In American presidential elections, you often hear the idea that your vote is extra important because you’re in a swing state, or (more commonly) that your particular vote is less important or doesn’t matter because you’re not in a swing state.
Neither is actually true - your vote in a non-swing state is pretty much as important as if you lived in a swing state.
I don’t mean this in a feel-good, symbolic sort of way. I mean it quite literally — your vote, for all practical purposes, is approximately equally likely to matter whether you’re in a swing state or not.
For the swing state distinction to be relevant, your vote “mattering” must be defined1 as whether your vote changes the outcome of the Presidential election. Calculating that probability is complicated: it requires you to not only calculate the probability that your state’s Presidential election is decided by 1 or fewer votes, but also the probability that changing the electoral votes of your state changes the ultimate outcome.
Luckily for us, three of the most qualified humans possible have already answered this question: in 2008, estimates ranged from less than 1 in 100 billion (if you live in DC, which has the minimum number of electors and where your vote is very unlikely to change the outcome) to about 1 in 10 million (if you live in Pennsylvania).
Naively, then, your vote is 10,000 times more likely to change the outcome in a swing state, which would suggest that if changing the outcome is your primary motivation to vote, you should in fact feel some greater compulsion to vote in a swing state.
But in a more practical sense, 1 in 10 million simply doesn’t matter. Humans do not respond to such low probabilities and for all intents and purposes treat them as impossible. For example, 1 in 10 million is about the odds that that you’ll die if you drive 20 miles, that you’ll have identical quadruplets, or even that you yourself will become President. Our brains don’t think of 1-in-10-million-events as “low probability events” - they are simply “things that won’t happen”, exactly the same as 1-in-100-billion-events.
So in other words, if you were going to vote in a swing state out of some concern that you would affect the outcome, you should feel approximately equally compelled to vote in a non-swing state, because you’re already operating in the realm of phantasmorgical probabilities.
Likewise, if you think your vote “doesn’t matter” because you’re in a non-swing state and thus unlikely to affect the outcome - well, your vote still wouldn’t matter even in a swing state, because you are still not going to affect the outcome.
Take Florida 2000 as an example. In the closest swing state of all time, which would have tipped the closest Presidential election in modern history, your individual vote still wouldn’t have “mattered” any more than a vote anywhere else - not even if you had 500 bonus votes. Indeed, in all of recorded human history, no election with over about 100,0002 votes has ever been decided by one or fewer votes.
Does this mean you shouldn’t vote? Of course not - there are many reasons to vote other than expecting to be the single vote that changes the outcome.3 Critically, however, those reasons hold true regardless of whether you’re in a swing state.4 But if you only vote if your vote has a reasonable probability of changing the outcome, you will never vote, even in a swing state.
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As noted below, there are many ways to define how your vote matters. But the only definition that is relevant to the swing state distinction is this one. ↩︎
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Yes, this number is clearly cherry-picked. According to Wikipedia, a 1985 Australian state election and the 1839 Massachusetts gubernatorial election, were decided by 0 and 1 votes with ~105,000 and ~102,000 turnout, respectively. Maybe the lesson is that you should certainly vote if you expect turnout to be very close to 100,000, or if you have strong views on asbestos in Springfield Elementary. ↩︎
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Such as: local and state elections are far more impactful for most people and are far more likely to be decided by small margins, it feels good, and it validates your political debates on the Internet. But mostly - it’s a civic duty, like many other Kantian moral imperatives where the benefits accrue from everyone collectively making a seemingly irrational decision. ↩︎
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Of course, it also goes without saying that while all of this is true for an individual vote, it is most certainly not true for masses of votes. If you can affect a meaningful number of other people’s votes, you should absolutely do so in swing states. ↩︎