Dear Steve! > However, assuming the intensity difference between the A faction's 100 and > 80 is much less than the intensity difference between the B faction's 80 > and 0,
That was not the assumption I wanted anyone to make. Those of you who believe in measurable utility: please assume that the ratings reflect utilities in the *same* units. All others: please interpret the ratings A 100, C 80, B 0 as saying that the person would prefer C over each lottery that elects A with a probability of p less than 80%, and B with a probability of 1-p, and that the person would prefer over C each lottery that elects A with a probability of p above 80%, and B with a probability of 1-p. Yours, Jobst > -------------------------------- > Forest S replied: > > Under strategic voting with good information, any decent deterministic > > method (including Approval) would elect the Condorcet Winner A . > > Uncertainty as to the faction sizes could get C elected, but not > > necessarily. > > > > So some randomness is essential for the solution of this problem. > > > > The indeterminism has to be built into the method in order to make sure > > that it is there in all cases. > > > > Jobst's D2MAC would work here because the compromises' 80 percent > > rating is above the threshold for sure election when the two faction > > sizes differ by ten percent or more, if I remember correctly. > > > > If the compromise had only a 60 percent rating, for example, optimal > > strategy might give A a positive chance of winning. > > > > It is paradoxical that randomness, usually associated with uncertainty, > > is the key to making C the certain winner. > > > > Look up D2MAC in the archives for a more quantitative analysis. > > > > I hope that this doesn't prematurely take the wind out of the challenge. > > > > Forest > > > >>From: Jobst Heitzig <[EMAIL PROTECTED]> > >>Subject: [Election-Methods] Challenge: Elect the compromise when > >> there're only 2 factions > >>To: election-methods@lists.electorama.com > >>Message-ID: <[EMAIL PROTECTED]> > >>Content-Type: text/plain; charset=iso-8859-15 > >> > >>A common situation: 2 factions & 1 good compromise. > >> > >>The goal: Make sure the compromise wins. > >> > >>The problem: One of the 2 factions has a majority. > >> > >>A concrete example: true ratings are > >> 55 voters: A 100, C 80, B 0 > >> 45 voters: B 100, C 80, A 0 > >> > >>THE CHALLENGE: FIND A METHOD THAT WILL ELECT THE COMPROMISE (C)! > >> > >>The fine-print: voters are selfish and will vote strategically... > >> > >>Good luck & have fun :-) > >> > > > > ---- > > Election-Methods mailing list - see http://electorama.com/em for list info > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > _______________________________________________________________________ Jetzt neu! Schützen Sie Ihren PC mit McAfee und WEB.DE. 3 Monate kostenlos testen. http://www.pc-sicherheit.web.de/startseite/?mc=022220 ---- Election-Methods mailing list - see http://electorama.com/em for list info