by the beautiful weather and the hula dancers).

So let's say that Shaq travels to these three states, where he'll attempt a shot and will be awarded that state's electoral votes as a result. I say he's got a 77% chance of making the shot in North Carolina, so it's pretty safe that he'll collect North Carolina's 15 votes, and his 56% chance of making it in Ohio makes it a good bet that he'll got Ohio's 20 votes, but his 5% chance of making the shot in Hawaii means it would be unreasonable for him to get the 4 votes there, so it's probable that he walks away with 35 votes.

If I understand your method, you say that he's got a 77% chance of making his shot in North Carolina, so we expect him to get 11.55 votes, and a 56% chance of making the shot in Ohio, so we expect him to get 11.2 votes and a 5% chance of making it in Hawaii, so we expect him to get .2 votes, for a grand total of 22.95 votes.

Except, of course, that electoral votes aren't parcelled out in tenths and hundreths, or even in single votes, so there's just no way in hell Shaq can ever receive 22.95 votes, because 22.95 votes ** isn't a possible outcome**.

In fact, there are eight and only eight possible outcomes of Shaq's free throwing. He can win

0 votes

4 votes

15 votes

20 votes

4 + 15 = 19 votes

4 + 20 = 24 votes

15 + 20 = 35 votes or

4+15+20= 39 votes.

There are not other possible outcomes of this little gedankenexpermient.

So, you can say that the median number of votes Shaq can get is 19.5, but that doesn't mean he can walk away with 19.5 votes, because that outcome just doesn't exist.

Now, if we were to take and kidnap Shaq and force him to perform this experiment 100 or 1000 or many many times, then you would be justified in expecting that, on average, Shaq would have been awarded 11.55 votes on the basis of his shooting in North Carolina, but on ** no** specific shot in North Carolina (not a single one) did he

**win 11.55 votes. When Shaq left the arena in NC, he either had North Carolina's 15 votes in his pocket, or he didn't.**

*ever*Clear?

Oh, and please keep your sighs to yourself.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 01:38 AM | Permalink | Edit Comment | Delete Comment

If you flip a coin N times, you have an expected value of N/2 heads. If you roll a die N times and add up the numbers showing on the die, you have an expected value of [1*1/6 + 2*1/6...+6*2/6] 3.5N. If N = 1, then yes we get an "impossible" expected value of .5 for the coins, 3.5 for the die.

For the election, I simply do this with intrade.com's probabilities (I take the value of the last sale).

Bush's expected electoral votes =

(Alabama) .96*9 + (Alaska) .94*3 + ...(DC) .009*3

... = 266.9.

To take a fictional set of probabilities that indicate why this is better, simply suppose that Bush had a 50.1% chance at winning each state. I would say, wow, it looks like we're going to have a very close election. If you simply put all those states in the Bush column, you'd predict a 538-0 Bush wipeout.

Currently, New Hampshire is the only state with a greater than 50% shot at switching colors from 2000. That wouldn't be enough. The good news is that Bush has a weaker hold on his purple states than Kerry has on his. Here's a list of all states that neither candidate has a 60% shot at winning:

ARKANSAS 59

MISSOURI 58.7

NEVADA 58

OH 56

FLORIDA 50.2

newhampshire 48

PENN 42.3

WISC. 41.1

newmexico 41

This is promising for Kerry. Only 3 states (36 EVS) that Bush has a 40%+ shot at winning over. Kerry has a 40%+ shot at 6 states (73 EVs).

I hope that was helpful. Let me know if it wasn't.

Posted by: Ben at July 22, 2004 01:44 AM | Permalink | Edit Comment | Delete Comment

*By your method, we would predict Bush 538, Kerry 0.*

Absolutely untrue.

I'm trying to predict what the outcome of the electoral college vote will be, and I'm offered the data that traders think that Bush has a 77% chance of winning North Carolina, a 56% chance of winning Ohio and a 5% chance of winning Hawaii, and so on. I look at Bush's chances in each state. Since I'm making a straight up or down determination (no "leans", no "weaks" or "strongs"), if Bush's chances of winning the state are above 50%, I assign the state to Bush, and his total is increased by that state's number of electoral votes -- because that's the way the electoral college works, not proportionately.

Even if Bush's predicted chance of success is 50.2% (as in Florida), Bush gets the votes (27 in Florida's case. Tomorrow, when I make another projection, and Bush's chances in Florida have gone down to 49.9%, he ** doesn't** get it, and his total is reduced by Florida's 27 electoral votes, not by 0.3% of 27 electoral votes.

As I said before, counting votes by this method, ** the actual method used by the electoral college** results not in Bush 538 - Kerry 0, but Bush 274 - Kerry 264.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 01:50 AM | Permalink | Edit Comment | Delete Comment

Ed,

You say that you would predict Shaq getting 54 points on 100 free throws. But on any one free throw, he can only make it or miss it. You get 54 by adding .54 up 100 times, i.e. .54 *100. Suppose that Shaq was attempting 51 free throws and instead of 1 point for each shot, you awarded values like 3, 5, 27, even 55 for one. Let's say the maximum possible points is 538. How many points do you think Shaq would score?

You're right that my (basic probability) method will likely spit out an impossible value, like 290.5. If we care about such things we can round it. In either case, we'll be likely to be near the actual result.

Ben

Posted by: Ben at July 22, 2004 01:56 AM | Permalink | Edit Comment | Delete Comment

True, if every state was 50.1 percent, it would be foolish to ** predict** a Bush rout because assigning states straight up or down on that basis distorts things too much (which is why people use the qualifiers leaning, string and weak), but the plain unalterable fact of the matter is, if Bush did manage to win ever state with 50.1 percent of the vote, he will indeed receive 538 electoral votes, which is one reason people want to change the electoral college.

So if I were forced to use my methodology when polls or trading data showed Bush ahead in every state with 50.1 percent, I would have to bite the bullet and say Bush 538 - Kerry 0, and I would be correct if he pulled that miracle off. Using your methodology, however, you would predict that Bush would receive 278.538 electoral votes, which (again in that miracle outcome) would be statistically valid (perhaps) but wowuld bear no realtionship to what just happened.

I agree that if we ran the election multiple times (many many times), the outcome of repeated trials would be that Bush's average would approach 278.538 as a limit, but in none of those multiple outcomes would Bush ever receive that number of votes -- and we only run the election once.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:01 AM | Permalink | Edit Comment | Delete Comment

Ed,

That's fine if you want to use that method. It's a different method than you say you would use on free throws though. It also leads to fluctuations that aren't necessarily matched by events. Florida shifting between 50.1 and 49.9 due to thew fluctuations of the market will cause big changes in your method. Adding Edwards to the ticket caused a big drop in Bush's probability of winning in NC, but still it was above 50%. All told, the Edwards pick dropped Bush 8 electoral votes in one day by my method, much bigger than any other single day change. A recent Arizona poll that had Kerry up by 1 point dropped Bush's probability of winning AZ down by 12 points to 66%. This caused a small change using my method, no change in yours.

I like that my method is fairly steady, responding to actual changes in events.

Ben

Posted by: Ben at July 22, 2004 02:06 AM | Permalink | Edit Comment | Delete Comment

*You say that you would predict Shaq getting 54 points on 100 free throws. But on any one free throw, he can only make it or miss it. You get 54 by adding .54 up 100 times, i.e. .54 *100. Suppose that Shaq was attempting 51 free throws and instead of 1 point for each shot, you awarded values like 3, 5, 27, even 55 for one. Let's say the maximum possible points is 538. How many points do you think Shaq would score?
You're right that my (basic probability) method will likely spit out an impossible value, like 290.5. If we care about such things we can round it. In either case, we'll be likely to be near the actual result.*

If Bush's chance of winning in every state was 54%, then your analogy would be correct, and in that case, we would expect Shaq to walk away from his free-throws (where the first was worth 3, and the next 5, etc.) with 53.7 * 538 votes. And that would be the case because on the first free throw he sunk he would get 3 votes, and on the next (which he missed) he would get nothing, and on the third (good) he would get 27, and on the fourth (good) 55. At no time is he *ever* awarded 54% of 3, or 54% of 5, or 54% of 27 or 54% of 55, or even rounded or truncated versions of them. He either gets the 3 or he doesn't, because he either makes the shot or he doesn't.

Shaq's playing a game, and he makes 10 free-throws. Statistically, we expect him to make 54% of them. But when he makes the first one he gets 1 point, not 54% of 1 point, because that's the value of the reward he received for making the shot. The value of winning a state in the electoral college, is that state's number of electoral votes, which is indivisible.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:09 AM | Permalink | Edit Comment | Delete Comment

Ed,

If Bush was thought to have a 50.1% shot at winning each state, that's saying there is almost zero chance that he would win every state. It's just like a coin that gives heads when you flip it 50.1% of the time. If you flip that coin 51 times, there is almost no chance that you would get 51 heads, your best guess would be 26.

Suppose all the states that are currently >50% were at 99%. Suppose also that all the states

Ben

Posted by: Ben at July 22, 2004 02:15 AM | Permalink | Edit Comment | Delete Comment

*Florida shifting between 50.1 and 49.9 due to thew fluctuations of the market will cause big changes in your method.*

Yes, because on election day, the difference between Bush getting 49.9% of the vote and 50.1% of the vote in Florida is the difference between his receiving 27 electoral votes and receiving none.

Now, this brouhaha we're having comes about because I'm reporting up or down outcomes, where each candidate wins a state or he doesn't. In a more nuanced approach, there's a third catagory ("toss-up") where things are too close in that state to determine a probable outcome. We can add other qualifiers ("leaning," "weak," "strong") to help sort out the probablities as well. But under no circumstances, except in Nebraska and Maine, can you divide up a state's electoral votes and assign them proptionate to your data. You either assign it to one candidate or the other or demur from doing so. You can qualify your assignment, but in the end you got to say this state is for Bush or this state goes to Kerry, or I can't tell about this state. (In the 50.1 example, I wouldn't be making any predictions at all, because every state would be a toss-up.)

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:17 AM | Permalink | Edit Comment | Delete Comment

Ed,

Nobody's disputing that free throw points or a state's electoral votes (ignoring the exceptions) are indivisible. I'm just using expected values. Exactly like you do when talking about free throws.

Ben

Posted by: Ben at July 22, 2004 02:19 AM | Permalink | Edit Comment | Delete Comment

*Suppose all the states that are currently >50% were at 99%. Suppose also that all the states*

As I said, in this case of this reductio ad absurdum I would be calling every state a toss-up and wouldn't be surveying electoral college projections because no one would be making them.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:22 AM | Permalink | Edit Comment | Delete Comment

In what sense can Bush expect 11.55 electoral votes from North Carolina?

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:22 AM | Permalink | Edit Comment | Delete Comment

*Yes, because on election day, the difference between Bush getting 49.9% of the vote and 50.1% of the vote in Florida is the difference between his receiving 27 electoral votes and receiving none.*

I wrote this, but it's not actually true, of course, unless you assume that Kerry got all of the rest of the votes. In actual fact, a mere plurality is enough to win a state's e.v.s

I take Intrade's figure of 77 for North Carolina as meaning that there's a 77% chance of Bush winning the state, not that he'll receive 77% of the vote, but as a convention I've been interchanging the two.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:28 AM | Permalink | Edit Comment | Delete Comment

"In what sense can Bush expect 11.55 electoral v

votes from North Carolina?"

Have you ever seen the term "expected value"? It appears I was wrong in assuming everybody would know the concept.

It's the exact same sense that if Shaq has a free throw worth 3 points, he has an expected value of 3*.54 points. But we don't care if he makes that particular free throw, we want the best possible guess on how many points shaq will have after 51 free throws that total 538 points.

Why use a different method on these free throws than you use on the electoral college probabilites? The truth is, it doesn't matter to me if you don't want to use this method, but I find it scary that using it makes you think one must have a belief that fractional electoral votes are necessary.

Posted by: Ben at July 22, 2004 02:33 AM | Permalink | Edit Comment | Delete Comment

Scary all right.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:38 AM | Permalink | Edit Comment | Delete Comment

You know, I get it. The state's got a value of 15 votes, there's a 77 percent of winning the state so there exists a statistical entity called "expected value" which is 77 * 15. I get it.

It just doesn't have anything at all to do with what we're talking about here, which is counting up electoral votes.

You're welcome to your methodology. Enjoy.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 02:42 AM | Permalink | Edit Comment | Delete Comment

Ed,

I don't know how else to put it, but you really don't get it. Anybody that visits this site knows how counting up electoral votes works. The question is how to provide the best estimate.

I'm sorry if I seemed rude, but if you have any mathematically inclined friends, just ask them what they think.

Ben

Posted by: Ben at July 22, 2004 02:49 AM | Permalink | Edit Comment | Delete Comment

Anyway, for those of you who are like me and are too scarily ignorant to grok big-big concepts such as our rude friend Benton understands (they apparently neglected to teach me this stuff when I was at MIT in the 70s), and must resort to methodologies which have some actual corrrespondance with the real world, do take a look at my survey of 21 different projections and predictions -- but don't expect any value.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 03:20 AM | Permalink | Edit Comment | Delete Comment

Guys, guys... let's try to settle down here. This has been a very enlightening thread. There's no need for snippiness.

I'm still having a hard time, though, wrapping my head around what Ben is trying to do. I understand all the math behind it, but I'm still stuck on Ed's point that EVs are only awarded on a whole-state basis. Does the confusion perhaps stem from interchanging "likelihood of victory" with "percentage of vote captured?"

If we say Bush has a 50.1% chance of winning a particular state, those aren't very good odds. But if we say we think he's going to capture 50.1% of the vote (necessarily a plurality) in a particular state, he's guaranteed to collect all that state's EVs. It seems to me (maybe I'm wrong) that Ben is making the former assumption, while Ed is making the latter.

Posted by: DavidNYC at July 22, 2004 04:14 AM | Permalink | Edit Comment | Delete Comment

Sorry about getting snippy.

*Does the confusion perhaps stem from interchanging "likelihood of victory" with "percentage of vote captured?"*

If we say Bush has a 50.1% chance of winning a particular state, those aren't very good odds. But if we say we think he's going to capture 50.1% of the vote (necessarily a plurality) in a particular state, he's guaranteed to collect all that state's EVs. It seems to me (maybe I'm wrong) that Ben is making the former assumption, while Ed is making the latter.

Perhaps, but perhaps not.

In my own estimation of what the electoral college result would be based on conditions that exist at the current moment, I take each state that is in doubt and I look at all the polls, some of the very valuable information that Chris has worked up, as well as other miscellaneous data, combine it with my personal knowledge and experience, spit in the wind and make a judgment. If, for instance, Kerry is leading by one point in one poll, as just happened in Arizona, I don't (as Dave Wissing does) automatically assign the state to Kerry, because one lead inside the margin of error is not enough to overcome 13 polls over 9 months and all the other available data in Bush's favor, all of which creates a weight (a qualitative one, which I don't quantify) that makes it more difficult for things to turn in Kerry's favor. (Perhaps I should say it creates a kind of inertia which is hard to overcome.) So the state continues to be assigned to Bush, who gets its 10 electoral votes.

Now if another Kerry lead comes in, I'm going to start looking for a trend, and there's going to start to be some doubt in my mind that Bush is going to take Arizona, because Kerry is starting to overcome some of the state's inertia and move it in his direction. But my doubt about Bush's strength there, while it changes in some respect my expectations about the outcome, doesn't change the 10 votes Bush has been assigned. Bush will be assigned those 10 votes when I'm 95% sure he'll win the state, and he'll be assigned them when I'm 65% sure he'll do it. It won't be until enough data has accumulated to overcome the weight of the previous data and convince me that Kerry is actually leading the state that Bush's assigned value for AZ switches from 10 to 0, and Kerry's from 0 to 10.

At no time, despite my decreasing expectations for Bush in the state, does the value of the state change. It's either in Bush's column, or it's not. If it is, it's worth 10 votes, otherwise, he gets nothing, because the system has two states (on and off) and two values connected with those states (+10 and 0). In short, it's a digital system.

Now, you can certainly do what Ben is advocating and quantify Bush's or Kerry's strength and multiply that by the state's electoral votes and make a continuous curve of the state's "expected value" for each candidate depending on the how the data changes, but that implies an analog quality to the system that really isn't mirrored in the reality of the situation. Bush and Kerry (and the rest of us) can certainly think in terms of the probability of taking the state, that's eminently reasonable, but to intertwingle that probablity with the state's electoral vote value is not only unnecessary, it's positively deceptive, because it implies that there's some real world alternative between winning the state and losing it, and that's just not so. Creating a statistical entity, even one that's from a statistical standpoint valid in the abstract, which has no concrete relationship to the real world is an exercise in futility, and using it as an indicator of the state of play in the system is foolish.

Now, the contest is so close, and the electoral vote totals so relatively balanced, that Ben's totals are almost certainly going to be in the same ballpark as mine, so they are going to have the ** appearance** of validity, but in point of fact I don't believe that they're valid in the way he's using them, as I believe I can demonstrate in the next post.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 04:45 AM | Permalink | Edit Comment | Delete Comment

To answer your specific question about how to interpret the Intrade numbers, I see them as saying that traders think Bush has a 50.1% chance of winning the state (your first alternative), and not as saying that Bush will get 50.1% of the vote. As I wrote in one short post, I was informally switching between the two, which, strictly speaking, I shouldn't have done, but I believe my points remain valid nonetheless, since in an essentially two-party system, where other parties will normally poll 3% or less, it's usual for the winner to prevail by getting something very close to a majority, and not by a plurality, as is theoretically possible.

No, I think Ben is wrong because he's thinking of each state's electoral votes as a quantity that can be manipulated like any other quantity, whereas, in fact, that's not strictly true because of the dual nature of the system. * Within each state*, as I described above, the election is essentially digital, winner take all, which means that the number of the state's electoral votes has no real meaning or value

**. That number only really exists**

*inside the state***, in relation to the entire Electoral College, where it serves to weight the winner's victory. By manipulating the external number (the electoral vote count) by an internal number (the probablilty of winning the state), Ben is, in fact, performing a non-sensical calculation, mixing quantities associated with two different (although obviously related) systems.**

*outside of the state*Think about this hypothetical situation: There are two states, one with many electoral votes, let's say 55, and one which has a lot fewer, let's say 11. In the big state, Kerry's chances of winning are 70%, and Bush's chances are 70% in the smaller state. Under Ben's expected value system, which we're using to track the state of the electoral vote and how it will come out at the end, that gives Kerry .70*55 + .30*11 or 41.8 electoral votes (recognizing that these fractionated votes are just statistical indicators and not real votes), and Bush would have .30*55 + .70*11 or 24.2 votes.

Kerry 41.8 - Bush 24.2 looks like a good solid lead in electoral votes for Kerry -- in these two states he's about 17 and a half votes ahead! Even if we round up it's 42 - 24 and a solid lead of 18.

But is this in any respect a good approximation of the actual state of the system? I don't think so. A 70% chance of winning a state is a pretty damn good chance, one that's going to be very hard to overcome, so it's eminently reasonable to think that when the election comes, Kerry will win the bigger state and get its 55 votes, and Bush will win the smaller, and get its 11. When that happens, Kerry's advantage over Bush won't be anywhere near the predicted magnitude we'd expect from Ben's system, about 18 points, but almost 2 1/2 times that amount, 44 votes, which is exactly what would have been shown under the more reasonable system I'm advocating, one with corresponds closely with the real world.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 05:42 AM | Permalink | Edit Comment | Delete Comment

I see that I've managed to create some confusion in my last post. The "system I'm advocating" I referred to is not, in fact, the one I described in the post before, the one that I actually use for my own persomal projections. Instead, it's the system I've been referring to in my argument with Ben, where any state with an Intrade value for Bush over 50 is assigned to him, and anything else is assigned to Kerry.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 05:46 AM | Permalink | Edit Comment | Delete Comment

Add one more website to your list of electoral vote forecasts:

http://synapse.princeton.edu/~sam/pollcalc.html

Sam Wang is a professor at Princeton University using statistical analysis of state polls to arrive at outcomes with confidence levels expressed as percentages. Complete with red/blue map.

Check it out.

Posted by: pauloalto at July 22, 2004 07:04 AM | Permalink | Edit Comment | Delete Comment

*Sam Wang is a professor at Princeton University using statistical analysis of state polls to arrive at outcomes with confidence levels expressed as percentages. Complete with red/blue map.*

Thanks - I don't think he had the map there when I last went to the site, but I've added him to my survey.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 07:56 AM | Permalink | Edit Comment | Delete Comment

Let's take another example. Ohio and Pennsylvania are two crucial states, with 20 and 21 electoral votes respectively. As of yesterday, the value of the contracts for Bush winning those states were at 56.0 (Ohio) and 42.3 (Pennsylvania), so these are a fairly closely matched pair.

Now, either Kerry or Bush must win these states, so there are 4 distinct possible outcomes in this mini-system:

a. Kerry wins neither state

b. Kerry wins Ohio, Bush wins Pennsylvania

c. Kerry wins Pennsylvania, Bush wins Ohio

d. Kerry wins both

The projected chance of these outcomes happening, using the Intrade contract values, is:

a. .56 * .423 = 0.23688

b. .44 * .423 = 0.18612

c. .577 * .56 = 0.32312

d. .577 * .44 = 0.25388

(Note that a + b + c + d = 1)

As you can see, the most probable outcome is (c), Kerry winning Pennysylvania and Bush winning Ohio, which is exactly what we would expect from the contract values. Outcome (c) has a value to Kerry of 21 votes, and a value to Bush of 20. Using the system I employed to count up Intrade electoral votes, that is exactly how I would have assigned them, Kerry 21 - Bush 20.

Now, let's look at the system Ben used. To determine the expected value of each state, he multiplies the contract amount (i.e. chance of Bush winning) by the electoral vote value. So Bush would have .56*20 + .423*21 or a total expected value of 20.083 for these two states. Kerry would have a total expected value of .44*20 + .577*21 = 20.917. Rounding, we get Kerry 21 - Bush 20, which is exactly the same as mine.

But what happens when things change? Let's say that both Bush shores up his position in Ohio to a solid 65% chance of winning, but Kerry goes up as well, to 62%. By my system, the projection would still be Kerry 21 - Bush 20.

In Ben's system Bush now has .65*20 + .38*21 or 20.98, rounding to 21. Kerry has .35*20 + .62*21 or 20.02, rounded to 20 -- so now Ben's predicted has shifted to Kerry 20 - Bush 21, while mine has remained Kerry 21 - Bush 20, the most likely outcome in the real world.

OK, now let's stretch and say that traders look at what's going on and are really convinced that Pennsylvania is as settled as Texas and California, and the number in that state jumps precipitously. Pennsylvania is now trading at Bush 10% (i.e. Kerry 90%), while Ohio stays at Bush 65% (I'm just making these numbers up to illustrate a point, but there's nothing specific about them, the problem I'm describing will appear whatever the actual numbers might be.)

In my system, it's still Kerry 21 - Bush 20. In Ben's system, Kerry now has an expected value of .35*20 + .90*21 or 25.9, rounding to 26. Bush as an expected value of .65*20 + .10*21 or 15.1, rounded to 15. In other words, it's Kerry 26 - Bush 15.

So, to summarize

Ohio: Bush 56% and Pennsylvania: Bush 42.3% - Ben's system: Kerry 21 - Bush 20 / mine: Kerry 21 - Bush 20

Ohio: Bush 65% and Pennsylvania: Bush 38% - Ben's system: Kerry 20 - Bush 21 / mine: Kerry 21 - Bush 20

Ohio: Bush 65% and Pennsylvania: Bush 10% - Ben's system: Kerry 26 - Bush 15 / mine: Kerry 21 - Bush 20

It should be clear that in all three of these situations, the most likely outcome is that Kerry will win Pennsylvania and Bush will win Ohio (it was true at the beginning and the chances have only gone up as we went along) -- which means that in the real world the outcome would be that Kerry would win 21 votes and Bush would win 20. But whereas my system kept saying exactly that all along, because the electoral vote values never vary (because they can't), Ben's system shifted every time, until it was completely out of sync with reality.

What emerges here is what I alluded to before, that Ben's system only appears to have validity because the entire system is very close to an equilibrium. Roughly speaking, Bush and Kerry both have as many votes in strong states as each other, as many in weak states as each other, as many in toss-up states, and so on, so the errors in Ben's system get nearly cancelled out, and the remainder **looks** like it might be a legitimate reflection of the state of the system, because it's about the right magnitude. But, in fact, it's just a trick of the condition of the system.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 08:36 AM | Permalink | Edit Comment | Delete Comment

Ed and Ben are clearly arguing past each other with no real hope in sight of resolving the dispute. I'm going to give it a shot.

What Ben advocates makes perfect statistical sense, and the expected value method is a correct one...except that we have only 50 states, not 1000 or some other large sample size in which if Kerry has a 5% chance of winning 100 states he will win 5. In a large sample size, the bumps get smoothed out and we see a pretty clear picture of what would happen.

Ed's methodology would make sense for our small sample size...if of course we thought that every 52% state would fall in favor of the candidate who is favored 52% to 48%, but that clearly is not the case either. These are projections of probability in taking the state, so a 60% chance of taking a state probably means something like a 4% to 5% lead in the polls. Ben's method would say, well since we have 20 states for which this is the case, let's smooth those bumps out with expected value and we'll get a better current projection of what it will look like in November.

Since the projection falls into these two apparently irreconcilable traps, we cannot use either of them on their own. So, let's try combining the method.

For those states that are 75% or greater for one candidate, yes, we should probably just chalk it up as full electoral votes for the leader. Mississippi is at 95% Bush or something like that on Tradesports. Do we give Kerry 5% of those electoral votes...no? He's just not getting them. Those 150 "safe" EVs that each candidate has, throw them into their columns, because their not changing.

When we get down to below 75%, or some other arbitrary but meaningful cutoff (it's odd that one does not see many states between 75% and 65%) maybe we should start using expected value, as the probabilities start to get closer. This is not because the electoral college works like this, but because we are trying to get an accurate picture of what's going to happen in November. One cannot use these trading markets for anything else, because they say nothing about today, only about what people think will be the case on November 2nd.

Posted by: Joel W at July 22, 2004 08:57 AM | Permalink | Edit Comment | Delete Comment

Here's another way of thinking about it. Imagine a clear plastic map of the United States. Behind each state there is a red light and a blue light. There are rules for how each light gets turned on, and these can differ depending on circumstances. For instances, during an actual election, the light goes on corresponding to the candidate who has the largest number of votes in that state. When looking at polling, you can decide whether the light goes on when a candidate has any kind of lead (whether inside the margin of error or not), or only when the lead is outside the margin of error, or only when the lead is above a certain number or whatever you want. When looking at trading contracts at Intrade or Tradesports, you can decide that any value over 50% will turn on the light, or require 60% or 75% or whatever you desire. You can make the rules depending on what you want to measure, and you can certainly utilize probablistic analysis in making these rules.

But whatever your rules are for turning the lights on, the lights only go on and off. They don't get brighter at higher values, or dimmer at lower ones. They simply turn on at the threshold point you set, and that's it.

Now, with the lights on in each state, you can see which candidate won that state, and you can count the number of lights, but you don't know who actually won the election. To do that, you need a clear plastic overlay, on which is printed the electoral vote values for each state. With it in place, you can add up the values for all states with a red light and all states with a blue light, and whoever gets over 270 votes (if someone does, because depending on your rules some states may not be lit up at all) wins the election.

Note, though, that the values on the overlay are printed and do not change. They are not in any way effected by the rules you have utilized to determine when lights are turned on (i,e, when a state is won by one candidate or the other), because (1) they are unvarying constants and (2) they are a different part of the system from the part which determines whether lights are on or off.

You can't use the rules for the lights to alter the values on the overlays dynamically, and you can't use "expected value" to measure the state of the electoral college or project its outcome based on current conditions.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 09:23 AM | Permalink | Edit Comment | Delete Comment

*This is not because the electoral college works like this, but because we are trying to get an accurate picture of what's going to happen in November. One cannot use these trading markets for anything else, because they say nothing about today, only about what people think will be the case on November 2nd.*

An excellent point. Let me ponder a little the distinction between representing the current status of the system (i.e. it's hyopthetical status should the election be held today) and projecting its status on election day, and see if that makes any difference to me.

As for your compromise solution, it's certainly politic, but I'm not sure I buy it. Let me think about that as well.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 09:27 AM | Permalink | Edit Comment | Delete Comment

Ed,

Why do you object to my method, but include Ed Wang's? Ed Wang's is interesting, but he actually DOES make assumptions that don't apply to the real world. He assumes independence betweeen what happens in the states. That's why the probability is so high, I don't think anybody really believes Kerry has a 98% chance of winning right now.

Joel, why do you say 50 states are too small of a number? If you toss a coin 50 times, it will likely give close to 25 heads.

ben

Posted by: Ben at July 22, 2004 11:00 AM | Permalink | Edit Comment | Delete Comment

Here's my attempt at predicting the election: http://www.schak.com/270/ The methodology is pretty complex, but I've written it up in some detail---I use Kalman filtering, which is essentially a Bayesian strategy for discounting old polls. I state results for if-the-election-were-today (like Prof. Wang) and I project forward to election day because plenty can happen in the next 103 days. I also have some nifty electoral college cartograms that I designed myself.

Somebody said that it's not reasonable for Kerry to have a 98% chance of winning right now. I disagree. My analysis has Kerry handily winning all the blue states plus WV and NH if the election were held today. That brings him up to 269 votes. OH and FL would both be quite likely to go to Kerry if the election were today, and even MO is 50-50. Because Kerry would only need to pick up one out of OH, FL, and MO, 98% is reasonable. Of course, I expect the popular vote to be extremely close; Kerry wouldn't win by much, but he'd almost certainly win if the election were held today.

Also, on the surprisingly controversial subject of expected value, I do state an expected value for Kerry's electoral votes, but the likelihood-of-victory statistic is more important. It is possible, for example, for Kerry to have an expected value of over 270 votes, but still have less than a 50% chance of winning.

Posted by: Ben Schak at July 22, 2004 11:34 AM | Permalink | Edit Comment | Delete Comment

Ed,

Your Ohio-Penn example is different than the EC in that one state determines the entire electoral college. We wouldn't want to determine an expected value. We would simply say, it's irrelevant who wins Ohio, the probability of winning the whole election is simply the probability of winning Pennsylvania. In the real electoral college, any state could theoretically swing the election.

In the EC, I get the expected value for the electoral votes to get an intuitive feel for who's ahead. If one wanted to give a precise probability for the whole electoral college, it would be difficult to do without assuming independence (which clearly doesn't hold, e.g. if Kerry won Arizona, there's no chance he would lose Massachussets.)

Using my method on the real electoral map, but with fictional probabilities, it's not possible to construct an example where using my method would have somebody in the electoral lead who was actually a large underdog. This is quite straightforward to do for your method. Take for example, if Bush had 99% in all the red states - Florida, but 49% in all the blue state + Florida. Your method would give Kerry the electoral vote lead even though Bush would be the clear favorite. [Remembering that these percentages are probabilities of winning the states.]

Ben

Posted by: Ben at July 22, 2004 11:36 AM | Permalink | Edit Comment | Delete Comment

Ben,

If you believe the 98% figure, you should really enter the electronic markets. You could almost double your money.

What do you think the chances are that Kerry loses all three (OH, FL, and MO) are in November?

Ben

Posted by: Ben at July 22, 2004 11:40 AM | Permalink | Edit Comment | Delete Comment

Ben,

Your site is very interesting and I see that you concentrate on what would happen if the election were today rather than in November. Predicting for November forces one to be a bit more conservative, but I'll definitely be bookmarking your site.

Also, what I said about Dr. Wang's site wasn't quite right. I believe you need independence for the confidence intervals, but not for the probability of winning if the election's held today.

Ben

P.S. UPenn is a nice campus. I once saw Erdos give a talk there.

Posted by: Ben at July 22, 2004 11:56 AM | Permalink | Edit Comment | Delete Comment

*Take for example, if Bush had 99% in all the red states - Florida, but 49% in all the blue state + Florida. Your method would give Kerry the electoral vote lead even though Bush would be the clear favorite. [Remembering that these percentages are probabilities of winning the states.]*

Well, this is simply another reductio ad absurdum not terribly relevant to the issue at hand, because in this situation we wouldn't be using the up/down methodology, but one more similar to the one I, in fact, use in my own predictions -- and that's because we're deling with the real world and not a theoretical situation.

Most reasonable prognosticators would throw all those blue states & Florida into a "toss-up" category and credit Bush with the 251 votes from the other (99%) red states -- so the count wouldn't be Kerry 287 - Bush 251 as you imply, but Kerry 0 - Bush 251 - toss-up 287. They would do this (and I would agree with them), because they're interested in a real-world prediction and not in adhering to some particualar methodology.

If you want to adapt a Kerry/Bush/toss-up method with the Intrade data, giving each candidate everything over a certain threshold and withholding assignment of the others until they pass the threshhold, that's fine we me (I use both methods in my projection, and, in fact, prefer to say I'm currently predicting Kerry 291 - Bush 222 - ? [i.e. toss-up] 25, rather than Kerry 311 - Bush 227) but doing so won't make your expected value methodology any more accurate, as far as I can determine.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:22 PM | Permalink | Edit Comment | Delete Comment

*Your Ohio-Penn example is different than the EC in that one state determines the entire electoral college. We wouldn't want to determine an expected value.*

I'm afraid you misunderstand entirely. I was using the Ohio/Pennsylvania system as an exemplar representative of the entire electoral college as a whole, not because of their status as vital states. (For that reason I should have used two other well-matched states to illustrate the clear flaws in the expected value method, but the flaws are nevertheless demonstrated nonetheless, and the status of Ohio and Pennsylvania as "must win" states is irrelevant to the point I made, which stands.)

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:26 PM | Permalink | Edit Comment | Delete Comment

*Why do you object to my method, but include Ed Wang's?*

Because Ed Wang didn't add up the Intrade data using a flawed methodology and come up with a different result from mine.

If folks want to include expected value in their complex equations, that makes no nevermind to me, my survey is simply that, straight reportage. I don't quite believe in everything Chris does in his methodology, or Wayne in Missouri's, for that matter, and others I haven't even looked deeply at closely at all -- I'm just doing a survey and reporting the results. But the Intrade/Tradesports data isn't presented as a straightforward projection and has to be added up in some manner. Mine seems clear, obvious, and accurate to me, which is why I used it, and yours does not. Knowing that the methodology is fatally flawed, I see no reason to accept it.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:33 PM | Permalink | Edit Comment | Delete Comment

Ed,

I said nothing about Ohio/Pensylvania being vital states, I was taking them as a self contained example, an electoral college of 2 states and 41 votes. You're right that your method would give a higher (indeed the highest) probability of being precisely correct while mine would have no chance at that. It would also be more likely to be off by more electoral votes than "my" [quotes because once we have the probabilities, I believe Ben Schak, Dr. Wang, and I all use the same methods to calculate expected electoral votes. They use statistical analysis on the polling data to get the probabilies while I simply take them from the market.]

And there's no need to impugn motives, I'm also interested in real world predictions and only construct examples to make points. I like this method because it could be used in any election year and give good results. The all or nothing method won't necessarily do that. Indeed, most people use a toss-up category for the toss-up states, but in that case you're wasting the resource of precise (though possibly wrong, of course) numbers that intrade provides.

Ben

Posted by: Ben at July 22, 2004 12:42 PM | Permalink | Edit Comment | Delete Comment

*Here's my attempt at predicting the election: ">http://www.schak.com/270/*

I've added your site to my survey, and will include it in future updates.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:45 PM | Permalink | Edit Comment | Delete Comment

*I said nothing about Ohio/Pensylvania being vital states, I was taking them as a self contained example, an electoral college of 2 states and 41 votes.*

I see, sorry to have misunderstood.

But just as you wouldn't use the expected value methodology in this example, I wouldn't count votes in the same up/down way in the several reductions you've presented me as examples.

I'm (clearly), not a statistician, and therefore have no reason to accept or reject expected value as a technigue used in the course of some complex methodology, but when it's used baldly, as with the Intrade data, and comes up with what seems clearly (to me at least) an incorrect conclusion, I also see no reason to accept it in that instance.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:50 PM | Permalink | Edit Comment | Delete Comment

*One cannot use these trading markets for anything else, because they say nothing about today, only about what people think will be the case on November 2nd.*

Joel:

After thinking about it a bit, I'm not sure I agree with this.

What polls ask is usually something on the order of "If the election were held **right now**, who would you vote for?", and what the traders are telling us is something like "With what I know **right now**, here's what I expect will happen." These seem to me to be clearly related in some way, the common factor being the current real-world situation, which has to account for a large portion of the trader's available data.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 12:58 PM | Permalink | Edit Comment | Delete Comment

But Ed, I would use the expected value method for the Ohio-Pennsylvania example if we were simply trying to get a guess that would be closest to the real outcome rather than predict the winner of the mini-EC. True, you would have a chance at being exactly correct whereas I wouldn't. But if we look at one of your examples:

Ohio: Bush 65% and Pennsylvania: Bush 10% - Ben's system: Kerry 26 - Bush 15 / mine: Kerry 21 - Bush 20

In this case, we would expect my error to be smaller than yours. Your error (0) would be smaller in the case that Kerry wins Penn. and Bush wins Ohio, but even though it's the most likely outcome, there's still a good chance it won't happen. If you do a weighted average of our errors over all 4 cases, mine would be lower.

Ben

Posted by: Ben at July 22, 2004 12:59 PM | Permalink | Edit Comment | Delete Comment

Ed,

Your site needs an update, Florida's last trade was at 49.

Ben

Posted by: Ben at July 22, 2004 01:12 PM | Permalink | Edit Comment | Delete Comment

*Ohio: Bush 65% and Pennsylvania: Bush 10% - Ben's system: Kerry 26 - Bush 15 / mine: Kerry 21 - Bush 20*

In this case, we would expect my error to be smaller than yours. Your error (0) would be smaller in the case that Kerry wins Penn. and Bush wins Ohio, but even though it's the most likely outcome, there's still a good chance it won't happen. If you do a weighted average of our errors over all 4 cases, mine would be lower.

Actually, that turns out not to be the case.

Just to review, the 4 possible outcomes are:

a. Kerry wins neither state (Kerry 0 - Bush 41)

b. Kerry wins Ohio, Bush wins Pennsylvania (Kerry 20 - Bush 21)

c. Kerry wins Pennsylvania, Bush wins Ohio (Kerry 21 - Bush 20)

d. Kerry wins both (Kerry 41 - Bush 0)

And the probability of their occuring, using the hypthetical I presented are:

a. .65 * .10 = 0.065

b. .35 * .10 = 0.035

c. .90 * .65 = 0.585

d. .90 * .35 = 0.315

So the possibility of (c) **not** occuring is a fairly low 41.5 percent.

I calculate your weighted average error as 2.3875, and my weighted average error as 2.00375, so I don't see that your system (so-called for convenience) has any advantage there over mine (also so-called for convenience). Your average error is larger, and you get the wrong value in all four instances. My average error is smaller, and I get the correct value for the one outcome that's most likely to occur.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 01:40 PM | Permalink | Edit Comment | Delete Comment

*Your site needs an update, Florida's last trade was at 49.*

I updated it late last night already - but in general I don't plan to do hour-by-hour updates.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 01:43 PM | Permalink | Edit Comment | Delete Comment

Ed,

The standard way of calculating error is mean square error (MSE) or what amounts to the same thing, root mean square error (RMSE). My method is chosen precisely because it's shown (during the first few weeks of an undergraduate probability course) to minimize the error. If you choose an idiosyncratic error measure, then you will need another method to minimize error, but it will be highly unlikely to be your system.

This isn't to say that you shouldn't use your method on your webpage. I only entered into this debate when you logged on to argue that yours is correct and mine is wrong and attributed strange ideas to me. This is just a method I use for fun and shared with a few friends (who I went to graduate school in math with).

Ben

Posted by: Ben at July 22, 2004 02:01 PM | Permalink | Edit Comment | Delete Comment

Ed's method (counting the electoral votes for the one outcome with highest probability, and ignoring all other outcomes) tells you something about one scenario, but does not take into account whether that one scenario is 90% likely or only 1% likely, or how much it differs from the "average" scenario.

With all 50 states involved, there are billions of possible outcomes. Even the "most likely" outcome has a probability much much less than one in a million, and may be significantly different from the average outcome.

For example, suppose Bush's odds in the reddest states drop from 80-90% down to 50-60%, while Kerry's odds in several blue states rise from 60% to 95%. Then our expectations about the election should change significantly, but Ed's "vote counting" method will not reflect this change at all. He treates a 60% probability the same as a 90% probability. (In effect, treating both as 100% probabilities!)

Again, consider the example where every state has a 51% chance that Bush will win. The "highest-probability outcome" is that Bush gets 100% of the electoral college. But this outcome is very unlikely, and has a very high expected error by any reasonable measure.

Note: I have a BS in mathematics, but I am not a statistician. I agree that Ben's method is the correct way to predict (with minimum expected error) the electoral votes in the simplified case where the probability for each state is independent. In the real-life case where the probabilities are not independent, the InTrade market does not give enough information to calculate expected EVs.

Posted by: Matt Brubeck at July 22, 2004 03:11 PM | Permalink | Edit Comment | Delete Comment

Matt,

My background is in math too, but I don't know really know all that much about statistics either. I believe that the expected value is good regardless of whether the states are independent or not. [This was verified by a friend who does know a lot about statistics.] We just can't determine any sort of distribution without making some assumptions about independence.

Ben

Posted by: Ben at July 22, 2004 03:53 PM | Permalink | Edit Comment | Delete Comment

"I believe that the expected value is good regardless of whether the states are independent or not. [...] We just can't determine any sort of distribution without making some assumptions about independence."

Oh yes, that's right. Thanks for the correction.

Posted by: Matt Brubeck at July 22, 2004 04:18 PM | Permalink | Edit Comment | Delete Comment

*The standard way of calculating error is mean square error (MSE) or what amounts to the same thing, root mean square error (RMSE). My method is chosen precisely because it's shown (during the first few weeks of an undergraduate probability course) to minimize the error. If you choose an idiosyncratic error measure, then you will need another method to minimize error, but it will be highly unlikely to be your system.*

Really? I'm not doing a statistical analysis, I'm just counting.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 04:43 PM | Permalink | Edit Comment | Delete Comment

OK, non-statistician here, I look at this definition of "expected value" from Wikipedia:

*In probability (and especially gambling), the expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win per bet if bets with identical odds are repeated many times. Note that the value itself may not be expected in the general sense, it may be unlikely or even impossible.*

Two things I don't see in this situation to fit this definition:

(1) Where's the "random variable". We have a probability, but you're mutiplying it by each state's electoral vote, which is not a variable, but a constant.

(2) Where are the repetitions? Each event is singular, not repeated -- we don't hold the election 1000 times, we hold it once, and although the electoral college projection is updated based on new data, the new data doesn't form part of a series, but it counted independent of the previous value.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 04:49 PM | Permalink | Edit Comment | Delete Comment

So, even simpler example.

Today, State A, with 20 electoral votes has a Bush-win contract value of 30 percent, so its expected value is 6 for Bush and 14 for Kerry. In my counting system, I assign 0 votes for Bush and 20 for Kerry.

Next month, the state has shifted radically, and now has a Bush-win contract value of 70, so its expected values is now 14 for Bush and 6 for Kerry. In my system, I assign 20 votes for Bush and 0 for Kerry.

The following month, it's gone through the roof, with a Bush-win contract value of 90, so its expected value is 18 for Bush and 2 for Kerry. I continue to assign 20 votes for Bush and 0 for Kerry.

If the election had been held today, I would have assigned the correct number of electoral votes for the most likely (70%) occurence. If the election is held a month from today, I would again have assigned the correct number of electoral votes for the most likely occurence (70%). If the election is held in the following month I would again have assigned the correct number for the most likely (90%) occurrence. In no instance did you assign the right number, and your estimate of what number to add to the electoral college in the most likely scenarios was consistently wrong.

You may well be right that, on average, you were less wrong than I was when weighted for probability, but you also removed any chance of determining what the actual result of the electoral college would be, because (and this is a fundamental point, which I why I keep coming back to it) the states' values in the college are fixed, no matter what the probability of each candidate winning them, and these quanities are independent of each other and not related.

My opinion - it's folly to hang your hat on a method which seems designed to minimize average error, but gives up any chance at all of determining what the actual state of the system is at any one time, which is actually what we're interested in knowing, the very thing we're supposed to be determining.

So, great, you're not often very wrong, but you're never actually **right**. That sort of trade off has absolutely no appeal for me, and I don't really see its value for the specific system we're talking about.

And that, I think, is my last opinion on the subject.

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 05:08 PM | Permalink | Edit Comment | Delete Comment

There's a site called President Elect: (http://www.presidentelect.org/index.html) but it's not updated very often at all. They do promise to update it more frequently as the campaign picks up.

Posted by: Luis at July 22, 2004 05:48 PM | Permalink | Edit Comment | Delete Comment

"Where's the 'random variable'. We have a probability, but you're mutiplying it by each state's electoral vote, which is not a variable, but a constant."

In this case, the random variable (let's call it X) is the number of electoral votes won by Bush in the upcoming election. Ben is calculating E(X) -- the expected number of electoral votes.

"Where are the repetitions? Each event is singular, not repeated -- we don't hold the election 1000 times, we hold it once, and although the electoral college projection is updated based on new data, the new data doesn't form part of a series, but it counted independent of the previous value."

If I play a game where I can win $1 for calling a coin toss, my expected value from a single toss is 50 cents. This is true whether I plan to make one coin toss or many. The "50 cents" represents my best current estimate of my average return, based on all of the probable outcomes. Only one of those outcomes will actually occur, but I don't know which. I only know the probability and value of each possible outcome.

The expected value means that a rational investor would pay $0.49 to play the game, but not $0.51.

Suppose I am offering a special lottery ticket. If you buy the ticket now, then after the election I will pay you $1 for each of Kerry's electoral votes. How much will you pay for this ticket? The expected value tells us how much the rational investor should pay. (If I believe the above calculation based on the InTrade numbers reflects the true expected value, then I will recommend the lottery ticket as a sound addition to an investment portfolio if it costs less than $271.)

Furthermore, if I were in the lottery business, and accepting bets on many elections each year, the expected values tell me how much to charge for each election, if I want to break even in the long run (after repeating this experiment for many elections).

Some betting markets similar to InTrade actually do allow users to buy and sell tickets like this, which pay out based on the number of votes or points in an election or sporting event. So even though this example sounds contrived, it does have real world consequences for the bookmakers and bettors on these sites! There are other, more interesting consequences and ways to interpret the expected value, but this is one of the ones I find easiest to explain.

Posted by: Matt Brubeck at July 22, 2004 05:50 PM | Permalink | Edit Comment | Delete Comment

Ack! Sorry that comment was so long. :P

Posted by: Matt Brubeck at July 22, 2004 06:17 PM | Permalink | Edit Comment | Delete Comment

*There's a site called President Elect: (http://www.presidentelect.org/index.html) but it's not updated very often at all. They do promise to update it more frequently as the campaign picks up.*

Thanks, I'll hold on to the link, and if they start updating I'll add it to the survey (Right now their latest is dated 5/28).

Posted by: Ed Fitzgerald (unfutz) at July 22, 2004 09:56 PM | Permalink | Edit Comment | Delete Comment

One problem with all electoral vote predictors, including SSP: For the past forty years, whenever there is an incumbent president, the undecided voters have gone to the challenger at least 3 to 1 (or so I've been told). If that happens again (and given the intense dislike for Bush, this is quite likely), all of the electoral vote predictors will be way off--Kerry will do much better than they predict. I'd love to see an electoral vote predictor that distributes the undecideds 3-1, and then see what the projections are.

Posted by: science at July 23, 2004 03:39 PM | Permalink | Edit Comment | Delete Comment

Science,

I've seen that claim several places and am more than willing to believe it, but do you know where I could see the evidence? Any links?

Ben

Posted by: Ben at July 23, 2004 04:37 PM | Permalink | Edit Comment | Delete Comment

Ben--

Alas, I don't. If one checks the polls a week or so before the election and then the final results, it was certainly true for the 1976, 1980 and 1996 elections (Clinton's lead of 12 went down to 8). And there were very few undecideds in 1984. But I don't know of a specific reference.

Posted by: science at July 23, 2004 04:45 PM | Permalink | Edit Comment | Delete Comment

Updated Electoral College prediction / projection survey here.

Posted by: Ed Fitzgerald (unfutz) at July 25, 2004 07:19 PM | Permalink | Edit Comment | Delete Comment

I didn't read through the whole thread between Ed and Ben here, but I have been tracking, and indeed trading, the tradesports odds for a little over a year now and in the spreadsheet I use to track the prediction from this market I use Ben's methodology. I have also used Ed's methodology as a back-up that I track in the line below.

Posted by: tjs at July 25, 2004 08:32 PM | Permalink | Edit Comment | Delete Comment

Here's your evidence of incumbents breaking late:

http://www.pollingreport.com/incumbent.htm

From the article---

"In 127 cases out of 155, most or all of the undecideds went for the challenger:

DISPOSITION OF UNDECIDED VOTERS

Most to challenger 127

Split equally 9

Most to incumbent 19 "

If the race remains where it is at, Kerry will win by 4. But that's a big if.

Cut and paste the URL. The article is from 1989.

Posted by: LQC at July 26, 2004 08:14 AM | Permalink | Edit Comment | Delete Comment

Ed wrote:

"Most reasonable prognosticators would throw all those blue states & Florida into a "toss-up" category and credit Bush with the 251 votes from the other (99%) red states -- so the count wouldn't be Kerry 287 - Bush 251 as you imply, but Kerry 0 - Bush 251 - toss-up 287. They would do this (and I would agree with them), because they're interested in a real-world prediction and not in adhering to some particualar methodology."

Is it then fair to assume that if there are 287 "toss-up" votes, we should expect each candidate to win about half of them? I.e., wouldn't you expect Bush to win roughly 251 + 143.5 and Kerry to win roughly 143.5, give or take say 40 votes (or any similar value significantly less than 143.5 -- you pick). If you disagree with this, I'm confused and give up. If you agree, then you are accepting a very rough expected value, but one which ignores some useful information. Ben's method just carries this approach to its logical conclusion, wringing out nearly every bit of predictive information that can be obtained.

Also, I must note that if the probability of Bush taking PA is 90%, then 10% of the time (in fact, perhaps this time), Kerry will get those EV's "in the real world!". If there is no chance of Kerry getting them, the probability for Bush would need to be 100%.

On the other hand, you rightly point out that we are dealing with a relatively small number of discrete integer values, which raises a red flag for using continuous techniques. I have very rusty memories of statistical techniques that deal with this kind of graininess by tweaking the continuous approximation, but I'm not sure those tricks are meaningful here, and even if they are, the effect would be rather small.

Also, once the horserace polls go past about 60/40, the betting odds should be about 99%/1%, so it might be that the traders are not particularly rational in such extreme situations, and in fact over-estimate the underdog's chances. Ben's method would be significantly more sensitive to this kind of distortion, precisely because he is using every bit of (possibly bogus) information they provide. I think your intuitions are rightly picking up on this.

[I have a pet peeve that reporters will call 48/44 a "statistical tie", when in fact the betting odds could be something like 60/40, depending on the margin of error.]

Bottom line: I'd use Ben's basic method, but would collect the raw data from traders, time-and-bias-weighted poll results, historical trends, and my own intuitions, to get a robust set of probabilities. The net effect would be a relatively smooth-changing prediction that tracked day-to-day events.

Ok, a better bottom line: My thanks to all of you who actually take the time to crunch and display the numbers, since there is no way I could find the free time to do it myself.

Posted by: James McDonald at July 26, 2004 09:45 AM | Permalink | Edit Comment | Delete Comment

*Is it then fair to assume that if there are 287 "toss-up" votes, we should expect each candidate to win about half of them? I.e., wouldn't you expect Bush to win roughly 251 + 143.5 and Kerry to win roughly 143.5, give or take say 40 votes (or any similar value significantly less than 143.5 -- you pick). If you disagree with this, I'm confused and give up. If you agree, then you are accepting a very rough expected value, but one which ignores some useful information. Ben's method just carries this approach to its logical conclusion, wringing out nearly every bit of predictive information that can be obtained.*

No, the very existence of the "toss-up" category in this particular hypothetical is equqivalent to saying "I can't project these states", so I wouldn't have any particular expectations about them, and certainly wouldn't simply divide them in half as you've suggestedd. That's because what I'm interested in doing is not creating a number out of statistical techniques, but in "calling" each state and adding up that state's Electoral Votes for a total for each candidate.

In my own personal system, I do have a "toss-up" category, but resolve it by assigning that state to the candidate who's leading in the most recent poll -- but I keep in mind that my "real" projection is that I simply can't assign those states. In the hypothetical which generated the 287 toss-up votes, I'd probably be tempted to go to a similar system (assigning those states to the winner of the most recent poll), just to generate some small sense of where the election is, despite the obvious volatility that method would create, but I wouldn't (I don't think) use statistical techniques to generate a number which has no possibility of being achieved in the real world where electoral votes numbers are fundamental by state.

I suppose that's my own personal prejudice. I see each state's electoral votes as being (in the current system, and ignoring Nebraska and Maine) as being fundamental and indivisible and not simply numbers that can be manipulated willy-nilly.

Posted by: Ed Fitzgerald (unfutz) at July 26, 2004 12:37 PM | Permalink | Edit Comment | Delete Comment

LQC,

Thanks for that link.

tjs,

Do you have your spreadsheet posted anywhere, or perhaps a chart based on it? I'd be curious since I've only been tracking since beginning of July.

ben

Posted by: Ben at July 27, 2004 12:12 AM | Permalink | Edit Comment | Delete Comment

Dear all,

Sam Wang here. I am the poster of the calculation mentioned earlier: http://synapse.princeton.edu/~sam/pollcalc.html

I am a bit reluctant to enter such a lively fray. Instead of detailed commentary, I offer just a few notes.

1. The concept of expected value is perfectly reasonable. However, it does not take into account the shape of the distribution of outcomes. In the case of the states, which are "grainy" and where the grain sizes (i.e. the number of electoral votes per state) are so variable, big events near the 50-50 line (such as Ohio, Pennsylvania) have a big influence on the outcome. Presumably we are all interested in these borderline cases, so expected value is not quite nuanced enough. I'll demonstrate what I mean at the end of this posting.

2. The concept of "most probable outcome" is interesting, but is a bit extreme. As pointed out by someone else, with so many states the most probable outcome is still not very probable. (For the record, based on the numbers on my site, that probability is currently 7.3%.) This approach gives a reasonable snapshot and can be done with a hand calculator, but does not take advantage of modern computing power.

It might be better to refer to the most probable outcome as a "most likely outcome," since the word probable implies, to many people, an event that is more than 50% likely.

My calculation is, in a sense, a generalization of the likelihood concept. The idea is to calculate the number of electoral votes associated with every possible outcome, calculate the probability of that outcome, and add up all the probabilities that correspond to 270 EVs or more.

3. To state the obvious, the probability of Kerry or Bush winning any given state is hard to know in advance. This is the fundamental problem, and trumps all the other issues. I like the use of betting sites to estimate these probabilities, but that approach puts a lot of faith in the power of collective guessing. Also, it is certainly subject to the problem mentioned that states co-vary.

Instead of getting into this, I just use current polls. I should point out that my method is not subject to the problem of co-variation, at least not in an obvious way. This is because I calculate probabilities using polling data from the particular state in question. Although polls in different states are more likely to move together than independently, this does not change the fact that these polls are independent measurements.

I had intended my measure as a way of summarizing the flood of state polling data with a few simple measures that are easy to understand. I hadn't realized that I was entering a lively and contentious community!

Regards,

Sam Wang

P.S. Here is the promised example.

Imagine that there are only three states with a total of 100 electoral votes: A (45 votes), B (40 votes), and C (15 votes). If the probability of Kerry winning these states is 40%, 50% and 80%, then the expected value looks like a tie:

(45)(0.40) + (40)(0.50) + (15)(0.80) = 50.

The combinations that lead to getting a majority are

A and B and C (100 votes): 0.4*0.5*0.8=0.16.

B and C (55 votes): 0.6*0.5*0.8=0.24.

A and C (60 votes): 0.4*0.5*0.8=0.16.

A and B (85 votes): 0.4*0.5*0.2=0.04.

The total probability of a Kerry win is then 0.60, or 60%.

In this example, the most important grainy event is that the swing state, C, is 80% likely to go for Kerry. This skews the probability considerably. Therefore...watch those swing states!

Posted by: Sam Wang at July 28, 2004 01:36 AM | Permalink | Edit Comment | Delete Comment

*The concept of "most probable outcome" is interesting, but is a bit extreme. As pointed out by someone else, with so many states the most probable outcome is still not very probable.*

My Daddy always warned me that when academics said something was "interesting" you should cut and run, because they meant it was really, really dumb. (No he didn't, my father never said any such thing.)

I take your point about the value of using "likely" instead of "probable", but I have a question concerning the idea that the "most probable outcome" in a state is not very probable at all, because there are so many states.

If we were talking about a country in which the President was directly elected nationally by the result of the popular vote, it wouldn't matter how many administrative divisions the country was chopped up into, and (I assume) one wouldn't approach predicting election results by attempting to predict the outcome of each division and then (in some fashion) combining them together -- is that right? My assumption has been that we do what we do in the U.S. in trying to predict a Presidential election outcome because of the institution of the Electoral College, which essentially converts the result of 51 distinct and independent elections into an outcome for the country as a whole.

So, if that's the case, why would the number of states make any difference in calculating a projected outcome for the election, since we can deal with each state seperately and independent of any other, and then simply add the results together? Isn't introducing the combined probability of all the states a rather uninteresting red herring which masks the essential nature of the system and does not illuminate its inner workings?

(I'm not sure exactly what "co-variance" means, but I assume it's a measure of the dependence or independence of one state from another, and that knowing this would be necessary if a combined probability was to be calculated. But in the kind of system I'm advocating -- i.e. dealing with each state individually and then doing the completely mechanical process of addition to derive a final result -- I presume that this kind of inter-state interdependency would be represented in the polling data which provides the raw material we primarily deal with in "calling" or assigning a state's electoral votes for one candidate or the other, and that, therefore, it doesn't need to be introduced or accounted for.)

Posted by: Ed Fitzgerald (unfutz) at July 28, 2004 03:13 AM | Permalink | Edit Comment | Delete Comment

"1. The concept of expected value is perfectly reasonable. However, it does not take into account the shape of the distribution of outcomes. In the case of the states, which are "grainy" and where the grain sizes (i.e. the number of electoral votes per state) are so variable, big events near the 50-50 line (such as Ohio, Pennsylvania) have a big influence on the outcome. Presumably we are all interested in these borderline cases, so expected value is not quite nuanced enough. I'll demonstrate what I mean at the end of this posting."

Sam,

While this is certainly true in the abstract (and your example), indeed, you can come up with much more extreme examples such as the lottery, is it true for the EC? In the lottery, you have a >99% chance of getting a lower result than your expected value. In your EC work, have you found cases where the expected value is far off from the 50% point?

Another point: are you sure you can avoid making assumptions about independence?

Let's look at California, Oregon, and Washington.

Kerry's current probabilities (from intrade) are 91%, 64%, and 76%.

Assuming independence, his probability of winnng all three is 44%.

But isn't the true probability higher since the conditional probability for winning California if Kerry wins Oregon is probably 99.9%? This is backed up by the new market for a West Coast bundle which has the probability of Kerry winning all three at 55%.

Also, your work seems to do a great job at saying what would happen if the election were today, but surely we can't be 98% confident that Kerry will win in November.

ben

Posted by: Ben at July 28, 2004 01:33 PM | Permalink | Edit Comment | Delete Comment

Ed, I agree with your point that "we can deal with each state separately and independent of any other, and then simply add the results together." However, I think this requires either (1) making an up-or-down prediction about how each state will turn out, or (2) assessing the likelihood of a particular outcome and weighting this outcome accordingly.

This distinction matters a lot when we are not certain how a particular state will turn out. Current mystery states include Florida, Ohio, and Missouri. If polls indicated that Kerry had a 49% chance in all three, then there would be a nearly 7/8 chance that he would win at least one. That leads to a very different predicted outcome than assigning all three states to Bush. This leads well to my next point...

Ben, it's certainly true that the conditional probability of winning California, if Kerry wins Oregon, is near 1. But I think this illustrates that there is a vital distinction between what traders *think* will happen vs. empirical calculations from polling data.

Because some states are known to be more Democratic- or Republican-leaning than others:

(D R)

this information would figure into any rational trader's bids. Therefore, if you use those data, multiplying probabilities is not really kosher, for the reason that you give. A better approach might be to score anything above 50% as being for one candidate. I think you do this, right?

However, I think this would be less useful when probabilities are in the middle range. For instance, Bush winning Florida would not tell us that much about the likelihood of Ohio. (Though there might be some small amount of information - that would be an interesting thing to test with polling and election data.)

In regard to state polling data, in principle the measurements are all independent of one another, so these should be usable to calculate probability. The way I do it is to calculate an overall confidence interval on the margin between candidates, and convert that to a probability. This is like saying that we don't know exactly the rank ordering, and we are using the polling data to tell us the rank order. In this case, multiplying probabilities should be valid.

You are completely correct in saying that we can't be 98% confident of a Kerry victory in November. If you go over to my site now, you will see that the six-last-polls calculation is now at 87%. I have tried hard to avoid making a prediction, although it does leak through when I recommend actions. The calculation itself is a snapshot at a particular moment; that's all it is. Projecting forward in time requires a model for the probabilities and effects of many events. For some big things my educated guesses are: undecided voters should break for the challenger, third-party candidates will fade, and Iraq and the economy won't improve drastically. But other events are hard to predict. I left all this out; I intended to provide a pure calculation, to which one can add speculations. Anyway, as Johnny von Neumann (is said to have) said: prediction is hard, especially of the future!

Posted by: Sam Wang at July 28, 2004 05:16 PM | Permalink | Edit Comment | Delete Comment

"You are completely correct in saying that we can't be 98% confident of a Kerry victory in November. If you go over to my site now, you will see that the six-last-polls calculation is now at 87%. I have tried hard to avoid making a prediction, although it does leak through when I recommend actions."

Sam,

I see now that you have it at 85%, but I think the point still holds given the recommendations at your site. I don't think Kerry is any more of a sure thing than Tony Knowles is. It would be interesting if you tracked polls on the Senate races and did similar calculations.

Ben

Posted by: Ben at July 28, 2004 06:43 PM | Permalink | Edit Comment | Delete Comment

In regard to the particular example of giving to Kerry vs. giving to Knowles, I am interested in the idea of maximizing the ideological/policy return on one's contributions. My current argument goes as follows.

Since the Kerry campaign's budget is of order 100 times larger, my contribution is 1/100 the fraction of the total. A contribution to Knowles is proportionally 100 times larger, and will make more impact on the likelihood of his victory. If Kerry's chances of victory are near-saturated, this intensifies the effect. But - is the Senate a good place to contribute money?

Tracking Senate polls would be interesting, but I haven't run across a systematic source of information. One could consult the betting sites. In this case the probabilities might co-vary less. One simple calculation would be to estimate the probability of the Senate changing hands. The calculation is much simpler because the expected-value calculation would be all that was necessary.

Oh, heck, let's do it. Using the DailyKos Senate Outlook as the list, and Tradesports as the source of probabilities:

Republican seats (0 to +1 each):

Illinois - Obama. +0.93

Colorado - Salazar. No data: guess +0.7

Alaska - Knowles. +0.535

Oklahoma - Carson. No data: guess +0.6

Pennsylvania - Hoeffel +0.20

Missouri - Farmer +0.12

Democratic seats (0 to -1 each):

Georgia - No data: guess -0.9

South Carolina - Tenenbaum. No data: guess -0.5

North Carolina - Bowles. 72% D win, -0.28

Florida - primary. No data: guess -0.3

South Dakota - Daschle. 65% D win, -0.35

Louisiana - primary. 72% R win, -0.72

The midrange net expected value is about 0. However, note the massive uncertainty! These numbers are not worth cranking through my model in detail. However, just inspecting the numbers, it seems that the likelihood of picking up one or more seats (thus producing a tie or better for the Democrats) is, very roughly, about 1 in 4. However, note that this changes a lot even with a small swing - adding 10% per race translates to even odds.

This calculation can't be taken seriously because of the lack of information. However, one thing I get from it is that the Senate is a good place to put money if one wanted to push the outcome slightly in one direction. Since Knowles is at the 50-50 point and Alaska is a cheap ad market, he seems to be the best target. Other likely targets are CO, FL, OK, SC, LA. In case of a Democratic blowout, then PA and MO.

Posted by: Sam Wang at July 28, 2004 07:26 PM | Permalink | Edit Comment | Delete Comment

Sam,

I fully agree with your arguments in your post here. At this point, the marginal dollars we give to the close Senate and House campaigns can achieve much more. In fact, I may just go ahead and give to Knowles this weekend! :) But I'm still sweating the presidential election too, especially since I live in a swing state.

If you ever get your hands on a lot of senate polling data, it would be cool to see your results.

ben

p.s. I hope Tenenbaum is at .5 like you propose...

Ben

Posted by: ben at July 28, 2004 09:21 PM | Permalink | Edit Comment | Delete Comment

*Ed, I agree with your point that "we can deal with each state separately and independent of any other, and then simply add the results together." However, I think this requires either (1) making an up-or-down prediction about how each state will turn out, or (2) assessing the likelihood of a particular outcome and weighting this outcome accordingly.*

Don't these two choices exemplify the different methods advocated by Ben and I?

In my own personal method (hardly strict enough to call a "methodology"), I do indeed try to go up or down on each state, and only fall back on the "toss-up" status when I really can't resolve the information I'm relying on. (When forced to assign the toss-ups, in order to have a number comparable to other websites, I simply use the result of the latest available non-partisan poll.)

When I approached counting the Tradesports/Intrade figures, I simply extended this method to them as well, assigning any state about 50% to Bush, and anything below 50% to Kerry. (If there had been a contract selling for 50 I guess I would have been forced to make a toss-up category, but I could have done that in any event, assigning contracts withing a narrow band -- maybe 45 - 55? -- there, but in the survey I try to avoid the whole toss-up thing as much as possible, so I didn't.)

It didn't cross my mind at the time, as it obviously has now, that the contract data was a projection by the traders as to what the results would be on November 2nd, and that that might differ somewhat with what the other sites were saying. In fact, right now I'm somewhat confused, even in my own numbers, about whether we're presenting a snapshot of what the system is like at the present time ("if the election were held today...") or a projection as to what it will be on election day. I think basically the former, but with elements of the latter integrated into it (such as when I look at a close race and think "Well, the Nader vote will be less than that, and the undecideds will break for Kerry, so...").

In any case, given the two choices you present, it was inevitable that, as a statistical naif, I would opt for the first, since I don't have the skills or knowledge to try for the second.

Posted by: Ed Fitzgerald (unfutz) at July 28, 2004 10:01 PM | Permalink | Edit Comment | Delete Comment

Ed, what's funny is that I think your snapshot takes a picture of what people **today** think will happen **on Election Day**. Now there's a mind-bender!

Sam

Posted by: Sam Wang at July 28, 2004 10:22 PM | Permalink | Edit Comment | Delete Comment

New survey posted here.

Posted by: Ed Fitzgerald (unfutz) at August 1, 2004 04:09 AM | Permalink | Edit Comment | Delete Comment

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Posted by: melodias at November 3, 2004 12:57 PM | Permalink | Edit Comment | Delete Comment