[Election-Methods] Challenge: Elect the compromise

[seppley at alumni.caltech.edu]

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 <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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