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

[Andy Jennings]

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 <jameson.quinn at gmail.com>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 <elections at jenningsstory.com>
>
>>  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
>>
>>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20111212/f25f5082/attachment-0004.htm>