[EM] another CR/Approval method

[Forest Simmons]

I like it!

As far as I know this method is original with Kevin.


Both the "why" and the "how" of the method are easy to understand.

It's the best use of CR ballots that I've seen so far.  It's definitely
better than my MAX POWER CR.

Several of us have been stabbing around in the dark looking for something
like this.  It's going to be hard to find a better use for CR ballots.

Here's an idea along slightly different lines for using CR ballots:

Find the two candidates whose max opposition is least.

On each ballot that contributes to the max opposition of both of these
candidates, merge the top two levels.

Recalculate the max oppositions of all the candidates to find the new
front runners.

On each ballot that contributes to the max opposition of both of these
candidate, merge the top two levels.

Continue in this manner until there is no ballot that contributes to the
max opposition of both current front runners.

At this point the candidate with the least max opposition is elected.

In this method the mergers progress from the top down and are
irreversible, as in Bucklin, but unlike Bucklin this method does not
collapse all ballots in lock step.

A variation would allow voters to specify a minimum level for mergers.  In
this variation, the process would continue until every ballot that
contributes to the max opposition of both front runners is already
collapsed down to the voter specified minimum.

Another variation could use your viability idea.

For example, suppose that there are 5 candidates.

Mark as viable the four whose max opposition is least.

Merge the top two levels of all ballots that contribute to the max
opposition of all four of these viable candidates.

Now forget the previous viability marks, and mark as viable the three
candidates whose max opposition is least.

Merge the top two levels on all ballots that contribute to the max
opposition of all three of the currently viable candidates.

Now discard the viability marks, and mark as viable the two candidates
whose max opposition is least.

After one last collapse (on ballots that contribute to the max opposition
of both viable candidates), the candidate with the min max opposition is
elected.

Forest


On Thu, 25 Sep 2003, [iso-8859-1] Kevin Venzke wrote:

>
> 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
>
>
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