[EM] Multiwinner elections

[Paul Kislanko]

A theoretical, though impractical way to handle this would be as follows:

Have independent ballot-choices for place 1, place 2, etc. which each allow
the ranking of all candidates. The voter may choose to rank A>B>C>D... in
every position, in which case their "vote" degenerates into some variation
of IRV, but this would allow the voter to provide more information if she so
chooses. To count the votes:

1. Determine the place-1 winner (by whatever method you like).

2. Remove the place-1 winner from every position in all the place-2 ballots,
with lower-ranked candidates "inheriting" the vacated rankings and calculate
the place-2 winner.

Repeat step 2 (remove the place-2 winner from all the place 3 ballots, etc.)
until all seats have been filled.

There are circumstances where this approach works well, but I am not sure
what all the ramifications would be depending upon the method chosen to pick
a winner at each step.

-----Original Message-----
From: Andrew Myers <andru at cs.cornell.edu>
To: election-methods-electorama.com at electorama.com
<election-methods-electorama.com at electorama.com>
Date: Friday, January 02, 2004 2:36 PM
Subject: [EM] Multiwinner elections


>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
>----
>Election-methods mailing list - see http://electorama.com/em for list info