# [EM] Multiwinner elections

Paul Kislanko kislanko at airmail.net
Fri Jan 2 13:35:01 PST 2004

```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

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.
>
>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

```