1. "What is the PVI?"
Wikipedia's entry defines it as:
The index for each congressional district is derived by averaging its results from the prior two presidential elections and comparing them to national results. The index indicates which party's candidate was more successful in that district, as well as the number of percentage points by which its results exceeded the national average. The index is formatted as a letter + number; in a district whose CPVI score is R+2, recent Republican presidential candidates received 2 percentage points more votes than the national average. Likewise, a CPVI score of D+3 shows the Democrats received 3 percentage points more votes than the national average.
Essentially, what the PVI attempts to do is to determine just how Democratic or Republican a district is compared to the rest of the country, which helps to give a better idea where the most and least competitive districts are.
2. "So does that mean that PVIs can change over time?"
Yes, every presidential election, the PVI is recalculated in order to determine what the voting patterns in each district were like. While PVIs are typically used with congressional districts, since we don't have the new data for the 2008 elections at the CD level yet, we'll use two different states as an example (Illinois, Indiana). First of all, let's figure out what the PVI of both states were before the 2008 presidential election: (Illinois 2000 and 2004 data; Indiana 2000 and 2004 data) First of all, we know that in 2000 and 2004 George Bush won 48% and 51% of the vote respectively (averaged out, the Republican nominee's vote percentage is 49.5) while the Democratic nominees Al Gore and John Kerry both got 48% of the vote. Using Illinois first, since we know that both Kerry and Gore got 55% of the vote in the state, we can determine that Illinois's previous PVI is 55-48, which gives us a PVI of D+7 (meaning that Illinois voted 7 points more Democratic than the rest of the country over the 2000 and 2004 presidential elections). For Indiana, we know that George Bush won 57% and 60% of the vote respectively (for an average of 58.5%), subtracting George Bush's national average from this state average (58.5-49.5) we find that Indiana has a PVI of R+9 (meaning that Indiana voted 9 points more Republican than the rest of the country). Now, to recalculate this for 2008, we take out the 2000 numbers of Al Gore and George Bush's first run and we add in Barack Obama and John McCain's numbers (for the national numbers, the average changes to 50.5% Democratic to 48.5% Republican) we would also take the new averages for Illinois (adding Obama's 62% to Kerry's 55% and dividing by 2 gives us 58.5%) and Indiana (adding McCain's 49% to Bush 2004's 60% and dividing by 2 gives us an average of 54.5%). Using the equations from above, we find that Illinois's PVI is now D+8.5 (which means that it moved more Democratic relative to the country) while Indiana's PVI changed to R+4 (meaning that it is now voting quite a bit less Republican than the rest of the country).
3. "Wait a minute, even though Obama won Indiana, its PVI is still so slanted towards the Republicans?"
Yes indeed. To make this a little easier, remember that the United States itself has a constant PVI of 0 (because it is being compared to itself). Because of this, it is possible for Obama to actually win a district that Kerry lost and yet the state gets a more Republican PVI. Looking at Florida (2000 and 2004) we can see that George Bush got 48% and 52% in 2000 and 2004 (with an average score of 50%), which makes Florida's old PVI R+0.5. In 2008, John McCain got 49% of the vote in Florida, so adding Bush 2004 and McCain's performance and averaging them gives the state an average Republican vote of 50.5%, which, in the context of the 2004-2008 national Republican average of 48.5, we can determine that Florida has a PVI of R+2. So even though Obama won a state that Kerry did not, its PVI actually become more Republican!
4. "Wait a minute, what good is this measure if it decides that a state that went Democratic is actually Republican?"
Think of the country as being the "center", the "center" might be more Democratic and it might be more Republican at times, but regardless of which one it is, the country will always be at the "center". The PVI is attempting to tell us how far away from the center a given area is.
5. "Ok, so the PVI is a way of determining where a district is compared to the country, I understand that, but why is it that some districts with Republican PVIs of 10 or greater can sometimes have Democrats representing them (and vice-versa)?"
Former House Speaker Tip O'Neill once said that "All politics are local" and this is what he's talking about. Skilled politicians like Democrats Chet Edwards (TX-17) and Jim Matheson (UT-02) are able to survive in districts that are extremely Republican. Or there are states like North Dakota that, while tending to vote for Democrats for congress but vote for Republicans for president.
6. "Does this make the PVI system worthless then?"
No, since these districts are becoming fewer and fewer as the country becomes more polarized, the PVI is extremely useful in the vast majority of districts. Of course, the PVI does not tell us vital information, like whether or not there are viable candidates in the district, whether or not it traditionally is a split-ticket area, or on how scandals would work.
7. "Ok ok, I get what the PVI is and why it's useful, but why two presidential elections, why not just use one?"
Because using only one set of election data means that the new PVI would suggest that something massive has changed, even if it was only a one time thing. Two presidential elections lets us hedge our bets a bit. For example, we know that Indiana voted 3 points more Republican than the rest of the country, yet we also know that the last two elections had Indiana voting 9 points more Republican than the rest of the country, the idea is that we should not ignore the past.
8. "So then why not be even more cautious and use 3 or 4 different elections?"
My answer would be that, while I could definitely see incorporating three presidential elections into data for a given presidential year, doing this can hedge too much (for example, Gore did 6 points worse in Colorado than he did nationally, Kerry only did 1 point worse than he did nationally, and Obama did a point better nationally, if we did that, then Colorado would have a R+2 lean instead of being considered a D+0). It's up to each individual to decide whether or not more data should be added, but this is mostly the balance between having too much data and having too little.
9. "The PVI is meant for congressional districts, and shouldn't apply to states, yet you keep using states as your examples, why?"
As was mentioned earlier, the PVI is usually only calculated for congressional districts, but that doesn't mean that they are the only thing which has a PVI. So long as we have the data, we can figure out, not only what the PVI for each state is, we can also figure out the PVI of each county and even the precinct level. The reason why I'm not using congressional districts in my example is because the data isn't available yet.
And there is my explanation of the Partisan Voting Index, as a project, I'll probably start calculating the PVIs of each individual state (look for it on Election Inspection).