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!
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.
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