The problem is not well-posed, since the sincere ratings are not expressed in units, which means it's unclear whether C has the most utility for society.
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, here's another way to elect C: The 45 can pay 6 of the A faction to vote for C. (Not necessarily a payment of money.) We can expect members of the A faction to be willing to sell their votes fairly cheaply since they like C nearly as much as they like A, and we can expect members of the B faction to be willing to pay that price, since they like C much more than they like A and they can share the cost. (From an economics standpoint, transfers of wealth are not inefficient, all else being equal.) --Steve -------------------------------- 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: [email protected] >>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
