[EM] Help naming a new method
Andy Jennings
elections at jenningsstory.com
Sat Apr 2 23:16:09 PDT 2011
Hi all,
I have a new voting method and I think I need some help naming it. Let me
say, first of all, that I admit it may be too complicated for use by the
general public. It's a score aggregating method, like Score Voting.
Each voter scores each candidate on a scale of 0-100. Each candidate's
votes are aggregated independently, with their societal score given by
finding the largest number, x, such that x percent of the voters gave that
candidate a grade of x or higher.
So a candidate where 71% of the people gave a grade of 71 or higher (but the
same can't be said of 71+epsilon) will get a final score of 71.
It shares a strategy-resistance property with the median that any voter
whose score was above the societal score, if he were allowed to change his
vote, could do nothing to raise the societal score. (Also, a voter whose
score was below the societal score could do nothing to lower the societal
score.) This means that if you're only grading one candidate (e.g. choosing
an approval rating for the sitting president), then there is a strong
incentive for everyone to submit an honest vote.
Of course, if there are multiple candidates then there will always be some
instances where voters can benefit from voting dishonestly. If we are
entirely pessimistic and assume everyone is dishonest and gives fully
extreme scores, then where the median would return an extreme score, this
method does as good as approval voting or score voting. That is, it returns
the percentage of people who gave maximum grades.
It can be generalized to "find the largest number, x, such that F(x) percent
of the voters gave the candidate a grade of x or higher," for a
non-decreasing function F. F(x)=50, for example, is basically equivalent
to "find the median". But anything more complicated than F(x)=x is probably
hopeless for explaining to people. And the diagonal function F(x)=x has
some nice properties. For example, one voter can never unilaterally move
the output by more than 100/N, where N is the number of voters.
I thought of this method about three years ago. I've been sitting on it
since then, proving things for my doctoral thesis, which I finished last
fall. I did present this method at the Public Choice Society meeting about
a year ago. And I told Drs. Balinski and Laraki about it some time ago.
They make mention of it in their recently published book "Majority
Judgment".
I'd like to publish some things in a journal, but I'm thinking I may need a
better name for the method. So far, I've called it "the linear median" and
"the diagonal median". I've considered "the consensus median" or "the
consensus score", but that may be misleading, associating it with consensus
societies.
Any ideas?
Balinski and Laraki call it "the linear median" in their book. Is that good
enough?
Jameson, in particular, has been concerned about careful naming in the past,
so his input would be especially appreciated.
Thanks,
Andy Jennings
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