Help naming a new method
2011-04-03 06:16:09 GMT
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.
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.
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