[EM] STV question (was: re: Hare clustering)

[Kristofer Munsterhjelm]

On 10.02.2022 10:23, Colin Champion wrote:
> Kristofer posted some thoughts about Hare-clustered multi-member PR
> which I don't understand.
> 
> Would I be right in thinking that the aim of multi-member PR, under a
> spatial model, is to elect a set of candidates for a constituency such
> that the average distance from a voter to the nearest candidate is
> minimised? In this case, does it not follow that two candidates who are
> close to each other ("belong to the same party") will ideally never be
> elected?

The STV notion of proportionality is basically: if more than a Droop
quota all prefer a certain group of candidates (even if they do so in a
different order) to everybody else, then one candidate from that group
must be elected.

So this is different from your minimization concept, because suppose we
have this election:
150: A>B>C
149: B>A>C
  1: C>A>B

with two to elect. The Droop quota is 100 voters. Then the ABC bloc gets
one candidate, and the BAC bloc also gets one, so A and B are elected,
even if the C voter is very far from both A and B. Just like ranked
voting has no concept of strength of preference, nor does the Droop
proportionality criterion.

The Hare notion is more explicitly about giving each group of 1/n voters
"its own candidate". There's a concept of the core that I was thinking
of writing a post about, but I haven't got around to it yet, that makes
this idea more concrete.

But for simplicity, suppose that you have an 1D spatial model with
voters uniformly distributed over the line [-1..1]. Then the Hare notion
is that the group of voters corresponding to the negative region of the
line get one candidate, and the group of voters corresponding to the
positive get the other one. Just which negative value candidate and
which positive value candidate will be elected is up to the election
method, but it will be one positive and one negative (if such candidates
exist).

With the Hare quota notion, each group of 1/n voters directly decide who
will be elected and get "their own" representative. With the Droop
quota, there are s+1 Droop quotas for s seats. s of these quotas get to
choose what faction will be elected (as in the example above); the final
Droop quota doesn't get its own representative but instead gets to
influence what candidate is chosen from each winner faction.

Droop quota methods are usually less partisan (more consensus-based)
than Hare quota ones. The comparison is similar to D'Hondt vs Sainte-Lague.



To answer your question: in a partisan, suppose there are enough seats
that the scenario I mention is possible, and 30% of the voters vote for
party X, then even if party X's candidates are all located at the exact
same spot, the fact that 30% of the voters vote for X first means
they're all closer to X than anywhere else. So 30% of the seats will be
filled with party X clones.

But if the candidate distribution is a bit more fuzzy, then say, a green
voter who usually likes party X might favor some candidate from party Y
because this candidate is particularly green even if Y isn't a green
party. Then X won't get 30% of the vote: candidates closer to the voters
may benefit from voters who would vote for other parties if they were to
vote party line.

So it doesn't necessarily follow that party clones will never be
elected. That depends on the composition of the electorate.

-km