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Re: Generalizations...
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Blake Cretney
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Apr 13, 2002 17:13 PDT
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Bram Cohen wrote:
| | Stéphane Rouillon wrote:
| | I have read your archives (yes all of it !) and I am
particulary interested by the weighted version of ranked
pairs proposed by Mr. Bram Cohen, if I am not wrong.
1) Could someone summarize how it works with words
not with the code to help me understand it better?
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I've actually got a better method than the last one I described, so I'll
take a stab at summarizing it now.
You elect candidates one at a time, each time choosing the next winner out
of the remaining set by ranked pairs.
The first candidate is picked by ordinary ranked pairs. The second
candidate is again picked by using the ranked pairs algorithm on pairwise
scores, but the calculation of pairwise scores is altered based on the
already selected candidates and where they appear in everybody's ballots.
Let us say that there are N candidates to be selected, using V votes. Each
already selected candidate will weaken existing votes by V/(N+1). Let us
say that we are comparing candidates P and Q, after A has already
been selected. To do this, we figure out all votes for which A is ranked
higher than both P and Q, say there are x of them. We then reduce the
strength of each of these votes by x/(V/(N+1)). We then repeat for all
other already elected candidates. In the end, each vote will have some
remaining strength, and we can add up the strength of all of those which
ranked P first and all of those which ranked Q first and see which is
greater.
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Let me suggest an alternate way of doing it. If the ballot ranks P over
Q, and x elected candidates come before P on the ballot, then instead of
contributing 1 vote to the P vs. Q comparison, the ballot contributes
1/(2x+1) votes. That is analogous to using the St. Lague rule of
proportional representation.
---
Blake Cretney
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