[EM] proportional list

[Ross Hyman]

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.

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."

If one is only interested in a single-winner election, and one wants
to choose from the top of a Condorcet list or an IRV-topped Droop
compliant list, in which circumstances is one preferable to the other?

My answer to this is that it depends. If the voters are not polarized,
and can be represented by a fixed single peaked distribution with a
median that well characterizes the distribution, the Condorcet
candidate is probably better, to prevent center squeeze.

But if the electorate is divided into many factions, as I believe is
the case in the U.S., with those factions dynamically responding to
the presence and absence of candidates and the possibility of
candidates, in such a way that a fixed voter distribution in the
absence of the candidates is a theoretical abstraction with no
practical meaning, I think the IRV winner can be better, as there is
always support for it, no matter how many factions there may be.

Best,
Ross