[EM] This might be the method we've been looking for:

[Andy Jennings]

Yes, in standard game theory everyone would know the exact utility of the B
supporters in each outcome.

Here, those utilities are hidden, so there is some incentive for the B
supporters to lie and say they are indifferent between A and C.



On Mon, Dec 12, 2011 at 4:17 PM, <fsimmons at pcc.edu> wrote:

> Thanks for checking the details.
>
> In traditional game theory the rational stratetgies are based on the
> assumption of perfect knowledge, so
> the A faction would know if the B faction was lying about its real
> preferences.  Even knowing that the
> other faction knew that they were lying they could still threaten to
> defect, and even carry out their threat.
> There is no absolute way out of that.
>
> ----- Original Message -----
> From: Andy Jennings
> Date: Monday, December 12, 2011 12:40 pm
> Subject: Re: [EM] This might be the method we've been looking for:
> To: Jameson Quinn
> Cc: fsimmons at pcc.edu, election-methods at lists.electorama.com
>
> > You're right. I've drawn out the game theory matrix and the
> > honest outcome:
> > 49 C
> > 27 A>B
> > 24 B>A
> > is indeed the stable one, with A winning.
> >
> > So the only way for B to win is for his supporters to say they are
> > indifferent between A and C and threaten to bullet vote "B".
> > Then the A
> > supporters fall for it and vote "A=B" to prevent C from winning.
> > B wins.
> >
> > I wonder if this is sequence of events is likely at all.
> >
> > ~ Andy
> >
> >
> >
> > On Fri, Dec 9, 2011 at 2:31 PM, Jameson Quinn
> > wrote:
> > > No, the B group has nothing to gain by defecting; all they can
> > do is bring
> > > about a C win. Honestly, A group doesn't have a lot to gain
> > from defecting,
> > > either; either they win anyway, or they misread the election
> > and they're
> > > actually the B's.
> > >
> > > Jameson
> > >
> > > 2011/12/9 Andy Jennings
> > >
> > >> Here’s a method that seems to have the important properties
> > that we
> > >>> have been worrying about lately:
> > >>>
> > >>> (1) For each ballot beta, construct two matrices M1 and M2:
> > >>> In row X and column Y of matrix M1, enter a one if ballot
> > beta rates X
> > >>> above Y or if beta gives a top
> > >>> rating to X. Otherwise enter a zero.
> > >>> IN row X and column y of matrix M2, enter a 1 if y is rated
> > strictly>>> above x on beta. Otherwise enter a
> > >>> zero.
> > >>>
> > >>> (2) Sum the matrices M1 and M2 over all ballots beta.
> > >>>
> > >>> (3) Let M be the difference of these respective sums
> > >>> .
> > >>> (4) Elect the candidate who has the (algebraically)
> > greatest minimum
> > >>> row value in matrix M.
> > >>>
> > >>> Consider the scenario
> > >>> 49 C
> > >>> 27 A>B
> > >>> 24 B>A
> > >>> Since there are no equal top ratings, the method elects the same
> > >>> candidate A as minmax margins
> > >>> would.
> > >>>
> > >>> In the case
> > >>> 49 C
> > >>> 27 A>B
> > >>> 24 B
> > >>> There are no equal top ratings, so the method gives the same
> > result as
> > >>> minmax margins, namely C wins
> > >>> (by the tie breaking rule based on second lowest row value
> > between B and
> > >>> C).
> > >>>
> > >>> Now for
> > >>> 49 C
> > >>> 27 A=B
> > >>> 24 B
> > >>> In this case B wins, so the A supporters have a way of
> > stopping C from
> > >>> being elected when they know
> > >>> that the B voters really are indifferent between A and C.
> > >>>
> > >>> The equal top rule for matrix M1 essentially transforms
> > minmax into a
> > >>> method satisfying the FBC.
> > >>>
> > >>> Thoughts?
> > >>>
> > >>
> > >>
> > >> To me, it doesn't seem like this fully solves our Approval
> > Bad Example.
> > >> There still seems to be a chicken dilemma. Couldn't you
> > also say that the
> > >> B voters should equal-top-rank A to stop C from being elected:
> > >> 49 C
> > >> 27 A
> > >> 24 B=A
> > >> Then A wins, right?
> > >>
> > >> But now the A and B groups have a chicken dilemma. They should
> > >> equal-top-rank each other to prevent C from winning, but if
> > one group
> > >> defects and doesn't equal-top-rank the other, then they get
> > the outright
> > >> win.
> > >>
> > >> Am I wrong?
> > >>
> > >> ~ Andy
> > >>
> > >>
> > >>
> > >> ----
> > >> Election-Methods mailing list - see http://electorama.com/em
> > for list
> > >> info
> > >>
> > >>
> > >
> >
>
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