[EM] Election-Methods Digest, Vol 106, Issue 2

[Jameson Quinn]

2013/4/3 Forest Simmons <fsimmons at pcc.edu>

>
>
> On Wed, Apr 3, 2013 at 12:07 AM, Kristofer Munsterhjelm <
> km_elmet at lavabit.com> wrote:
>
>> On 04/03/2013 12:01 AM, Forest Simmons wrote:
>>
>>> Jobst has suggested that ballots be used to elicit voter's "consensus
>>> thresholds" for the various candidates.
>>>
>>> If your consensus threshold for candidate X is 80 percent, that means
>>> that you would be willing to support candidate X if more than 80 percent
>>> of the other voters were also willing to support candidate X, but would
>>> forbid your vote from counting towards the election of X if the total
>>> support for X would end up short of 80 percent.
>>>
>>> The higher the threshold that you give to X the more reluctant you are
>>> to join in a consensus, but as long as your threshold t for X is less
>>> than than 100 percent, a sufficiently large consensus (i.e. larger than
>>> t percent) would garner your support, as long as it it is the largest
>>> consensus that qualifies for your support.
>>>
>>> A threshold of zero signifies that you are willing to support X no
>>> matter how small the consensus, as long as no larger consensus qualifies
>>> for your support.
>>>
>>> I suggest that we use score ballots on a scale of 0 to 100 with the
>>> convention that the score and the threshold for a candidate are related
>>> by  s+t=100.
>>>
>>> So given the score ballots, here's how the method is counted:
>>>
>>> For each candidate X let p(X) be the largest number p between 0 and 100
>>> such that p(X) ballots award a score strictly greater than 100-p to
>>> candidate X.
>>>
>>> The candidate X with the largest value of p(X) wins the election.
>>>
>>
>> I think a similar method has been suggested before. I don't remember what
>> it was called, but it had a very distinct name.
>>
>> It went: for each candidate x, let f(x) be the highest number so that at
>> least f(x)% rate the candidate above f(x).
>>
>> I *think* it went like that, at least. Sorry that I don't remember the
>> details!
>
>
> Good memory, that was Andy Jennings' Chiastic method.  Graphically these
> two methods are based on different diagonals of the same rectangle.
>

Different, how? It seems to me they're just the same, but with the numbers
reversed.

>
>>
>>  If there are two or more candidates that share this maximum value of p,
>>> then choose from the tied set the candidate ranked the highest in the
>>> following order:
>>>
>>> Candidate X precedes candidate Y if X is scored above zero on more
>>> ballots than Y.  If this doesn't break the tie, then X precedes Y if X
>>> is scored above one on more ballots than Y.  If that still doesn't break
>>> the tie, then X precedes Y if X is scored above two on more ballots than
>>> Y, etc.
>>>
>>> In the unlikely event that the tie isn't broken before you get to 100,
>>> choose the winner from the remaining tied candidates by random ballot.
>>>
>>
>> I imagine Random Pair would also work.
>>
>>
>>  The psychological value of this method is that it appeals to our natural
>>> community spirit which includes a willingness to go along with the group
>>> consensus when the consensus is strong enough, as long as there is no
>>> hope for a better consensus, and as long as it isn't a candidate that we
>>> would rate at zero.
>>>
>>
>> That's an interesting point. I don't think that factor has been
>> considered much in mechanism design in general. Condorcet, say, is usually
>> advocated on the basis that it provides good results and resists enough
>> strategy, and then one adds the reasoning "it looks like a tournament, so
>> should be familiar" afterwards.
>>
>> Perhaps there's some value in making methods that appeal to the right
>> sentiment, even if one has to trade off "objective" qualities (like BR,
>> strategy resistance or criterion compliance) to get there. The trouble is
>> that we can't quantify this, nor how much of sentiment-appeal makes up for
>> deficiencies elsewhere, at least not without performing costly experiments.
>
>
I'm currently doing such "costly experiments" on Amazon MTurk (with money
from Harvard). I'm evaluating Approval, Borda, Condorcet (3-candidate, so
the differences between the most common varieties doesn't matter), GMJ,
IRV, Plurality, Score, and SODA (with honest-declaring and
mutually-rational-assigning AI candidates), with an 18-voter, 3-candidate
scenario in factions of 8, 4, and 6 (with utilities for each voter of 0-3,
summing to 12, 16, and 11). I'll let the list know as results are available.

Jameson
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