Donald Saari's recent book on voting "A Mathematician Looks at Voting" http://www.amazon.com/exec/obidos/tg/detail/-/0821828479/002-0156857-0623262... is really fun to read and contains lots of paradoxical things that can happen in election schemes. On the TV the other day, an "analyst" offered the opinion that we can expect many more extremely close elections for US President and at midterms because 1) polling is better; 2) money is being deployed more efficiently. This started me thinking about modelling votes by "buying them." Ie ignore all the (probably inessential, anyway) actual differences between candidates, and just assume that each "side" has a certain amount of money to be spent buying votes. Is there a sense in which that analyst is right for certain assumptions (I'm not sure what they might be?) Thane Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm ----- Original Message ----- From: "Henry Baker" <hbaker1@pipeline.com> To: <math-fun@CS.Arizona.EDU> Sent: Saturday, November 16, 2002 7:53 AM Subject: [math-fun] Majorities & minorities
In the last day or two, the Senate Judiciary Committee voted to allow one of Bush's appointees to move forward to a vote in the whole Senate.
I'm not interested in the politics of this appointee, but to the curious way the vote was recorded.
Although the Democrats have the most votes in the Committee, they held a 'voice vote' in which the appointee was approved. They then recorded the votes individually, showing that more individuals voted against than for.
(I guess this is a form of 'dark matter' votes, wherein the sum total is large enough, but a census of individuals can't turn up enough to account for the total.)
If this bizarre event is allowed to stand, it will go down as yet another form of legal hubris, along with stopping clocks, and making pi rational.
I'm curious if there are any real mathematical situations wherein a class loses, but when considered as individuals, they win. I presume we'd have to be talking about infinite sets, though, in order to even entertain such a notion.
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