[EM] proportional list

[Kristofer Munsterhjelm]

On 2025-06-23 19:05, Ross Hyman via Election-Methods wrote:
> Dear all,
> I would like to draw your attention to a pre-print I have uploaded to arxiv.
> https://arxiv.org/abs/2506.12318
> A House Monotone, Coherent, and Droop Proportional Ranked Candidate
> Voting Method
> Ross Hyman
> Subjects: Theoretical Economics (econ.TH)
> A Ranked candidate voting method based on Phragmen's procedure is
> described that can be used to produce a top-down proportional
> candidate list. The method complies with the Droop proportionality
> criterion satisfied by Single Transferable Vote. It also complies with
> house monotonicity and coherence, which are the ranked-candidate
> analogs of the divisor methods properties of always avoiding the
> Alabama and New State paradoxes. The highest ranked candidate in the
> list is the Instant Runoff winner, which is in at least one Droop
> proportional set of N winners for all N.

As I understood it from my first glance, the main differences between 
your method and Aziz's methods are
	- vs bottom-up: yours is top-down and thus elects the same top 
candidate as the base method (QPQ/IRV).
	- vs top-down: yours doesn't need to go through every solid coalition.

Is that correct, or did I miss some other properties?

> If I were to rewrite the paper for an audience interested primarily in
> single-winner elections. I would emphasise the following things:
> 
> A Droop proportional list has the property that the top N candidates
> in the list, for any N, satisfy the Droop proportionality criterion
> for N winners.
> 
> A Droop proportional list is a candidate list in which independence of
> irrelevant alternatives is not a desirable election criterion. For
> proportionally to be complied with, the weight of a ballot's input in
> deciding the relative ordering of candidates A and B should depend on
> the placement of other candidates on the ballot, since these other
> candidates can be elected to a high position on the list and reduce
> the weight of the ballot for deciding lower positions.
> 
> In general, the Condorcet winner cannot always be at the top of a
> proportional list.  It is easy to devise ballot sets where two
> candidates each have more than a third of the vote, so they must be in
> the top two positions, and neither is the Condorcet winner.
> 
> The Instant Runoff winner can always be at the top of a proportional
> list. There will always be a Droop proportional compliant set of N
> winners, for any N, that includes the IRV winner. I prove this in the
> paper. I also suggest in the paper that this property of the IRV
> winner is a way to give quantitative meaning to the term "core
> support."

This is why I think house monotonicity comes with a cost. In a 
left-center-right situation like the one you described, you can either 
have center squeeze (if your proportional ordering is, say, Left > Right 
 > Center), or you can have disproportionality (Center > Right > Left).

So IMHO, for a general multiwinner method, unless there's a particular 
reason, house monotonicity is not desirable. Party lists require house 
monotonicity so you have no choice there, but with a setting like STV, 
there shouldn't be any reason to require house monotonicity.

(It would be interesting to find out how parties solve this problem in 
countries with party list. No matter how the party draws up the list, 
those who do so are faced with the same trade-off since the party list 
format forces house monotonicity.)

-km