On Philosophy

December 7, 2007

The Hidden Rationality Of Voters

Filed under: Political Philosophy — Peter @ 12:00 am

The fact that democracy often doesn’t live up to the expectations many people have for it usually results in one entity or another being blamed for its deficiencies. Who gets blamed depends on the individual doing the blaming, but sometimes the voters themselves are considered to be the weak link. Obviously the media plays a large role in the outcome of elections, as people are likely to vote for the candidates that receive the most attention. Additionally voters seem to have a habit of voting strategically, meaning that they will tend to vote only for the candidates that seem most likely to win, even if they personally prefer someone else, to the detriment of small parties. And the strategy of some voters seems not to be to vote at all. Together these facts might seem to point to the voters as the weak link in democracy; if they would just vote for the candidate that they actually preferred then the outcome of the democratic process would be closer to the social optimum. By not acting as they “should” the voters make it impossible for democracy to work properly, and so it is only their own fault when it doesn’t, or so it might be claimed.

I will grant that most people appear to vote strategically and to be heavily biased by the media. But the fact that people behave in that manner and that it isn’t a manner best suited to democracy doesn’t necessarily mean that it is voters who are at fault. We can imagine hypothetical political systems that require the individuals within them must act in ways significantly against their best interests to work, say by giving up a hand in order to vote. If such a system doesn’t work in practice it is not the fault of the individuals living under it, even though they could have made it work if they had chosen to, it is the fault of the system for being ill-suited to the people living under it. On the other hand if it turns out that voters really don’t have a good reason to vote “strategically” then we can assign blame to them, and say that they suffering from mental defects that prevent them from acting appropriately, which they should try to overcome. To determine which is the case in reality we must examine “strategic” voting and its origins more carefully.

Let’s begin by just assuming that voters are perfectly rational, and if it turns out that the perfectly rational person would vote strategically then obviously we can’t fault actual people from doing so. Furthermore let us assume for the sake of simplicity that the perfectly rational person attempts to maximize the expected value of their actions, which means that they act so as to obtain the largest reward, proportional to its probability. Whether that is actually the perfectly rational course of action is a matter of some debate, but it is close enough for our purposes here. So what is the expected value of voting for any given candidate? One way to calculate that value is via the following formula: (value of that candidate winning – value of some other candidate winning) * probability that, with all other votes counted, the candidate will be one vote away from victory – the cost of voting, with the expected value of not voting simply being 0. Obviously to make this calculation we need to estimate a number of things that we can only know with certainty after the election is over. We need to estimate the number of people who will vote, in order to partially determine the likelihood of a single vote mattering. We also need to estimate what percentage of people will vote for each candidate, which allows us to calculate both the value of some other candidate winning, which we can take either as the value of the most likely candidate other than the one under consideration winning, or as some weighted sum determined by the value of the other candidates winning and their likelihood of winning if the candidate under consideration loses, and to calculate the probability that the vote cast will make a difference, as that is more likely in close races than in those where one candidate seems far ahead. On first glance this might seem to imply that no rational person would vote, since the probability of one vote making a difference is very low given the number of people voting. But since people do vote we can charitably assume that they are rational and that the cost of voting is very low, or that the cost of voting is offset by hidden benefits, such as a sense that one has fulfilled their civic duty.

If this accurately models how the perfectly rational person would vote then they would vote strategically, and thus the voting behavior of the average person would be vindicated. Allow me to explain. First of all it demonstrates that the ease at which the media seems to be able to distort voting behavior can actually be explained as part of rational voting behavior. When I was discussing how the rational voter would evaluate their options I mentioned that they needed to be able to estimate how other people would vote. And one way of generating such estimates is to pay attention to the media, because you can assume that the media will show people the candidates that they are the most interested in, and that other people’s voting behavior will be influenced by it as well. Which means that the candidates portrayed as the most electable will receive the most votes simply because the rational voters expect their votes to make the most difference by voting for one of those candidates. It also explains why people are more likely to vote in close races, because it is much more likely for a vote to make a difference in a close race than it is where one candidate is clearly in the lead. Thus in a close race the voter gets more value out of their vote. And, finally, it explains why people vote for candidates that aren’t their first choice, but who are more likely to win, over the candidate they like best if that candidate seems far behind. Obviously it would be better for them if the candidate they liked best won instead of their second or third choice. However, we must also take into account the fact that if their first choice is significantly behind then it is extremely unlikely that a vote for them will make a difference, and so voting for their second choice may be many times more likely to make a difference. Thus, unless they prefer their first choice many times more than their second, an unlikely situation, it will be rational for them to vote for their second choice.

But it might be argued that this analysis of the perfectly rational voter is missing something important. Isn’t a society in which everyone votes for their preferred candidate based only on reflection on the candidate’s individual qualities desirable, since it will lead to socially optimal choices and diminish the ability of money to influence the outcome of elections by buying media time? I agree that it is desirable, and it would be nice to live in a world where everyone voted that way. However, just because we desire to live in such a world doesn’t necessarily mean that we should vote that way, because if we are the only ones motivated by these considerations then we will just be throwing our vote away by getting less value from it than we otherwise could have. To illustrate allow me to present a contrived scenario to illustrate why optimistically voting is a bad idea. Consider then a set-up with a large number of people in which everyone has the option of either paying $1000 to a central pool or contributing nothing. If everyone pays up then everyone will receive their $1000 back plus and additional $1000. However, if some people don’t contribute then those who fail to contribute will receive $1 and those who contributed will lose their $1000. What is rational to do in this situation? Well, it depends on what we think other people will do. Unless we have talked to everyone before hand, and trust them to take the actions that they have said they would, we must estimate that there is a chance, however small, that any given person won’t contribute. Since there many people present the probability that someone won’t contribute is thus high, and so it is rational not to contribute. This illustrates how our expectations regarding other people’s likely behavior must be taken into account when we are deciding what to do, and not to be dazzled by what might happen if everyone acted in a certain way, because we know they probably won’t. So to reflect the fact that a world in which everyone voted “honestly” is somewhat desirable we might add an additional term to calculating the value of voting for the candidate that is preferred over the others, the value of such a world times the probability that voting in that way will contribute to bringing it about. Since that probability is very small, as the majority of people will continue to vote strategically since it benefits them to do so, and thus it doesn’t really affect the results already established.

So, given that the rational voter will vote strategically, you can hardly blame people from doing just that. Thus if strategic voting is bad then the system is bad for encouraging that behavior; it is not the voters who are at fault. I’m not even convinced that strategic voting is intrinsically bad, although the fact that voting behavior can be influenced by an easily purchased media is somewhat disturbing. But, unfortunately, we can’t just ignore the media when deciding how to vote, because we need some estimates in order to vote rationally, and a bad estimate based on the media attention given to the candidates is probably superior to no estimate at all. But that is something we might be able to fix, in a relatively easy way. Instead of forcing people to develop their own estimates about how other people will vote from a biased media and polls the government could create a web site that tracked the popularity of the candidates (the government would have to run it to prevent the possibility of corruption and cheating in general). Obviously such an online poll would affect the way people eventually vote, but it at least this way that influence will be a result of accurate information without an agenda.

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