Here’s a more germane objection: a single vote, in reality (as opposed to in “should universes”) never truly comes even close to deciding an election. When the votes are close to a tie, the courts step in, as in Bush v. Gore. There are recounts and challenges. The power of connections and influence by judicial politics completely overwhelms the effect of a single vote.
Don’t you think it perverse to derive the value of voting from the very high value of the outcome of an extraordinary event?
Take an electorate with 1,000,000,000 voters, deciding between A and B. If 550 million vote for A, and 450 million vote for B, then A is 90% likely to win. Conversely, if B leads 550 million to A’s 450 million, B is 90% likely to win. With very finely balanced vote totals both candidates have sizable chances at winning depending on the outcomes of recounts, etc (although the actual vote total in a recount certainly matters for the recount and challenge process!).
Say we make a graph, assigning a probability of victory for A for every A vote total between 450 million and 550 million. Over the whole range, there needs to be an 80% swing in win probability, on net. So, if we count every change in win probability as vote totals increase, the average change in win probability per vote for A has to be (80%)/(100 million) over this range.
So if the polls leave you with a roughly uniform distribution over vote totals between 450 and 550 million votes for A, then you should assign a probability of about 1 in 125 million to being decisive, despite recalls and court challenges and so on. This will reflect being the marginal vote that pushes a key vote total one way or the other, making a lead large enough that a judge or official doesn’t bother to do a recount, being the decisive vote in a recount, increasing the vote margin from 999 to 1000, a psychologically significant difference, and so forth.
Here’s a more germane objection: a single vote, in reality (as opposed to in “should universes”) never truly comes even close to deciding an election. When the votes are close to a tie, the courts step in, as in Bush v. Gore. There are recounts and challenges. The power of connections and influence by judicial politics completely overwhelms the effect of a single vote.
Don’t you think it perverse to derive the value of voting from the very high value of the outcome of an extraordinary event?
Take an electorate with 1,000,000,000 voters, deciding between A and B. If 550 million vote for A, and 450 million vote for B, then A is 90% likely to win. Conversely, if B leads 550 million to A’s 450 million, B is 90% likely to win. With very finely balanced vote totals both candidates have sizable chances at winning depending on the outcomes of recounts, etc (although the actual vote total in a recount certainly matters for the recount and challenge process!).
Say we make a graph, assigning a probability of victory for A for every A vote total between 450 million and 550 million. Over the whole range, there needs to be an 80% swing in win probability, on net. So, if we count every change in win probability as vote totals increase, the average change in win probability per vote for A has to be (80%)/(100 million) over this range.
So if the polls leave you with a roughly uniform distribution over vote totals between 450 and 550 million votes for A, then you should assign a probability of about 1 in 125 million to being decisive, despite recalls and court challenges and so on. This will reflect being the marginal vote that pushes a key vote total one way or the other, making a lead large enough that a judge or official doesn’t bother to do a recount, being the decisive vote in a recount, increasing the vote margin from 999 to 1000, a psychologically significant difference, and so forth.