[EM] three tier approval

[LAYTON Craig]

Richard wrote:

>I was just trying to interpret your meaning, which I took to 
>be that "more likely to pick a CW" is relative to ordinary 
>Approval's likelihood to do so.

Certainly, that would be the case.  It would still, however, weed out low
utility Condorcet Winners.

>As for "three tiered approval condorcet winner", I don't know how 
>meaningful that concept is. I could define "approval CW" for 
>ordinary Approval but it's not a very helpful concept.

No, you're right.  However, given that the method uses a pairwise count, it
is useful to point out that conflicting pairwise victories shouldn't be that
common (or at least not as common as Condorcet methods).  If nothing else,
it makes the method "cleaner", and allows RP to be replaced by simpler
counting proceedures.

>It's neither; it means that I haven't seen that particular 
>scoring method proposed (though maybe I've missed it). 
>Whether the scoring idea is a good one or a bad one needs to 
>be studied.

The scoring can always be tweaked.  I know it isn't a good idea to mash
methods together, but it might be interesting to see how a system like this
might work using these ballots (optimal number of candidates is 4-8);

Rank all the candidates in order of how much approval they recieve (strongly
approve = approve for this count); eliminate the bottom candidate.  Conduct
a pairwise count (1 point for a win, 0 points for a loss); eliminate loser
(using reverse RP(m), for instance).  Conduct a ratings count (2 points for
strongly approve, 1 point for approve, 0 points for dissaprove) to find the
final ranking.

Another alternative would be to use my original points system, but use the
ratings count if there is no unbeaten pairwise winner.

I'm just trying to play around with the idea of maximising utility outcomes
over approval, without suffering the significant strategic collapse of
Cardinal Ratings & perhaps increasing the probability of electing the
sincere Condorcet Winner if it doesn't conflict with the other two goals.