[EM] another CR/Approval method

[Kevin Venzke]

I probably shouldn't have tacked this method description onto a reply to
Gervase, and anyway I have a couple of corrections to make to it, so I'll
post it again:

I wrote:
> The voter gives ratings to the candidates.
> mark all candidates as "viable."
> i=0  (keeps track of iterations)
> while more than two candidates are marked "viable":
>    Every ballot is converted to an approval ballot, by approving all candidates
>      preferred to the average rating (on that ballot) of all viable candidates.
>    i=i+1
>    mark all candidates "viable" except the "i" approval losers, who are marked
>      "not viable."
> Elect the approval winner of the last iteration.

First I want to point out that the approval tallies are not preserved between
iterations.  Once we find the "i" approval losers, the tallies are thrown out.
Also, the approval ballots MAY approve candidates who are no longer viable,
and those candidates can become viable again.

Instead of "while more than two candidates," it should say "while more than
one candidate," because otherwise we never count the ballots when only two
candidates are marked "viable."  In making this change, we can finish the method
description with "Elect the viable candidate," because there will only be
one.

Also, it would be sensible for the (artificial) approval ballots to give a half
vote to candidates who lie precisely on the average, since there's no justification
either way to approve or disapprove such candidates.

So the method definition should go:
> The voter gives ratings to the candidates.
> mark all candidates as "viable."
> i=0  (keeps track of iterations)
> while more than one candidate is marked "viable":
[OR: "while (numberofcandidates - i) > 1:"]
>    Every ballot is converted to an approval ballot, by approving all candidates
>      preferred to the average rating (on that ballot) of all viable candidates,
>      and giving half approval to candidates rated equal to that average rating.
>    i=i+1
>    mark all candidates "viable" except the "i" approval losers, who are marked
>      "not viable."
>    Discard all the approval votes.
[end of the while loop]
> Elect the only remaining "viable" candidate.


> The idea is that the voters begin in the dark when it comes to the odds, and
> initially probably approve too many candidates.  But in each iteration, one
> more candidate is considered to have no odds.  No one is eliminated, however.
> 
> Personally I think such a method would be more stable than methods where the
> cutoff moves based on the rating of the current front-runner(s).

I think this method is similar in spirit to Forest's Max Power method.  Instead
of merging less consequential ranks, though, it flags (and can unflag) failing 
candidates.

I like the method because it resolves cycles by looking at ratings.  Suppose the
(ranked) ballots are 40 ABC, 35 BCA, 25 CAB.  Any of those three could win in this
CR method, depending on which factions were more or less willing to compromise.


Kevin Venzke
stepjak at yahoo.fr


___________________________________________________________
Do You Yahoo!? -- Une adresse @yahoo.fr gratuite et en français !
Yahoo! Mail : http://fr.mail.yahoo.com