[EM] CR, MCA; another CR/Approval method

[Kevin Venzke]

Gervase,

 --- Gervase Lam <gervase at group.force9.co.uk> a écrit : 
> 3-level Cardinal Ratings? :-)  Consistency and Participation compliant 
> whereas MCA isn't!  Add to that Later-No-Harm?
>
> At the moment, I think 3-level CR is better than MCA.  Sure, 3-level CR 
> has got the same problem as any another Cardinal Ratings method in that 
> the generally best strategy is to vote only at the extremes of the 
> Cardinal Ratings scale.  But, as Forest said when describing Max Power 
> "Cardinal Ratings", if the voters want to vote at the extremes, let them.

Right, but Forest meant that there was simply no harm in voting at the extremes.
It could/would be more desirable to not vote that way.  In CR you should
always vote at the extremes.

> The same thing could also be said about MCA.  MCA is a Median Rating 
> method and Median Rating methods have the same voting extreme problem.
> 
> I think you discovered using random ballots and found that the middle slot 
> in MCA "is almost never used.  It is used when a candidate's worth 
> [utility] happens to equal the mean worth."  Well, could the same thing be 
> said about 3-level CR?

I found that for zero-info elections, for when you don't know who's likely to
win or lose.  When you have information, it can be useful to use the middle
slot.  But in CR it should never be useful to use it, I think.

> I was just wondering whether the 'classic' Approval strategy could be 
> adapted to 3-level CR.

Sure.  Use the middle slot only for candidates whose utility is precisely
equal to your expectation for the election.  (Same as in zero-info MCA,
actually: Use the middle rank when the formula can't decide between the first
and last.)  If there is an even number of slots, the CR voter will have to
flip a coin in this case (same as in Approval).


Here is a CR method that simulates repeated approval balloting.  It may not
be original:

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.

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).

Kevin Venzke
stepjak at yahoo.fr


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