[EM] MCA and median

[Kevin Venzke]

Gervase,

 --- Gervase Lam <gervase at group.force9.co.uk> a écrit :
 > > > (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.
> 
> All I was trying to do here was to point out that if you applied the above 
> rules to a 2 or 3 level ballot, you would respectively get Approval and 
> MCA.

Hmm.  I tried to disprove this, but I think you're right.  I guess
Approval strategy wouldn't be the rule, since I think people would use
the middle rank in MCA.

Interestingly, we could reverse the order of steps 2 and 3, and no longer
get MCA out of it.  Example: candidates A and B are the only two whose
median rank is the 2nd rank.  B has more 1st and 3rd rankings.  B wins
although he is more disapproved than A.  (MCA would elect A.)

> 
> > 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
> 
> Possibly.  With MCA, the theory is that the need for you to vote 
> "thumbs-up" (i.e. the Favoured vote) for candidates you are indifferent 
> about (i.e. the Acceptable vote) is lower.  The only time you would need 
> to do this is if it is predicted that one of your "thumbs-down" candidates 
> will win by tallying over 50% of the Favoured votes.  In other words, it 
> is predicted that your "thumbs-down" candidate would have a median of 
> Favoured.
> 
> Extending from the 3 levels of MCA to a larger number of levels, a similar 
> rule could be applied.  You need to raise the level of a candidate on your 
> ballot if the predicted median level of another candidate, who you rate 
> less, is higher.  You would need to raise it to at least the level of the 
> other candidate's predicted median.  Or something like that.
> 
> Hmmm.  The above paragraph makes it sound like the (strong) favourite 
> betrayal criterion is not satisfied if more than 3 levels were used.  Is 
> this correct?

Strong FBC is not met with any number of levels.  (I don't believe it's met
by any method.)  There's always the possibility that you could prevent your
disapproved candidate from winning with a majority of Favorite rankings, by
helping a compromise candidate get an even larger majority of Favorites.

Kevin Venzke
stepjak at yahoo.fr


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