Dan Bishop wrote:
Kristofer Munsterhjelm wrote:
To be more concrete, in a 2-candidate election, the first candidate
should be the one closest to the point where 33% of the voters are
below (closer to zero than) this candidate, and the second candidate
should be the one closest to the point where 67% of the voters are
below this candidate, the first candidate notwithstanding.
This is exactly what STV-CLE does.
James-Green Armytage devised some examples where STV-CLE seems to work
poorly. Are those problems with STV-CLE in particular, or with my
"percentile voter" generalization? I can't say for sure because his
examples don't fit into a 1D space.
However, I would choose a goal of minimizing the "mean minimum political
distance" (expected average distance between a voter and the nearest
winning candidate). On a uniform linear spectrum, the minimum is 1/(4k),
which occurs by electing the set {(n-1/2)/k for n=1 to k}. This reduces
to {1/2} when k=1, so is a generalization of the Condorcet Criterion.
However, it can also be applied to a multidimensional political spectrum.
The problem with measuring closest distance is that the closest
candidates can cloak disproportionality further out. Consider something
like this:
0| .x. A ... B ... C ... D ... E .y. |1
Half the electorate is at position x, closer to A than to any other
candidate, and the other half is at position y, closer to E than to any
other candidate. Say you're going to elect four candidates. Obviously, A
and E should be in the outcome. To be fair, the next ones should be D
and B, but you can pick any without changing the mean minimum political
distance. For instance, you could be biased towards E and pick {A, D, E}.
----
Election-Methods mailing list - see http://electorama.com/em for list info
