[Election-Methods] Challenge: Elect the compromise

[Jobst Heitzig]

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 <abd at lomaxdesign.com>
> Gesendet: 22.08.07 23:59:08
> An:  election-methods at lists.electorama.com
> Betreff: Re: [Election-Methods] Challenge: Elect the compromise


> 
> At 03:32 PM 8/22/2007, seppley at alumni.caltech.edu 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 <heitzig-j at web.de>
> > >>Subject: [Election-Methods] Challenge: Elect the compromise when
> > >>      there're        only 2 factions
> > >>To: election-methods at lists.electorama.com
> > >>Message-ID: <445065910 at web.de>
> > >>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
> > >
> >
> >----
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> 
> ----
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> 


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