From kragen@dnaco.net Fri Aug 21 15:42:22 1998 Date: Fri, 21 Aug 1998 15:42:21 -0400 (EDT) From: Kragen Reply-To: Kragen To: mobrien@erinet.com Subject: social choice theory Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Keywords: X-UID: 1328 Status: O X-Status: There's a 200-year-old branch of math called "social choice theory" or "group choice theory", about how people make decisions in groups. There's a theorem in it from 1951 called "Arrow's Impossibility Theorem", which says, essentially, that voting methods can never work very well -- any conceivable voting method will come up with absurdly unfair (or just absurd) results in some circumstances. Every voting system has one of the following flaws: - if everyone prefers X to Y (Clinton to Jeffrey Dahmer, for example), then Y might still come out ahead of X in the outcome of the vote; - one person's vote is decisive and everyone else's is irrelevant, i.e., there is a dictator; - the introduction of another candidate for the results of the voting may cause the relative rankings of the already-existing candidates to shift. For example, in 1992, the introduction of Perot into the race may have caused Bush to lose to Clinton. See http://socs.berkeley.edu/~sgoldman/101a/arrow.pdf http://www.kellogg.nwu.edu/research/math/papers/1162.pdf http://www.elsevier.co.jp/hes/books/01/03/022/0103022.htm http://instruction.elgin.cc.il.us/classes/mth101/summary1.htm http://www.astro.virginia.edu/~eww6n/math/SocialChoiceTheory.html http://inforge.unil.ch/isdss97/papers/49.htm Another reason to cultivate the skills of consultation. Also interesting is the Delphi approach: http://eies.njit.edu/~turoff/Papers/delphi3.html Kragen -- Kragen Sitaker We are forming cells within a global brain and we are excited that we might start to think collectively. What becomes of us still hangs crucially on how we think individually. -- Tim Berners-Lee, inventor of the Web