[EM] Participation criterion: a thought

[Gervase Lam]

> Date: Sun, 21 Sep 2003 12:13:52 +0200 (CEST)
> From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
> Subject: Re: [EM] Participation criterion: a thought

> For the last couple of weeks I've been trying to come up with the
> smallest possible modification to Approval that would still meet
> Participation, but I still haven't got anything.
>
> Can anyone come up with anything here?

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.

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?

Mike Ossipoff suggested 3-level CR.  In the same thread he and Alex Small 
had a discussion about whether there was any point in using the middle 
slot in 3-level CR.  I think it was early this year?

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

(1) Give the top slot to the best front runner together with the other 
runners who you think are better than this front runner?
(2) Give the bottom slot to the worst front runner together with the other 
runners who you think are worst than this front runner?
(3) Put the remaining runners into the middle slot?

I think the only problem might be that the front runner won't get as much 
gain away from the runners in the middle slot in comparison with Approval. 
 But, do you care?  Isn't your primary aim to get as much distance between 
your favoured front runner and your unfavoured front runner?

Thanks,
Gervase.