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22 January 2009

Studying the 2008 primaries with prediction markets: Malhotra and Snowberg

With Obama now in office the rest of the country may be about ready to move on from the 2008 election, but political scientists are of course still finding plenty to write about. Neil Malhotra and Erik Snowberg recently circulated a working paper in which they use data from political prediction markets in 2008 to examine two key questions about presidential primaries: whether primaries constrain politicians from appealing to the middle of the electorate and whether states with early primaries play a disproportionately large role in choosing the nominee. It's a very short and preliminary working paper that applies some novel methods to interesting data. Ultimately the paper can't say all that much about these big questions, not just because 2008 was an unusual year but also because of the limitations of prediction market data and the usual problems of confounding. But there is some interesting stuff in the paper and I expect it will improve in revision -- I hope these comments can help.

The most clever insight in the paper is that you can combine data from different prediction markets to estimate an interesting conditional probability -- the probability that a primary candidate will win the general election conditional on winning the nomination. (If p(G) is the probability of winning the general election and p(N) is the probability of winning the nomination (both of which are evident in prediction market contract prices), p(G|N) -- the probability of winning the general election if nominated -- can be calculated as p(G)/p(N).) In the first part of the paper, the authors focus on how individual primaries in the 2008 election affected this conditional probability for each candidate. This is interesting because classic theories in political science posit that primary elections force candidates to take positions that satisfy their partisans but hurt their general election prospects by making it harder for them to appeal to the electoral middle. If that is the case, then ceteris paribus one would expect that the conditional election probabilities would have gone down for Obama and Clinton each time it looked like the primary season would become more drawn out -- which is what happened as results of several of the primaries rolled in.

As it turns out, p(G|N) didn't move much in most primaries; if anything, it went up when the primary season seemed likely to extend longer (e.g. for Obama in New Hampshire). Perhaps this was because of the much talked about positive countervailing factors -- i.e. the extended primary season actually sharpened each candidate's electoral machines and increased their free media exposure. Of course, Malhotra and Snowberg have no way of knowing whether the binding effect of primaries exists and was almost perfectly counterbalanced by these positive factors, or whether none of these factors really mattered very much.

There is yet another possibility, which is that conditional probabilities did not move much for most primaries because most primaries did not change the market's view of how long the primary season would be. Knowing how the conditional probability changed during a particular primary only tells us something about whether having more primaries helps or hurts candidates' general election prospects if that primary changed people's expectations about how long the primary season would be. There were certainly primaries where this was the case (New Hampshire and Ohio/Texas come to mind) but for most of the primaries there was very little new information about how many more primaries would follow. Malhotra and Snowberg proceed as if they were looking for an average effect of a primary taking place on a candidate's conditional general election prospects, but if they want to talk about how having more primaries affects candidates' electability in the general election, they need to focus more squarely on cases where expectations about the length of the primary season actually changed (and, ideally, not much else changed). I would say the March Ohio/Texas primary was the best case of that, and at that time Barack Obama's p(G|N) dropped by 3 points -- a good indication that the market assumed that the net effect of a longer season on general election prospects was negative. (Although of course that primary also presumably revealed new information about whether Obama would be able to carry Ohio in the general election -- it's hard to disentangle these things.)

The second part of the paper explicitly considers the problem of assessing how "surprised" the prediction markets were in particular primaries (without explaining why this was not an issue in the first part), and employs a pretty ad hoc means of upweighting effect estimates for the relatively unsurprising contests. Some kind of correction makes sense but it seemed to me that the correction was so important in producing their results that it should be explained more fully in further revisions of the paper.

So to sum up, I liked the use of prediction markets to estimate the conditional general election probability for a candidate at a point in time, and I think it's worth getting some estimates of how particular events moved this probability. I think at this stage the conclusions are a bit underdeveloped and oversold, considering how many factors are at play and how unclear it is what information each primary introduced. But I look forward to future revisions.

Posted by Andy Eggers at 10:18 AM