Dear Abd ul-Rahman and Steve, why not just trade winning probability instead of votes?
What I mean is: try Asset Voting with Random Ballot instead of Plurality as its base method... Jobst > -----Ursprüngliche Nachricht----- > Von: Abd ul-Rahman Lomax <[EMAIL PROTECTED]> > Gesendet: 22.08.07 23:59:08 > An: [email protected] > Betreff: Re: [Election-Methods] Challenge: Elect the compromise > > At 03:32 PM 8/22/2007, [EMAIL PROTECTED] wrote: > >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.) > > That's correct. It is doable. It might also be illegal, here. But > there could be ways to do it legally, as mentioned, it would not > necessarily be a payment of money. But for these factions to trust > each other could be a problem. If C is elected, what is to keep the B > voters from simply not paying? > > Nevertheless, that kind of proposal is similar to what I mentioned > about systems that would encourage voters to vote true utilities. In > this case, the B supporters shift the utilities of some "selfish A > voters" so that they, selfishly, will change their votes. To pay the > minimum, the B voters could auction off the right to receive > payments, which payments would be conditional on C winning. Since the > A voters are, as described, selfish, some would sell their votes > fairly cheaply. > > Technically, they are not selling votes, they are bidding an amount > that they would receive if C wins. For them, it is like a hedge. The > bidding is in reverse, that is, it starts high and comes down. It > deserves more thought... > > > >--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 > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > _____________________________________________________________________ Der WEB.DE SmartSurfer hilft bis zu 70% Ihrer Onlinekosten zu sparen! http://smartsurfer.web.de/?mc=100071&distributionid=000000000066 ---- Election-Methods mailing list - see http://electorama.com/em for list info
