[EM] MCA and median

[Kevin Venzke]

Gervase,
 
> This past weekend, I was thinking over how MCA could be made more
> sensitive to the difference between the top two levels (i.e. if no
> candidate obtains > 50% of favored, then the favored and acceptable levels
> are considered the same).

If I understand you, you're saying you want to increase the practical
difference between ranking a candidate "Favorite" vs. just "Approved" in
MCA.  I think the best option with three ranks is probably Condorcet
restricted to that many.

Also, a few weeks ago I posted a method called "Conditional Approval,"
also with three ranks, which simulates an Approval election in which the
voters could withhold their second-rank approval until/unless someone
they ranked last (third) takes the lead.  This creates considerable
difference between ranking someone first vs. second, although the method
isn't summable like MCA, and I believe it doesn't meet Weak FBC.

> However, I then realised that if the "top" 50% of the votes for a
> candidate are at worst at a certain level, then that certain level must be
> the median for the candidate.  It may be easier to see things if I define 
> the following "N-level" voting method:
> 
> (1) The winning candidate is the candidate with the highest median rank or
> score.
> (2) If more than one candidate satisfies (1), then break the tie by making
> the candidate with the least number of votes below the median the winner.
> (3) If more than one candidate satisfies (2), then break the tie by making
> the candidate with the most number of votes above the median the winner.

I like this idea, but won't voters use Approval strategy?  I mean, as a
voter, your ranking of a candidate only matters if you're the median voter
for that candidate.  In that case, I'd expect to vote either "thumbs-up"
or "thumbs-down" with no middle rankings.

Kevin Venzke
stepjak at yahoo.fr


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