[EM] Re: [Condorcet] RE: (crossposted) Revisiting Copeland
robla at robla.net
Fri Sep 9 11:41:06 PDT 2005
On Fri, 2005-09-09 at 16:52 +0200, Kevin Venzke wrote:
> I couldn't support Copeland unless you use a tiebreaker that satisfies
> minimal defense. Otherwise:
> 49 A
> 24 B
> 27 C>B
> A could be elected, for instance with a plurality tiebreaker.
> You suggested in a later message that plurality should be applied by
> eliminating Copeland non-winners first, and then counting first preferences.
> But I don't believe that is monotonic.
> I don't have to tell you that a plurality tiebreaker would bring massive
> favorite betrayal incentive.
Yup, you're right. Plurality doesn't make much sense as a tiebreaker.
I had forgotten how easy cycles can be if there's not incentive to
provide full rankings.
Minmax(wv) really isn't terribly complicated as a tiebreaker for
Copeland. More importantly, it's very easy to explain the morals of the
mechanics. Here's a layman's description of Copeland//Minmax(wv):
* Voters use a ballot to rank all candidates.
* Simulate all possible head-to-head contests between every candidate
in the election. For example, in a three-way race between Ann, Bob, and
Cy, we will use the ranked ballots to determine how each voter would
have voted in three different head-to-head elections: one between Ann
and Bob, one between Ann and Cy, and one between Bob and Cy.
* If there is a candidate who wins all head-to-head elections wins the
overall election. In the vast majority of cases, one candidate will
emerge as the winner.
* In the event that there is no candidate who wins all head-to-head
contests, we calculate the win-loss-tie standings of each candidate.
For each win, the candidate receives one point, for each tie, the
candidate receives 1/2 point, and for each loss, the candidate receives
no points. For example, if Ann beats Bob, Bob beats Cy, and Cy beats
Ann, then each candidate will have one win, one loss, and no ties
(1-1-0). Therefore, they each receive one point.
* In the event that there is still a tie in the standings, choose the
candidate who received the least votes against them in any head-to-head
matchup between the tied candidates. Consider this example:
* Ann beats Bob 55 to 45
* Bob beats Cy 56 to 44
* Cy beats Ann 51 to 49
This means that up to 51 voters voted against Ann, up to 55 voters voted
against Bob, and up to 56 voters voted against Cy. Since Ann had the
fewest votes against her in any head-to-head matchup, she wins the
That's the description. Mechanically speaking, all steps in the process
are very similar to what many are already used to in sports. I'm not
sure if there's a sports precedent for the minmax part, but I wouldn't
be entirely surprised if there was. It's certainly not too far afield
of what is generally done.
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