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on condorcet's paradox [Nov. 7th, 2007|10:36 am]
In an election where you pick two of three candidates (or write in), can the result of voting among the three candidates sum to ~100%?


I suppose, each vote can be divided by 2 times the number of total voters (each voter votes twice) to give an ultimate "percentage". But, to my way of thinking, this means that Araujo's 25.3% return means that his name was on over 50% of the ballots, and he didn't win. Consider this:

of candidates A+B+C, pick two, if four people vote A+B,A+B,A+C,B+C: A=B=3/8= 38%. c=2/8=25%. And yet, fifty percent of people voted for C. If I detest the incumbents equally, by having to vote for two (and choosing randomly or the lesser of evils) I entrench incumbency.

Conversely, this means that if they didn't divide like that, and that's a percent of votes cast, that only 38% of people voted for the most popular candidate.

And, that's of people who actually showed up to vote.

How is this democracy a republic just?

update: as of 2pm, the vote is TIED for Measure F. Yes, your vote does matter, even when you're ready to damn it all.

[User Picture]From: shoutingboy
2007-11-07 08:44 pm (UTC)
'...can the result of voting among the three candidates sum to ~100%?'

I'd say no, but only because I'd calculate the totals based on the presumption that they sum to 100%. The way I'd do it (and I strongly suspect the way they do it in real life) is:

Count the number of votes each candidate got. Call Alfred's total A, Betty's is B, Carl's is C, and so on. The total number of votes cast is equal to the sum of all the candidates' totals (A+B+C...+N); call that T. T is going to equal something shy of twice the number of voters, since everyone can vote for two but not everyone will.

Alfred's vote percentage is A/T, Betty's is B/T, and so on. F'r'ex, suppose there are 100 voters, and every one of them votes for two candidates (so T = 200). Thirty of the voters cast one of their two for Alfred (A = 30). Alfred's vote percentage is 30/200 = 15%.

"How is this democracy a republic just?"

I think "least unjust" is what we're aiming for. If you've got a better scheme in mind, feel free to send it to Mr. Arrow.
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[User Picture]From: hbergeronx
2007-11-07 09:23 pm (UTC)
I understand the math: what I don't know and don't trust is if San Bruno does. (seeing as he's the patron saint of the demonically posessed, and all :)

There were so many things wrong in how I perceived last night (lapis_lazuli summarized them pretty well) that I'm overwhelmed, and bereft of my usual logical placidity.
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