Newcomb’s Paradox of Voting

Election Day, November 3, 2020, is a stressful time for you. Of course, it’s a big day for all Americans, but this time you have an unusually personal stake in the election. That’s because out of some 320 million Americans, you were selected by political pundit and psephologist Nate Silver as the perfect ‘bellwether voter’. And while you have no doubt as to who you’d vote for, it’s not a done deal if you’ll actually bother to show up to the polling place. And according to the seers of Fivethirtyeight, whether you do or not will decide the election with a 99% chance.

You see, this election is all about turnout; with very few undecided voters, the candidate who wins will be decided by who shows up. Fivethirtyeight have been modelling turnout for a few years now, and in each case they’ve managed to identify a specific individual voter whose voting behaviour would reliably predict the election. Class, race, age, sex, education, geographical location, personality type, hair colour, even star signs go into their fiendishly complex models, which pick out a single individual whose turnout – in 99% of simulations and actual past races at least – will reliably track which candidate wins.

This year, you got a surprise phone call from Nate himself to give you the good news: this year, you are the bellwether voter. The next day, the Fivethirtyeight team showed up and gave you a barrage of psychometric tests, all of which confirmed that you, more so than any other American, were statistically decisive for the election: show up and the Yellow Party wins. Don’t show up, and the Purple Party wins. That’s because your decision to vote (or not) would near-perfectly predict whether tens of millions of other Americans like you turned out. Thankfully, Nate Silver agreed to preserve your anonymity – otherwise the media would doubtless have shown up your doorstep, and thousands of people would have bombarded you with exhortations and imprecations to vote (or not). Not only would that be very annoying, but the causal interference it would produce would compromise your status as bellwether voter.

You had of course determined that you would vote; as a member of the Yellow Party, you would be devastated if the Purple Party were to win. Not only are their values deeply at odds with your own, but the consequences of a Purple administration would have a significant negative impact on your own life and the lives of your friends, family, and community members.

And yet somehow you haven’t gotten around to actually voting yet. It’s now 5:35pm, and your polling station closes at 6pm. It’s only a 15 minute walk there, and you’re lucky enough to live in an area where you won’t have to wait in line. And yet… it’s raining hard. There’s a great show just started on TV. And you have a pizza arriving in twenty minutes. You’d much rather stay on your comfortable couch.

Of course, any costs you’d incur from voting are trivial compared to the costs of a Purple administration; you’d happily suffer far more onerous burdens to prevent that happening. But at this point, you realise, you have no ability to actually causally impact the results of the election. Not only do you not live in a swing state, you know that the overwhelming majority of votes have already been cast. The odds of you having an impact on who wins are effectively zero. At this point, either the Purple candidate has already won, or the Yellow candidate has already won, and either way, it’s not going to make the world a better place if you have to get off your couch, get soaked in the rain, and miss the season finale of The Bachelorette; it will only serve to impose a minor but still annoying cost on you.

And yet a little voice at the back of your mind reminds you: 99% of the time in the past, whether or not Fivethirtyeight’s nominated bellwether voter has actually showed up to vote has predicted the election. If you don’t leave the house, then you can be all but certain that the Purple Team will win. And if you do go out and vote, you can walk home with a spring in your step, confident that the Yellows have clinched it.

But then you catch yourself: that’s just magical thinking and delusions of grandeur! It’s not like you’re actually any more causally relevant to the election than any other voter. It’s just that you coincidentally sit at a point of exceptional statistical relevance, such that your voting behaviour will provide information about the voting behaviour of many other Americans. You can’t actually change whether anyone else shows up to the polls. And besides, the vast majority of those people have either already voted or decided not to bother. To assign yourself any special causal powers at this point is tantamount to believing in backwards causation.

You sit deep in thought for a while. You quickly pull up Wikipedia to see if it can give you any guidance. You skim articles on Causal Decision Theory and Evidential Decision Theory, as well as some more niche alternatives like Timeless Decision Theory.

You look up and glance at the clock. 5:40pm. You can still make it if you leave now.

Reluctantly, you pull yourself up from the couch and slip on a pair of shoes. You’re going to show up. Not because you’re made up your mind about the best decision-theoretic course of action. But because it’s your civic fucking duty.

(Note: this scenario is a bit farfetched, but it captures the broad structure of a wonderful philosophical problem called Newcomb’s Paradox. I don’t know if others have thought of this example, but it occurred to me a few years ago in an epistemology class. It’s obviously unrealistic: in the real world, Fivethirtyeight isn’t that accurate, and other factors – such as the impact on your mood, and your contribution to the popular vote – would come into play. These caveats aside, I think it nicely illustrates why decision-theory is messy. And why it’s important to vote!)


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