[Election-Methods] Challenge: Elect the compromise

[Abd ul-Rahman Lomax]

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 :-)
> >>
> >
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