[Election-Methods] Challenge: Elect the compromise

[Jobst Heitzig]

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 <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
> >
> 
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
> 


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