Thursday, October 11, 2012

Stuck in the middle with you?

Duncan Black's median voter theorem is a classic result in voting theory. Anthony Downs extended the results to electoral competition.

In a nutshell, if there are two candidates competing for election in a one dimensional policy space, and voter preferences over the policy space are single peaked, the candidate that is positioned closest to the position of the median voter will win.

Heuristically, we might think that over the course of a campaign, candidates' positions might move toward that of the median voter.

But look at this amazing chart from Henry Farrell John Sides (clic the pic for an even more counterintuitive image):

What is up? Anthony Downs, you got some 'splainin' to do!


1. Candidates take non median positions to win primary, then are "trapped" at or near that position in the general election.  Perhaps, but these guys appear to be moving AWAY from the mean.

2. Voter preference distribution is not symmetric so average  does not equal median. Maybe, but it's hard to believe the median would be either more conservative than Romney or more liberal than Obama.

3. The policy space is multi-dimensional. This is my cherished view, on which I've written exactly one paper that only got published in a special issue of Public Choice that I edited (though it has been cited a few times at least. I always get bashed over the head with the Poole-Rosenthal work claiming that politics really is one dimensional.


4. Negative ads work. Black & Downs never conceived of the modern world of political attack ads.

Other thoughts? Tell me in the comments.


John Thacker said...

There's a distinction between the candidates' actual positions and the perception, no?

Perhaps this is the effect of partisans locking in to support Their Team combined with negative attack ads designed to characterize the other person as extreme.

Chris Lawrence said...

What John said; while the candidates may be converging on the median voter post-primary (and there's ample evidence of this, at least on Romney's side; Obama didn't have a meaningful primary contest so his positions are relatively fixed this time around), this effect is likely offset by low public awareness of candidate positions until the general election campaign increases their salience to the mass public.

If you disaggregated the trend by level of political knowledge (no idea if YouGov has this or not) I suspect you'd find that among more knowledgeable respondents you'd find support for your hypothesis 1, convergence to the median voter after the primaries.

Angus said...

But the candidates have to get to the perception of the median voter, though, right? You can't tell her, "look dammit, I'm at your true position. Vote for me!"

I do like the idea that the data show negative ads work.

That is a good one.

Anonymous said...

The preferences of the public are endogenous to the preferences of elites. Look at the work on issue evolution. Look at Zaller's theory, and evidence, to support it on why people form opinions. Look at Politicians Don't Pander by Jacobs and Shapiro in which they show how politicians use polls to polls to sell their own ideas to the public. The idea that politicians follow voters is at most in part correct; voters also follow politicians.

Gabriel said...

Anthony Downs want you to believe in the median voter theorem. But what he's not telling you is he's applying a model originally developed to explain where hot dog vendors would locate on a boardwalk. Do you really want to compare your vote to buying a hot dog?

Median voter theorem: wrong for social science, wrong for America.

(paid for by the committee to explain partisan polarization)

Dave said...

Downs' original theory argued that extremists could pull candidates away from the center if there are enough of them among voters. This is because extremists may abstain from voting if they perceive that their candidate is too close to the other candidate.

Related to the effects of primaries, there is a new paper from Tomz and Van Houweling that shows that voters punish candidates for breaking promises, even when the promise is to do something against the voter's preference. Presidential candidates have made promises while running for other offices and in the pres. primary, and they want to avoid punishment for breaking those promises.

The movement away from voters may have nothing to do with the candidates' actual policy positions, but instead result from voter learning. It seems obvious to me that Romney's stances have moved to the center since the primary, or rather, he focuses on the stances that appeal more to moderates but don't offend his base. But voters are much less informed about candidates earlier in the campaign, so the data from earlier this year is likely full of noise. It would be interesting to see how the opinion of the same informed voter in time t changed (or didn't) in time t+(a few months). In addition, each candidate tries to make the other look more extreme through campaign media, which is part of how voters learn about candidates. Thus, when voters are finally getting around to learning more about the candidates, they're also seeing the negative ads from the other side.

Brad Hutchings said...

Romney has a lot of room to move away from median voter?

Kindred Winecoff said...

There are alternative spatial models:

@mjensley said...

Voter learning and projection effects (i.e., conservatives/Republicans place Obama as more extreme over the course of the campaign, whereas liberals/Democrats place Romney as more extreme as they learn more about him). Plus Hinich and Mungowitz (1994) told us that we should believe not what candidates pronounce, or in others they cannot credibly commit changing policy positions, voters will not buy it, so better to stay committed to your ideology.

Anonymous said...

The chart is definitely antithetical to my perception and Houston at The Economist's perception of Romney's "dash to the center".

Florenz Plassmann said...

The median voter is endogenous if you need to account for voter participation, and voters at the extreme end of the spectrum might not vote if a candidate moves towards the current median voter. Given the tea party and the occupy movement with voters closer to the ends of the spectrum than to the middle, the fear that those voters might decide not to vote at all seems a reasonable explanation why the candidates don't move closer towards each other.

Anonymous said...

I just can't see motivated voters abstaining (e.g. dissatisfied tea partiers). If they are motivated to rally, to blog, to yammer etc. then why wouldn't they follow through by voting? Voting is costly yes, but those motivated voters have already spent so much up front ... it makes no sense to abandon that investment at the end.

I must be dense here (likely the problem) but to me there are two types of voters, vote by ideology (so vote Republican because you believe in say small government even though you're aware that Republican policies don't necessarily produce that) or vote by single issue (and each voter has it's own Becker household production function that would determine which one on any given day would be paramount).

So if the ideologue vote is a given, then a candidate wouldn't trend toward the center, he/she would trend toward the proxy issue that signals what the independent cares about. And those proxy issues tend to be the most divisive politically (e.g. abortion, there is no middle). In that scenario, a slight trend away from the median voter by the candidates towards the end of a campaign would make sense.