Chocolate and Gold Coins

Tuesday, July 19, 2005

Your Vote Does Count

I recently had lunch with Bryan Caplan (and Alex Tabarrok) but he didn’t mention that he is writing a book about voter irrationality. Here is a recent Econlog post in which Bryan talks about his research. I wished we could have talked about that subject because I do know something about this subject.

One thing that has puzzled economists is why people vote against their interest: many rich people would vote for higher taxes on the rich, many poor people would vote against it. Another puzzling point is why people bother voting at all: the probability that your vote would make a difference in an election is small. These turn out to be related issues.

What is the probability that your vote would make a difference? There are two possibilities: there are an even number of voters not including you, they split 50-50, and you cast the deciding vote, and there are an odd number of voters not including you, you make it a perfect tie, and a coin flip or some other means causes your preferred candidate to become elected. In the each case, you only make a difference is with probability 50%, so on average you vote makes a difference is .75 times p (Update this should be 0.5 time p - my bad), where p is the probability that the election will be within one vote of a tie.

What is the probability p? Politics tends to create two candidates who both can garner at least 40% of the vote. None of the recent U.S. Presidential elections have been more lopsided than 40-60. So if there are 100 million voters, a rough approximation of the probability p is to assume that the winner has equal possibility of getting 50 million votes or 60 million votes or anything in between, (it’s actually more likely he will get closer to 50 million, but we’ll ignore that here). So the probability p of a near tie is about 1 chance in 10 million, or 10 times more likely than the probability that you would win a random lottery of the same number of people. So the probability that your vote would be decisive is 5 times more likely in a general election than in a lottery of the same number of people.

Now, what is the benefit of voting? If you only include the benefit that you receive, it would never justify your bothering to vote. But voting is one of those rare circumstances where your actions affect others much more than they affect you. An intelligent vote could provide benefits not only to you, but also to society in general. Wouldn’t it have been nice if more people had voted against Adolf Hitler , Robert Mugabe, or Hugo Chavez when they had the chance? The outcomes of elections can be the difference between war and peace, socialism and capitalism, poverty and prosperity. The total benefit to society could be enormous.

Suppose that you are more intelligent and virtuous than average (otherwise definitely don’t vote). Suppose that there are two candidates and one is good and one is bad, but the bad candidate is clever and he might just win. If the bad candidate wins, it will cost $2000 to every good person in the country. You naturally don’t care about the loss in benefits to the bad people who might have benefited from the election of the bad candidate, but how much is it worth to you that the other people benefit from the election of the good candidate? Even virtuous people care more for their own family than for the family of strangers, but it would not be unreasonable for people to feel very bad about actions that might hurt a lot of people. Let us say that if you get to help strangers, the benefit to you is 10% of the benefit to the stranger. So the benefit of the good person getter elected to you is $100 times number of people in society times the probability that your vote makes a difference. The probability is small, but the benefit is huge. In this case the net benefit is $500 or a little less than 40% of the benefit to you personally.

I don’t know about you, but I don’t know anything else I will be doing in the next year that would generate a benefit of $500 for about an hour of time. It is certainly worthwhile voting.

Several observations:
1. Only vote for candidates who have a chance at winning, never throw your vote away on a third party spoiler candidate. It would be like throwing $500 away.
2. It is not worthwhile voting if you know nothing about the two candidates. It is worthwhile learning about them.
3. Be honest with yourself. Everyone thinks that they are voting for the “good” candidate but at most, only 60% ever does. You might be voting for the “bad” candidate.
4. It really doesn’t matter what you will likely get from an election since the probability that your vote would be pivotal is small. What matters is which candidate is best for society. Only vote for the candidate who will bring about the most net benefit to society.
5. If you are selfish and really don’t care about other people, definitely don’t bother voting.

Update: read this follow-up piece: How Altruistic Are You?


  • "Let us say that if you get to help strangers, the benefit to you is 10% of the benefit to the stranger. So the benefit of the good person getter elected to you is $100 times number of people in society times the probability that your vote makes a difference." Implying the (assumed) benefit of $1000 for every person in society?

    By Anonymous Anonymous, at 2:58 PM  

  • The benefit of $750 is your ex-ante benefit from participating in the election. Ex post, depending if your candidate wins, you either get $2000 or nothing. The important thing is that if you didn't vote and the bad guy one by one vote, your life would be destroyed by self loathing. The $750 benefit is largely for avoiding this "hell".

    By Blogger Michael Higgins, at 3:28 PM  

  • Interesting...

    Isn't the premise of the post that we know what "good" is or that we can easily find it out? Or that "good" may mean the same thing to different sections of society?

    When Hitler stood for election, how would the people have had a foreboding of his atrocities? Maybe given the circumstances, he seemed the best candidate.

    Even if we assume the candidate has held office and we know about him that he is "good," maybe he would have to abide by a bad stand taken by party that he belongs to.

    Suppose we can decide the goodness of the candidate by the issues he promises to address. E.g., if in Tamilnadu (India), a candidate focuses (in his campaign) on inter-linking of rivers as a solution to the water problem faced in the state. This issue is very complicated and would need detailed knowledge of various subjects to decide if inter-linking of rivers is advantageous or not, and the general public may jump to wrong conclusions easily on this issue.

    By Anonymous Srikanth, at 9:36 PM  

  • Hi Srikanth
    I'm assuming that you are enlightened and you, by virtue of your superior education and knowledge, know the good candidate from the bad one. In the case of Hitler, he actually wrote a book about what he was going to do long before he ran for office. People should have known that he was bad, but the Germans we split between Nazis and communists, and voters abandoned common sense.

    It is an obvious fact that in any election, the losing candidate gets a lot of votes - sometimes almost 50%. It may be that there really isn't any difference between candidates, but sometimes there is, and sometimes the voters could have seen the difference if they had put in a little more effort into seeing the difference.

    By Blogger Michael Higgins, at 1:12 PM  

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