Fan de Condorcet wrote:
James,
You wrote:
Given sincere votes, this may be interesting, but if votes are not necessarily sincere, it would be quite possible for all candidates to receive a social utility of 0. That is, the lower quartile feature makes the method into a kind of 3/4 supermajority method.
However, scoring candidates by the median rather than the mean might be an
improvement on standard cardinal ratings. Has this been discussed before?
Yes. I once happened to stumble across an archived message, originally posted by Rob Lanphier, in which he suggested just this. It wasn't long before he shot down his own idea in a follow-up message.
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001603.html
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/1998-April/001607.html
Some other problems with Median Ratings:
* It adds a complication to the vote counting: If there are c candidates and r possible ratings, there need to be c*r entries in the summation array, rather than just c (as in standard Cardinal Ratings).
* The previous problem is minor if you choose a reasonably small value of r. But by doing so, you introduce another problem:
Ballots based on a 0-100 scale:
A=74, B=42, ...
A=61, B=87, ...
A=61, B=59, ...
A=23, B=25, ...
A=97, B=72, ...
Median ratings: A=61, B=59
The same ballots rounded for a 0-10 scale:
A=7, B=4, ...
A=6, B=9, ...
A=6, B=6, ...
A=2, B=3, ...
A=10, B=7, ...
Median ratings: A=6, B=6
* It fails Neutrality of Spoiled Ballots.
A=1, B=4 A=2, B=4 A=8, B=4 A=9, B=4
With these ballots, the median ratings are A=5 and B=4, so A wins. However, if the ballot (A=0, B=0) is added, then the median ratings become A=2 and B=4, so B wins.
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