re: #502 Obdicut

No, you didn’t. You referenced a wikipedia page about an entire area of mathematics. Do you not know what ‘show your math’ means?

Look at it this way: what if there were 10,000 people total going to the polls in your state, including you? What are the chances of you being the ‘deciding’ vote then?

I answered this very question already. But here goes again.

The “real” answer is insanely complicated. But a model can be analyzed. In the model, the question is, what are the odds that the election will be so close that a single voter switching sides can flip the election?

In the model, the voters are flipping coins to decide who they’ll vote for. They go into the booth, flip, and vote. The odds that after all 10 thousand votes have been cast, it’s a tie, are 0.0079786461393821537604, or (like I wrote earlier) a little less than 1 percent. The formula is C[10000,5000]/2^10000. Binomial coefficient.

The reason for this formula is that in general, if you have n voters, there are C[n,m] different bit strings with exactly m votes for a particular candidate, out of the two on offer. All bit strings are by premise equally likely since everybody’s flipping a coin in the model, so the set of strings that yield a tie, C[10K,5K] of them, has a probability of C[10K,5K]/2^(10K) of occurring.

The quick and dirty answer, recall, was 1 percent on the dot.

A practical related question might be, what good will it do to spend on campaign commercials in a state where the election is known to be close and many voters have not made up their minds? And would you do better to spend in a big state, or a small state. (Assume the cost of getting your message to an individual voter is the same either way.)

You’d have to spend ten times as much money on CA as on WV, to reach everybody. Your chance of flipping the election would drop by a factor of 1 in 3 or 4, because CA has ten times as many people, roughly. But the payoff, if you do flip it, is ten times as big. So dollar for dollar, a campaign commercial that must be paid for viewer by viewer pays best in a big swing state. Courting voters in big swing states is the smart move. In that sense, voters in such states have more voting power.

It’s somewhat realistic to think of voters as not having made up their minds, because voters may know who they prefer, but whether they actually go and vote is often pretty much a matter of chance. And there are a good many voters who say they’re undecided, right down to the wire. Elections really do partake of probability.