[EM] Party lists and candidate multiwinner elections

[Kristofer Munsterhjelm]

On 10/20/2014 05:24 AM, rbj at audioimagination.com wrote:
>   "Kristofer Munsterhjelm" <km_elmet at t-online.de> write:
>
>  > Say we have two settings: one is an ordinary multiwinner election with,
>  > say, 10 seats.
>
> BTW, another remarkable real-life fact about local elections in my part
> of Vermont (besides we had IRV and an election that is a classic example
> of what happens when IRV does not election the Condorcet Winner) is that
> in the Vermont State Senate, we have the *largest* legislative district
> in the entire U.S. in terms of the number of winners.  the Chittenden
> Senate District elects 6 state senators at large throughout the whole
> district.  there is no other legislative district in the U.S. with that
> many seats.
>
> and we're having an election coming up in 2 weeks.  it's a real
> cluster-fuck.  it's nearly the same as Approval Voting: vote for at most
> 6 candidates and the top 6 vote-getters win seats in the Vermont State
> Senate.  i dunno whether to vote for my second or third preference
> since, even though they may be running "alongside" my favorite candidate
> in the same party, they are really running against their colleagues in
> the same party.  in fact, in this liberal district (containing
> Burlington and suburbs), one of the 6 Democrat candidates will be bumped
> off (like musical chairs) because a single Republican candidate is
> expected to win re-election securely.  really weird voting dynamics,
> especially for a governmental election.
>
> this is when Proportional Voting (using, dare i say?, the Single
> Transferable Vote) would be possibly useful.

Bruce Schneier (I think) once said of crypto: "a lot of rounds solve 
many ills", in reference to that many types of cryptographic break 
against symmetric methods with few rounds would disappear if you just 
let the round count go high enough. Well, in PR, a lot of seats solve 
many ills, too. STV being mistaken in one of the seats is not nearly as 
bad as IRV being mistaken in its single seat, particularly not when STV 
can compensate; though it doesn't make an error go away entirely, unlike 
in the crypto example.

>  > The other is a party list PR election to a very large
>  > assembly (say 500 seats), but where the number of distinct parties has
>  > been limited to 10. That is, no more than 10 parties may be represented
>  > in that large council.
>  >
>  > Furthermore, assume that the voters' ballots are completely identical in
>  > the two settings. So if a voter in setting two ranks party A > party B >
>  > party C, then in setting one he would rank candidate A > candidate B >
>  > candidate C.
>
> just a curiosity: does this mean that Candidate C of Party A is
> preferred over Candidate A of Party B?  what if the voter doesn't like
> that, is it impossible to rank differently?

I'm just imagining two parallel universes. In the first, there's an 
election that uses a multiwinner method, and 10 seats. In the other, 
there's party list, and exactly 10 parties will win. (Disregard 
universes where not both are true). The ballot sets in both universes 
are identical, so each voter in the first setting votes for the 
candidates in the same order as he would the parties in the second setting.

In other words, each candidate (in the first universe) has a 
corresponding party (in the second). In universe 1, there're candidates 
X_1...X_n, and in universe 2, there are parties X_1...X_n. We don't know 
anything more than that, and it's closed party list, so the voters can't 
rank the members of the parties in setting 2. They can, however, rank 
the parties themselves (or rate them, if the methods used are rated).

Then the question is: will the parties that get at least one seat in 
setting one be the same as the candidates that get elected in setting two?