Commit in September

The Quote of the Day goes to Invisible Children for this Facebook status:

Our friends at the Millennium Campus Network need your help to get 72 million children in a school.

They're going to achieve Millennium Development Goal #2 and set a World Record by having 72 million children in one school.

Joking aside, I do highly recommend singing the petition at Commit in September.

A lot of people don't like these things because they seem useless. Does it really matter that one more person signs the petition? Probably not. But even if there is a tiny probability that one extra e-mail, call, meeting or signature makes a difference, the payoff is massive. When you multiply a tiny number by a massive number you get . . . well, it depends on how tiny and how massive. So you might as well sign because it might be massive. (These models are hard to calibrate so I won't try. But here is an irrelevant fact I will mention to bias your views: based on a model estimated by Gelman et al. though, the expected payoff to voting in a swing state is at least on the order of $10,000.)

Another reason people don't like to sign these things is that they don't think these policy issues matter. Foreign aid doesn't work right? The only way to make a difference is to get your hands dirty, they say. But most small projects are utter failures. If I had to put money on it, your money and time would be better spent dealing with (and preventing) mental illness in the U.S., unless you're working on vaccinations or clean water. In contrast, PEPFAR has put 2 million people on ARVs for several years. That's means that an investment of a few hundred thousand signatures, letters, and calls yielded about 10 million life-years or about 100 life-years per signature. If the average impact of signing at Commit in September is something like 100 life-years isn't it worth 2 minutes?

Is it rational to vote?

Does it make sense to vote?

The short answer is "probably, since you'll feel better about having done your civic duty." But when people ask this question I think what they mean is "the cost of voting is about 10 minutes of your time, the benefit is a tiny probability multiplied by something huge--is that tiny multiplied by huge a big or small?

Gelman et al. estimate the probability your vote would have mattered in the 2008 election. The probability varies by state so they plot by state in this graph:

These probabilities are tiny. (And I think they are vast overestimates.) But look at the historic average growth rates for different income groups when Democrats are in office vs Republicans. The fact that Democrats have higher growth rates for all groups probably has little to do with policy. Democrats just happened to get voted into office at the right times of the business cycle. The fact that the growth is relatively even (and somewhat convergent) is possibly also an artifact of the Democrats being in office when there was a lot of growth in college and high school education, while the Republicans have presided during a period of more rapid technological change (or some such narrative).

But it's definitely possible that Democratic and Republican policies have something to do with the fact that income growth lags for the poorest under Republicans and is greatest for the poorest under Democrats. Suppose that we adjust the growth rates so the means are the same; then, by eye-balling, it looks like growth would be around 1% greater per year for the poorest income deciles. Using the numbers in this graph that means about $144 billion in value over 4 years for the bottom two income quintiles.

Suppose your time is worth $20 an hour. It takes ~10 minutes to vote. The value from voting is $144 billion worth of aid to the poor and working class. What would the probability need to be (at least) for the expected benefit of voting to exceed its cost? If you weight income to yourself and to others equally then it's just 1 in 43 billion.

Which means it rational (in the sense of expected value), for Democrats at least, to vote in almost every state in the union. That's definitely not a result most philosophers intuit (and is probably an artifact of greater overestimated probabilities).

But what if these numbers are right? Shouldn't the possibility be widely noted in the literature? And shouldn't estimates of the probability of your vote mattering note that there is a big difference between a 1 in 10²⁰ chance, which implies voting is irrational, and a 1 in 10⁹ or 1 in 10¹² chance, which may imply voting is rational?