# [EM] Party lists and candidate multiwinner elections

Kristofer Munsterhjelm km_elmet at t-online.de
Mon Oct 20 09:42:00 PDT 2014

```On 10/20/2014 05:49 PM, Kathy Dopp wrote:
> 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.

I don't mean that the party members are turned into candidates and the
voters vote over them, but that the parties themselves are turned into
candidates.

Here's an example with SNTV and Webster, with one very large party and
two small ones:

500 seats:

12000 voters: Party A
300 voters: Party B
10 voters: Party C

The divisor is 24.6, so A gets 488 seats and B gets 12. k = 2.

Now let's turn to SNTV, which is multiwinner plurality. Now the

12000: A
300: B
10: C

SNTV just consists of taking the p greatest vote-winners in a p-seat
election, and here we have k=2 seats, so the winners are A and B.

So the represented parties in Webster were {A, B}, and the winners of
2-seat SNTV were also {A, B}. As far as I can see, this will always be
the case when the party list method is a divisor method and the
multiwinner method is SNTV because the monotone nature of the divisor
method means the k parties with the greatest number of Plurality votes
get represented (where what k you end up with differs based on the
ballots and on which divisor method is in use).

Now I know that SNTV is a bad multiwinner method, but it should give an
idea of the kind of result I'm thinking about. I'm just wondering if
this kind of equivalence is a good property, in part because my own PR
method seems to obey it.

In one sense, it seems to be, since the monotonicity implies that more
deserving candidates/parties get a shot at the seats first (as long as
the number of seats is large enough that compromises aren't needed). But
I'll mention more in my reply to Toby.
```