Your vote matters — probably more than you think

(This post is meant to persuade you to vote. If you already want to vote but don’t have a concrete voting plan, check out this post.)

In 10th grade civics class I learned about two moral arguments in favor of voting in elections. The first of these appeals to a notion of civic duty: as a citizen of a democracy, you have a moral duty to vote in elections. The second is about political efficacy: your vote could determine the outcome of an election, which can make your town, or state, or country, or the world, a better place. Put simply, an appeal to political efficacy says that your vote matters.

At the time I thought the political efficacy argument was a silly one. Sure, an election you’re voting in could be decided by one vote, but the probability of that is very small. On the other hand, the civic duty argument appealed to me. Intuitively, “you ought to vote” is a pretty good principle for a society to have, because without it the democratic system wouldn’t function.

Nowadays I don’t know what I think of the civic duty argument — I kind of like it but have some reservations. On the other hand, I now believe that the argument from political efficacy is entirely, spectacularly correct.

Concretely, I wasn’t wrong about the probability of one vote changing an election outcome — it is indeed small! A good argument for political efficacy doesn’t deny that; instead, it says: the effect of your vote if it does sway the election is really high — high enough that voting is the right thing to do, even if it comes at a small personal cost. My goal in this post is to persuade you of this argument — I think it’s surprisingly accurate even if you don’t live in a state where the outcome is expected to be close! For the most part I’ll talk about the presidential election, but I’ll briefly touch on other elections at the end of the post.

(By the way, I’m not going to argue that it’s in your selfish interest to vote; whether that’s true mostly depends on whether you feel good about voting. Instead I’ll argue that voting is the ethically correct thing to do, because (in expectation) it will make the world a better place.)

A good way to make decisions is to think about their consequences in expectation, or on average over the possible outcomes, weighted by how likely they are. Should you go racing down the highway? Probably not: although it will most likely be fun, there’s a good chance of you or someone else getting seriously hurt, and that’s not worth it. Should you go skydiving? Probably, if it sounds like fun: although there’s a chance of dying, that chance is super low, and it’s probably worth the risk. The principle here is that you weigh the pros and cons by multiplying the consequences (positive and negative) by how likely they are to transpire.

In this same spirit, most likely your vote won’t change the outcome of the election and nothing will change as a result of the hour you spend voting. But on the off chance that your vote decides the election, the consequences are enormous. So, to figure out the expected value of your vote, you need to multiply the probability that your vote is decisive by the magnitude of the consequences if your vote proves to tip the election. We therefore need to estimate both of these numbers.

Estimating the probability that your vote is decisive turns out not to be that hard! It’s by no means trivial — you need a good probabilistic model of the presidential election — but luckily we already have one. There are several prominent 2020 presidential election models, one of which is published by The Economist. If you scroll down to “Key states”, you’ll see a column called “chance of voter deciding election”. If you live in New Hampshire, congratulations — as of October 6th, there is a one in 6.9 million chance that your vote will decide the entire presidential election, the highest of anywhere in the country! These probabilities are orders of magnitude higher in swing states than in safe states. For example, as a New York voter I only have a one in 2 billion chance of deciding the election. Here’s a map of these probabilities.

If you want to know the probability for your state, click here, scroll down to “Key states”, and look in the “chance of voter deciding election” column.

The second question — the impact of flipping the presidential election — is much harder to answer quantitatively, but let’s try anyway. Here are just a few consequences of this election (let me know if you think I’ve significantly mis-analyzed any of these):

• President Trump has hurt the United States COVID response in many ways, including discouraging mask-wearing, interfering with CDC guidelines on testing, and most recently rejecting FDA vaccine guidelines to benefit himself politically. COVID has claimed hundreds of thousands of lives in the U.S. and it will probably claim a hundred thousand more. But the number of lives claimed will depend significantly on the response of the federal government. Electing Biden has the potential to save tens of thousands of lives for COVID-related reasons alone. And this doesn’t even factor in that millions fewer people that would catch the virus, saving hundreds of thousands from serious long-term health problems.
• The future of American healthcare depends significantly on this election. Donald Trump wants to get rid of Obamacare, whereas Joe Biden wants to expand it by adding a public option. Obamacare caused the number of uninsured Americans to drop from 47 million to 27 million. If Biden is elected and a public option is implemented, I would expect this number to drop further. If Trump is elected, I expect the number to go back up (it is likely that Obamacare will be gutted by the Supreme Court and not replaced). So, something like 30 million more Americans will be uninsured if Trump wins than if Biden does. This probably amounts to a difference of tens or hundreds of thousands of lives, as people are way less likely to seek health care such as cancer screenings if they don’t have insurance.
• The EPA estimates that the Clean Air Act prevents 230,000 premature deaths per year. Donald Trump has been weakening air pollution regulations; Biden is likely to re-strengthen them. As a ballpark guess, if these differences amount to a 10% weakening of the Clean Air Act for 10 years, re-electing Trump will again cost hundreds of thousands of lives.
• As a separate environmental issue, it seems quite plausible that Biden would pass substantial climate change legislation; the opportunity might not exist again for decades because of Republicans’ systemic advantage in the Senate. Climate change is expected to kill 250 thousand people per year in the next few decades, and more after that. If this election makes a 1% difference in the global course of climate change over the next 100 years, that amounts again to hundreds of thousands of lives. (These are mostly not American lives, but non-American lives are just as valuable!)
• Paul Krugman estimates that Trump’s trade war will cause a 2 to 3 percent decline in GDP for the duration of the trade war. The Bank of Finland estimates the decline at 0.7%. Let’s compromise and say that the actual decline is 1%, and say that Trump’s re-election will make the trade war last for four more years than it would otherwise. The global GDP is $80 trillion, so a 1% decline for four years is a cost of $3.2 trillion. How do we compare this enormous dollar amount to our previous “lives lost” metric? The United States government values a life at 5 to 10 million dollars, meaning that it considers a life-saving measure worth implementing if it costs less than 5 to 10 million dollars per life. This number is likely substantially lower in lower-income countries, so let’s say that on average $1 million saves a life. If these calculations are right, the trade war has cost millions of lives.
• Before Trump took office, the United States took in 70 thousand refugees per year. Trump has steadily brought that number down to near zero. So having Trump for four more years will deny hundreds of thousands of refugees a home in America — often a matter of life and death, and nearly always a huge difference in quality of life.

Now, maybe you think the trade war was worth it, or that the economic costs of air pollution regulations outweigh their benefits, or that Biden’s policies are equally bad. I would disagree, but unless the differences between the candidates magically come close to canceling out, my point still stands: The stakes are high. They’re on the order of millions of lives.

You probably see where I’m going. Say that you live in a swing state, so your chance of flipping the outcome of the election is one in a few million. If you flip the outcome, you save a few million lives. In expectation, your vote amounts to a life saved. Wow, that sure is an unexpected value!

I live in New York. I only have a one in 2 billion chance of flipping the election. My vote is only worth a thousandth of a life, also known as approximately one month. That’s right: even if you’re voting in a state as safe as New York, your vote still saves a month of a person’s life in expectation. And if you’re interested in having an even larger impact, you can try to vote swap with someone who wants to vote third party in a swing state!

(Of course, your impact is only positive if you’re voting for the candidate who is, in fact, better. In this presidential election, though, I think the choice is pretty clear.)

Note, by the way, that you don’t need to buy all of the arguments I made in the above bullet points to buy my main point. Maybe you think I mis-analyzed the consequences of the trade war; if so, the remaining bullet points still add up to a million or so lives! There are also tons of other factors — some of which may be even more important — that I’ve left off. (I’ve left off some even bigger consequences amounting to tens of millions of lives in my estimation because they’re more speculative; if you’re interested in reading about these, see this footnote.¹)

What about elections besides the one for president? For the U.S. Senate, the argument for political efficacy still holds very strongly: if you live in a state with a close Senate race, it will likely be decided by just tens of thousands of votes, which means that your odds of flipping the race by voting are on the order of one in ten thousand or a hundred thousand. Since the Senate is likely to be close, flipping a seat could make a huge difference in terms of what legislation gets passed, probably amounting to a difference of at least tens of thousands of lives.

Similarly, if you live in a congressional district with a close race, your vote matters a lot. Democrats will likely keep the House of Representatives, but FiveThirtyEight gives Republicans a 6% chance of taking back the chamber (as of October 8th). In the event that the race for control of the House ends up close, it’s likely that Trump will win reelection and Republicans will control the Senate. In that case your vote may determine whether or not we have a divided federal government, which is really important in terms of which laws get passed and whether there is effective congressional oversight of the executive branch.

And of course there are local races, and those can matter a lot too. Naturally, a single local race matters less for the world than the race for president, but because there are fewer voters, your vote has a correspondingly higher chance of flipping the outcome! I don’t have numbers for you here, but my strong intuition is that it’s worth your while to vote in local races as well.

So, that was a lot of text to justify a rather simple thesis: Vote! It’s a low-effort way to do a surprisingly large amount of good.

(Edit: see saprmarks’s comment for a counterpoint.)

^{1. Metaculus estimates a 13% chance of global thermonuclear war by 2070, a base rate of 0.2% per year. I’d also argue that nuclear war is more likely — maybe twice as likely — under Trump than under Biden, because Trump is much more likely to act rashly. Let’s say a nuclear war is 0.2 percentage points more likely per year under a Trump administration. That’s a 0.8 percentage point increase in the probability of nuclear war over the next four years if Trump is re-elected. How many people would a nuclear war kill in expectation, including long-term consequences? Probably at least a billion (and it will cause way more people to not exist, if you care about that; adjust your calculations accordingly). That’s 8 million expected lives.}

^{Then there’s the issue of the potential end of American democracy, which I believe to be more likely under a Trump administration, since Trump has consistently undermined our democratic institutions. You could imagine all sorts of nightmare scenarios where the world’s greatest powers are all authoritarian. It would be a dark world to live in, one where almost everyone would be substantially worse off. This is perhaps a 2% chance (small but not that small: after all, democracies do sometimes collapse) of half a billion lost life-equivalents. Another 10 million expected lives.}

^{But, as I’ve argued before, decisions involving scenarios with low-probability high-stakes events are really thorny. Am I falling for some sort of fallacy here? Maybe — that’s why I left these out of the body of the post. But probabilities on the order of 1% to 2% aren’t so low: they happen all the time! It seems quite incorrect to leave these considerations out when making such decisions.↩}