[EM] Multiwinner elections

[Andrew Myers]

Condorcet methods like beatpath winner can be used to obtain a ranking
of the candidates but they don't seem to be good for elections in which
the goal is proportional representation.  I'm curious whether people
know about generalizations of beatpath winner that make sense for this
purpose.

There seems to be something fundamentally problematic about this goal
because the voter can't give enough information by simply ranking
preferences.  Suppose a voter likes candidates A > B > C.  That's enough
information to use for a single-winner election, but it doesn't tell us
enough for a multiwinner election. Suppose that when the other voter's
preferences are taken into account, the choice comes down to either
getting A elected (but not B or C), or getting B and C elected (but not
A).  Even though the voter prefers A to B or C individually, we can't
tell whether that voter would prefer A to the B+C combination.

Does anyone have any pointers? Thanks.

-- Andrew