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

Forest Simmons fsimmons at pcc.edu
Wed Apr 3 17:40:05 PDT 2013

```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
>>
>> 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.

>
>
>  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
> 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.
>

If I am not mistaken, both methods (Chiastic and this one) are
strategically equivalent to Approval from a game theoretic point of view.
But psychologically they are quite different.  I think that this new
version is much less likely to elicit approval style responses (at the
extremes) than ordinary Range voting for example, or even the median method
with J in the title (I can't think of it at the moment).
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