[EM] Multiwinner elections

[Bart Ingles]

I can only think of a few ways to derive the required information from
ballots (I don't think I even want to get into aggregation methods
here):

1) allow the voters to assign a rating to each candidate, so that the
B+C will be chosen if their combined score is higher than A, for
example.  This might be the simplest, but there will be incentive to
misrepresent your sincere ratings (which may or may not be a problem).

2) Impute a rating based on preference order, which is essentially what
Borda attempts to do.  The method could then look at Borda scores of
combinations of candidates, in addition to single candidates, for a
given ballot.

3) Allow voters to rank combinations of candidates, as well as single
candidates.  Thus if I like A > B > C > D, and there are two seats to
fill, I might rank:

    AB > AC > BC > A > B > C

4) Cumulative voting, where voters speculate on the best combination of
candidates that they believe they can elect.  For example, if you are a
Green, and A is the Green candidate in the example above, you might
divide your cumulative vote between B and C.

Bart Ingles


Andrew Myers wrote:
> 
> 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.