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.
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.