# Voting is like donating thousands of dollars to charity

(Share this post to encourage folks with rational, altruistic leanings to vote more. I originally posted this to LessWrong in 2012, but I figured it was worth re-posting.)

Summary:  It’s often argued that voting is irrational, because the probability of affecting the outcome is so small. But the outcome itself is extremely large when you consider its impact on other people. I estimate that for most people, voting is worth a charitable donation of somewhere between \$100 and \$1.5 million. For me, the value came out to around \$56,000. So I figure something on the order of \$1000 is a reasonable evaluation (after all, I’m writing this post because the number turned out to be large according to this method, so regression to the mean suggests I err on the conservative side), and that’s big enough to make me do it.

Moreover, in swing states the value is much higher, so taking a 10% chance at convincing a friend in a swing state to vote similarly to you is probably worth thousands of expected donation dollars, too. (This is an important move to consider if you’re in a fairly robustly red-or-blue state like New York, California, or Texas where Gelman et al estimate that “the probability of a decisive vote is closer to 1 in a billion.”) I find EV calculations like this for voting or vote-trading to be much more compelling than the typical attempts to justify voting purely in terms of signal value or the resulting sense of pride in fulfilling a civic duty.

### Result

I don’t know which candidate would turn out “better for the world” in my estimation, but I’d consider myself as having at least a 55%*1/(100 million) chance of affecting the outcome in the better-for-the-world direction, and a 45%*1/(100 million) chance of affecting it in the worse-for-the-world direction, so in expectation I’m donating at least around

(55%-45%)*1/(100 million)*(\$100 billion) = \$100

Again, this was pretty conservative:

• Say you’re more like 70% sure,
• Say you’re a randomly chosen american, so your probability of a decisive vote is around 1/10 million;
• Say the outcome matters more on the order of a \$700 billion in charitable donations, given that Obama and Romney’s budgets differ on around \$7 trillion, and say 10% of that is stuff that money is being used as well as moving charitable donations about things you care about.

That makes (70%-30%)*1/(10 million)*(\$700 billion) = \$28,000. Going further, if you’re

• 90% sure,
• voting in Virginia — 1/(3.5 million), and
• care about the whole \$7 trillion dollar difference in budgets, you get (90%-30%)*1/(3.5 million)*(\$7 trillion) = \$1.2 million. This is so large, it becomes a valuable use of time to take 1% chances at convincing other people to vote… which you can hopefully do by sharing this post with them. ### Discussion Now, I’m sure all these values are quite wrong in the sense that taking account everything we know about the current election would give very different answers. If anyone has a more nuanced model of the electoral college than Gelman et al, or a way of helping me better estimate how much the outcome matters to me, please post it! My \$700 billion outcome value still feels a bit out-of-a-hat-ish.

But the intuition to take away here is that a country is a very large operation, much larger than the number of people in it, and that’s what makes voting worth it… if you care about other people. If you don’t care about others, voting is probably not worth it to you. That expected \$100 – \$1,500,000 is going to get spread around to 300 million people… you’re not expecting much of it yourself! That’s a nice conclusion, isn’t it? Nice people should vote, and selfish people shouldn’t?

Of course, politics is the mind killer, and there are debates to be had about whether voting in the current system is immoral because the right thing to do is abstain in silent protest that we aren’t using approval voting, which has better properties than the current system… but I don’t think that’s how to get a new voting system. I think while we’re making whatever efforts we can to build a better global community, it’s no sacrifice to vote in the current system if it’s really worth that much in expected donations.

So if you weren’t going to vote already, give some thought to this expected donation angle, and maybe you’ll start. Maybe you’ll start telling your swing state friends to vote, too. And if you do vote to experience a sense of pride in doing your civic duty, I say go ahead and keep feeling it!

### An image summary

Thanks to Gavan Wilhite and his team for putting together an infographic to summarize these ideas:

### Related reading

I’ve found a few papers by authors with similar thoughts to these:

Also, I found this this interesting Overcoming Bias post, by Andrew Gelman as well.

1 A nitpick, for people like me who are very particular about what they mean by utility: in this post, I’m calculating expected altruistic dollars, not expected utility. However, while our personal utility functions are (or would be, if we managed to have them!) certainly non-linear in the amount of money we spend on ourselves, there is a compelling argument for having the altruistic part of your utility function be approximately linear in altruistic dollars: there are just so many dollars in the world, and it’s reasonable to assume utility is approximately differentiable in commodities. So on the scale of the world, your effect on how altruistic dollars are spent is small enough that you should value them approximately linearly.

2 (Added in response to an email from Ben Hoffman on Oct 28, 2016) This “\$100 billion valuation” step is really two steps combined: a comparison of government cost-effectiveness to the cost-effectiveness of a typical charitable donation, and an estimate of the difference between the two different governments you’d get under different presidents. You could also take into account world-wide externalities here, like the impact of wars. All things considered, I’d be pretty surprised if the difference in candidates over their 4-year term was worth less than an order of magnitude bellow \$100 billion typical-charity dollars.

Comments are closed.