# [EM] Party lists and candidate multiwinner elections

Kathy Dopp kathy.dopp at gmail.com
Mon Oct 20 08:49:36 PDT 2014

```On Mon, Oct 20, 2014 at 11:22 AM, Kristofer Munsterhjelm
<km_elmet at t-online.de> wrote:
> So with that in mind, let me alter the example.
>
> You have a set of ballots that rank (or rate, or approve, etc) n candidates.
> First, consider the candidates to be parties and run a party list election
> with, say, 500 seats. k parties will be elected. Then run a k-seat
> multiwinner election using the same ballots, but let the candidates be
> individuals.
>
> Would there then be any situation where the set of parties that got at least
> one seat in the assembly would ideally differ from the set of candidates
> that got elected in the k-seat multiwinner election? If so, when and why?

You have the same number of voters but in the second election you have
500 - k fewer seats, so I'd say that, if you are asking are the k
candidates from the same k political parties, I'd say "no" because
some of those k parties won many more seats in the 500 set assembly
because those k political parties may have widely divergent support,
say one of the k parties had 50% of the support and another of the k
parties had only 1/100th of the support (not enough to merit one of k
seats).

Increasing the size of any legislature always decreases the size of a
voter group who merits at least one seat proportionately in it, and
vice-versa.

>
> The reason I use a very large number of seats is to keep what one might call
> "quantization effects" to complicate the picture. Such effects happen when
> there aren't enough seats to represent each faction fairly, and thus a
> method might need to elect a compromise candidate instead. So, again, a
> better formal question might be "let the number of seats tend to infinity
> and the number of parties to elect be fixed at k. Assuming the party list
> method stabilizes in the limit, is or should then the subset of parties
> elected in a party list method be the same as the corresponding candidates
> elected by a k-winner multiwinner election method with the same ballots?".
> But again, I admit that it might be hard to reason about. Hence my
> unrestricted party list formulation.

--

Kathy Dopp
Town of Colonie, NY 12304
"A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas
Jefferson

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View my working papers on my SSRN:
http://ssrn.com/author=1451051
```