gelman and social voting
Loyal readers know that we’ve been duking it out over voting. Well, I’ve read Gelman’s paper on social voting. The main idea is that people may value the effects of policies on others. Thus, you can build a model where the utility of pivotal voting is not zero, even in large elections. Comments::
- First, the model has the benefit of addressing a basic feature of voting. People vote because they think they are making others better off. Wealthy people often favor higher taxes because they think gov’t spending can make people better off, even if it decreases personal wealth.
- Second, just because the value of a pivotal vote is not mathematically zero doesn’t mean it’s not treated as zero by a lot of people. Do rational choice explanations not consider that people round down? The value of preventing nuclear war may be positive, but differences in school policy, for example, have nearly zero utility for most voters.
- Third, empirically, close elections are pretty rare according to Mulligan and Hunter. Nearly zero probability in state and congressional contests – much closer to 0 than 1/N.
Other random thought: The model actually addresses what we think other people should value. It doesn’t explain voting when the policy’s targets feel the policy is negative. For example, if conservative voters really valued the utility of gay citizens, they wouldn’t vote against gay marriage. So the Gelman model is really a sort of weird social psychology model of what voters think other people want, which draws us away from voting models focusing on direct pay offs to voting.
Dr. Rojas,
You are right. Gelman et. al. do not explain why one would vote if the policy’s target is perceived as negative by the voter. However, this theory appears to be pretty explanatory for why one would NOT vote for candidates who support their egoistic self-interest on issues such as social security, minimum wages, and child care. For example, a wealthy, non-married, and childless woman may not vote for candidates who support slashing funding for childcare, although she does not stand to benefit directly from childcare subsidies.
This appears to be a pretty powerful and useful model that breaks from the convential wisdom of sociotropic and self-interested voting.
Brian Pitt
September 2, 2008 at 4:50 pm
Fabio,
Why do you say that the probability of a tied congressional election is “much closer to 0 than 1/N”? In the period from 1900-1992, there were 20,597 congressional elections, of which 6 were decided by fewer than 10 votes and 49 were decided by fewer than 100 votes. This suggests an empirical estimate of the probability of a tied election of approx 1 in 80,000, which is indeed in the order of 1/N.
Andrew Gelman
September 2, 2008 at 6:03 pm
Andrew: My bad!
fabiorojas
September 2, 2008 at 6:17 pm
Andrew: As Fabio mentions in his comment, do you really think individuals treat 1/80,000 as significantly different from zero? (I suspect if a high-school civics teacher told students, “Of course your vote counts! It has a 1-in-80,000 chance of determining the outcome!” he or she would be punched in the nose at the next PTA meeting.)
Fabio: I don’t think the first bullet point is correct. Do you have some argument or evidence for that? My sense is that wealthy people very often favor high income taxes, but rarely support high wealth taxes. The obvious explanation is that they wish to slow down marginal changes in wealth, i.e., to keep other people from becoming as wealthy as them.
Peter Klein
September 2, 2008 at 7:15 pm
Andrew G.: Apparently we divide differently. My math suggests that 0/20,597 yields a predicted probability of 0, not 0.0000125.
andrewperrin
September 2, 2008 at 7:33 pm
G-man: Given AP’s correction, it’s now your bad!
fabiorojas
September 2, 2008 at 7:38 pm
Peter,
1. Saying that a decision is rational is not the same as saying that people make the decision _because_ it is rational. Lost of ink has been spilled saying that people vote, ha ha, isn’t that silly because it isn’t rational. Our point in the paper is that, no, it _is_ rational, or at least it can be if you have other-regarding preferences (which is consistent with survey responses, political donations, and other evidence). If you want to say that, yes, voting is rational but people do it for irrational reasons, that’s fine.
2. Yes, I think people distinguish between various low probabilities. At least, they do when buying lottery tickets, which is one analogy that I used.
3. Take a look at the paper by Dale Miller, The Norm of Self-Interest; see here:
http://www.stat.columbia.edu/~cook/movabletype/archives/2007/04/the_norm_of_sel.html
4. Most rich people do not favor higher income taxes. But some rich people do. The correlation between income and conservative economic ideology is positive but moderate (something like 0.1 or 0.2, it varies by state, as shown on page 90 of our Red State, Blue State book). I don’t think there’s any need to resort to a complicated argument about relative economic position; it’s enough to say that some people have liberal economic views and favor income redistribution.
Andrew Gelman
September 2, 2008 at 7:45 pm
Fabio, AP:
What is relevant for the decision is the prospective probability. If elections have been within 100 votes approx 50/20,000 times, then an empirical estimate of “the probability that the election is within 100 votes” is 50/20,000 or 1 in 400. Given that an election is within 100 votes, the probability it is tied is approximately 1 in 200. (1/200)*(1/400) = 1/80,000. The point is that the 50 occurrences of within-100-vote elections are a large enough sample size to estimate an empirical probability, then you go to the model from there.
It’s a subtle point and is also a nice illustration of why statistics is considered a separate field, not merely part of mathematics or social science or whatever. We spend a lot of time thinking about how to estimate probabilities. Even something as simple as an “empirical estimate” gets complicated when the number of cases is low.
For another, simpler, example, suppose you take a random sample survey of 500 Americans, and there are no women from Wyoming in the sample. Does this mean that there are no women in Wyoming? No. Fewer than 1/1000th of Americans are women from Wyoming, so it is no shocker that zero appeared in the sample. But the probability of getting a woman from Wyoming in a randomly sample of Americans is not zero.
Similarly, given the probability of a tied congressional election is about 1/80,000 (it depends on the conditions, of course, with the probability being high in closely-split districts and much much closer to zero in one-party-dominated districts like where I live), it’s no surprise that the past 20,000 or so elections have had no ties. Doesn’t mean the probability is zero, though. Just a bit lower than 1/20,000.
Andrew Gelman
September 2, 2008 at 7:59 pm
Gel-Man: You are right about estimated probabilities – it is tricky. If a bunch of PhD’s can’t tell the difference between 1/80,000 and 0, then it’ll be obvious to average voters. And which voters are supposed to do this calculation correctly? And then add it up for the whole population?
fabiorojas
September 2, 2008 at 8:14 pm
Fabio,
I appreciate the time that you and your colleagues have put into thinking about our paper. Just to clarify, I’m saying that, under a reasonable model, voting _is_ rational. I’m not saying that people vote _because_ it’s rational. We discuss this distinction a bit in Section 5.2 of our paper.
I actually made this point in an earlier comment a few hours ago that seems to have been eaten by your blog. (The comment included an html link and so maybe it got flagged as spam.)
Andrew Gelman
September 2, 2008 at 8:37 pm
A-Gel: If you ever lose a comment, just email me or another orgtheorist, and we’ll get it posted.
On a serious note: when reading your article, I felt like it was a logically coherent model, but doesn’t jive terribly well with how I understand people’s behavior.
For example, this weekend, as part of my field work, I spent a fair amount of time with political campaign professionals. They just accept that (a) most people don’t vote most of the time, (b) among voters, a big chunk are straight ticket voters, which suggests inflexible toward financial aspects of policy (e.g., people who vote based on the Iraq War or gun rights no matter how the benefit directly) and (c) elections are driven by a very small chunks of the electorate you have to relentlessly target. (d) this small chunk of voters is not terribly well informed and susceptible to emotional appeals, rather than policy nuts and bolts.
This suggests to me that: (a) If Gelman is right, then about 70% of the people simply can’t be bothered to do a positive utility action. (b) If people have high rates of political ignorance and go on guts, then they just won’t do the calculation. That’s why when I think of voting, I start with socio/psychological factors like ideology, personality, networks, etc.
“I appreciate the time that you and your colleagues have put into thinking about our paper. ”
No problem. Orgtheory: we’re here to do social science.
fabiorojas
September 2, 2008 at 8:59 pm
Andrew — thanks for notifying us about your comment potentially getting stuck in the spam filter — indeed it did. I just resurrected the comment, it can be found above @ 7:45pm. (The filter rarely makes this error, sorry.)
tf
September 2, 2008 at 9:37 pm
And just to clarify, I too found the Gelman paper very interesting and worthwhile. However, I continue to think culture matters much more than the paper suggests — that is, that it’s more plausible that voters (a) feel good about the act of voting; (b) feel good about having voted and others seeing that they have; (c) feel connected to the polity through voting; or (d) prefer that the reported margins be more on their side; than that they (e) choose to vote on the virtually-zero chance that this will be the first time in the history of the country that a single vote would be pivotal.
A couple of other thoughts:
1.) Particularly after Florida ’00, I think most voters recognize that the measurement apparatus isn’t fine grained enough to register a one-vote margin accurately anyway.
2.) I recognize what A-Gel points out, which is that people don’t necessarily vote because they’re rational just because voting can be rational. But then I suppose I’m not convinced of the reason for the article!
3.) Voting can also be rational because of preferences (a)-(d) above; this suggests the near-tautological character of the strong version of RAT.
andrewperrin
September 3, 2008 at 12:10 am
The probability of being decisive is nicely explored by Chamberlain and Rothschild (JET 1981), who Gelman cites, and Palfrey and Rosenthal (PC 1983), who he doesn’t. Both make the point that that probability is often a lot higher that one might guess. While Gelman explains that insight a lot better than they do, the point remains that we are simply not very good natural statisticians. The average voter isn’t likely to have a better grasp on these probabilities than the average political scientist. For them, 1/80,000 or even 1/200 may as well be zero (or for some, 10 percent).
Having thought about this issue for a long time, I am inclined to believe that the primary instrumental purpose of voting is to influence the behavior of whoever is elected, the secondary purpose, influencing the behavior of those who might not otherwise choose to vote (Palfrey and Rosenthal’s point), and, a distant third, the likelihood of casting a deciding vote.
Fred Thompson
September 3, 2008 at 12:53 am
fabiorojas wrote: “This suggests to me that: (a) If Gelman is right, then about 70% of the people simply can’t be bothered to do a positive utility action. (b) If people have high rates of political ignorance and go on guts, then they just won’t do the calculation. That’s why when I think of voting, I start with socio/psychological factors like ideology, personality, networks, etc.”
The proportion of people who vote varies from election to election. Gelman’s paper gives a rather nice account of why it is rational for that to vary. It is pretty easy to find elections for which 70% of the electorate do vote. I also think that political analysts seem to underestimate the proportion of people who vote on the issues (and generally such claims are anecdotal whereas what limited data there are suggest policies/issues are pretty important). I think psychological factors are important too and Gelman’s model seems to fit with some of psychological accounts of voter behaviour quite well (as discussed in his paper). What I think is missing is an understanding of the psychological mechanisms that make voting behaviour align with this rational analysis. Clearly, people don’t do formal utility calculations prior to voting (and Gelman never suggests they do).
Thom
Thom
September 4, 2008 at 1:58 pm
[...] and voting before, but I still see some confusion out there (for example, in some of the discussion here). Our discussion is here (with longer article here). But let me try to clarify briefly right [...]
Rationality and voting | Red State, Blue State, Rich State, Poor State
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