Analyzing a Voting System (Math Geeks Please Help!)

[latefordinner]

just the reverse of how many trials do I have to do before I can say with x amount of certainty that this coin is rigged.

[Wyman]

BTW, the electoral college changes your answer to this question.

[pvn]

[ QUOTE ]
I'm testing a theory about the US voting system and I'd like a little help devising a formula to tell me the likelihood that one vote will make or break the election.

The assumptions are that there are n number of participating voters, two candidates A and B, and all voters will vote with a 50-50 likelihood of either candidate. What is the formula to determine the likelihood that the same number will show up for both sides?

There is probably going to be a resolution problem, because for even numbers a vote count of n/2 on either side yields, and ((n/2) +/- 1) depicts voting situations where one vote did make a difference...but for odd numbers, the countable outcomes would be ((n/2) +/- .5) with no stalemate.

Can anyone figure out a simple formula for this?

[/ QUOTE ]

Yes. I posted exactly what you're looking for in politics a while back, in a discussion about how worthless your vote is.

[jstnrgrs]

Sort of unrelated, but I was reading in the paper the other day that in Natck, MA, the vote for town moderator was 1772-1772.

[hmkpoker]

[ QUOTE ]
Sort of unrelated, but I was reading in the paper the other day that in Natck, MA, the vote for town moderator was 1772-1772.

[/ QUOTE ]

There's a big difference between local elections and federal elections. Do you think a national popular election would ever come down to 50,000,000-50,000,000?

[CallMeIshmael]

I think an interesting question is:

once we all concede that voting, as is now, is clearly irrational (which I certainly agree with), then when does it become rational?

I mean, if all I had to do was click one button on the internet, then I really think the decision becomes rational. IF this is true, then where is the line crossed?

[hmkpoker]

[ QUOTE ]
I think an interesting question is:

once we all concede that voting, as is now, is clearly irrational (which I certainly agree with), then when does it become rational?

I mean, if all I had to do was click one button on the internet, then I really think the decision becomes rational. IF this is true, then where is the line crossed?

[/ QUOTE ]

There really is no universal way to calculate this. Not only would we have to factor in a number of other annoying variables (for example, what is the probability that the candidate you elect will do what you want him to do?), but the pure, utilitarian EV of voting is going to be almost infinitely outweighted by the satisfaction of voting (or not voting) independently of any results. Most voters are completely unaffected by the actual chances of their vote mattering, because it is "the right thing to do." My brother's roommate (at Penn State) drove back to the southern border in his home state of Virginia in '04 to vote for Bush. That's a long drive, and a solid red state. Even if his odds of affecting the outcome were 1/infinity (zero), he'd still do it.

This should actually concern people. When voting populations become large and rational consequence-driven incentives diminish, the system must select against rational, consequence-oriented people. The winning candidates in these elections are selected by deontologically/morally-oriented people, which is not very representative of the population.

[pvn]

[ QUOTE ]
This should actually concern people. When voting populations become large and rational consequence-driven incentives diminish, the system must select against rational, consequence-oriented people. The winning candidates in these elections are selected by deontologically/morally-oriented people, which is not very representative of the population.



[/ QUOTE ]

gold star.

[jstnrgrs]

[ QUOTE ]
[ QUOTE ]
Sort of unrelated, but I was reading in the paper the other day that in Natck, MA, the vote for town moderator was 1772-1772.

[/ QUOTE ]

There's a big difference between local elections and federal elections. Do you think a national popular election would ever come down to 50,000,000-50,000,000?

[/ QUOTE ]

No, I understand the difference. But even with 3000 voters, I would have thought that the chance of a tie would be nearly 0.

[hmkpoker]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Sort of unrelated, but I was reading in the paper the other day that in Natck, MA, the vote for town moderator was 1772-1772.

[/ QUOTE ]

There's a big difference between local elections and federal elections. Do you think a national popular election would ever come down to 50,000,000-50,000,000?

[/ QUOTE ]

No, I understand the difference. But even with 3000 voters, I would have thought that the chance of a tie would be nearly 0.

[/ QUOTE ]

If 3,000 voters flip coins to select their candidate, the probability of a tie is a little better than one in a hundred. Now granted the true probability in these elections is probably not an exact coinflip, so the odds will be a bit worse, but even with a few powers of ten added on against the unlikelihood, you still have to account for the fact that there are TONS of these local elections taking place throughout the country. The USA has tons of small towns with tiny populations that are all having these elections. The odds that one of these four-digit populations will produce a tie now and then is actually very, very high.

For all practical purposes, you are guaranteed to see a tie in a local election (over a period of, say, several years), and guaranteed never to see a tie in a federally-sized election, even if it is purely popular, ever.