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BGonline.org Forums
My take on the Giants list
Posted By: Taper_Mike In Response To: My take on the Giants list (Timothy Chow)
Date: Tuesday, 23 February 2016, at 9:59 a.m.
Thanks for the link to Arrow's theorem. It's an interesting and somewhat depressing result. If there is no perfect way to do the job, then perhaps it is still possible to identify when one method is egregiously worse than another.
For instance, the current voting method assigns a weight to each name on a ballot based on rank. The weight is 33 - rank, so, for instance, the top rank on a ballot counts for 32 votes, and the the 32nd rank counts for 1 vote. Colin has proposed a drastically different method. His idea is to weight each name on a ballot with 1 vote, i.e., ballots are not ranked. Is there any effective way to determine if one of these two methods is "better" than the other?
@Bob: having now read the first half the Wikipedia article on Arrow's theorem, I understand that Tim was referring to the very general conditions that theorem posits are desirable for any ranking system.
I found that I did not agree with all of them. One, for instance, stated that, "The introduction of a third candidate to a two-candidate election should not affect the outcome of the election unless the third candidate wins."
In my own lifetime, we have the example Bill Clinton's first election in 1992. Clinton did not get a majority of the popular vote; he won that election by a plurality. Ross Perot polled significantly, as I recall, winning somewhere around 15% of the popular vote. My assessment is that Perot pulled more from George Bush (41) than he did from Clinton. It is not clear that Clinton would have won if there had not been a Perot candidacy. In this election, the introduction of of third candidate may well have affected the outcome of the election.
The theorem posits that in a "fair" election, a losing third candidate should not affect the outcome of the election. That may be fine assumption for those who live in an ivory tower. It the real world I inhabit, however, I would never expect such an precondition to be true.
In addition, Wikipedia reports that, "Voting systems that use cardinal utility (which conveys more information than rank orders; see the subsection discussing the cardinal utility approach to overcoming the negative conclusion) are not covered by the theorem. The theorem can also be sidestepped by weakening the notion of independence."
One way or another, a methodology must be chosen for ranking the votes cast in the Giants balloting. Are all methods really equally bad? Are there not some methods that are clearly worse than the average "bad" method? Where does the current method stand is this regard? Is it one of the "good" bad methods, or is it one of the "bad" bad methods?
Mike
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