[EM] IRV et al v. EPR

[Kristofer Munsterhjelm]

On 2018-07-16 20:09, Jameson Quinn wrote:
> This system as described is very close to being an excellent 
> "Proportional Majority Judgment" method, but has one key flaw. When a 
> candidate is elected with more than 1 quota of support, all of their 
> supporting ballots are marked as used. To give a proportional method and 
> to minimize strategic incentives, only 1 quota of supporting ballots 
> should be marked as used. This could be done through some ordering 
> criterion (highest support for winner/lowest support for others), by 
> proportionally reweighting ballots, or by using up randomly-chosen 
> ballots; the differences between these three options would be relatively 
> minor.
> 
> This reflects the basic way to transform any single-winner method into a 
> proportional multi-winner method: find single winners sequentially, and 
> then for each of those winners, "use up" the one quota of ballots that 
> "contributed most" to making that candidate the winner. There's room for 
> judgment calls in defining "contributed most", but other than that this 
> is a general template that IMO gives an optimal combination of good and 
> practical from methods as varied as IRV (which becomes STV), MJ, STAR, 
> Score, approval, Condorcet... in short, almost any single-winner method.

Most of those multiwinner methods have unweighted winners. In EPR (as I 
understand it), each winner has a different weight in the assembly, and 
thus instead of discarding just a quota and then redistributing the 
surplus, it's possible to assign more than a quota to a single winner, 
who benefits from this "supermajority" by an increased weight.

To use SNTV as an example, suppose you have a Plurality election of the 
type:

A: 100
B: 80
C: 30
D: 20

and three to elect. If you use ordinary SNTV, then the voters who voted 
for A wasted their votes, since they voted in excess of what was 
required to have A win. However, with weighted voting, it's a simple 
matter of letting A have a weight of 47.6% of the total vote, B have a 
weight of 38.1% and so on.

Suppose e.g. that the A- and B-voters both had D as their second 
preference. Unweighted, the wasted votes for A and B deprived D of his 
victory, as in SNTV, some fractions of the A- and B-voters could have 
strategically voted for D instead to get him above C's count, and that's 
what a better method with surplus redistribution would have done anyway.

In a weighted method, the A and B-voters get compensated for C being 
elected, in the form of A and B having a greater share of power; and 
this is preferable from the point of view of A- and B-voters because 
they get to contribute directly to the power of their first choice 
candidates instead of having that power go to their second choice.

With all that said, there's another argument that could be made in favor 
of doing surplus redistribution, which is that under tactical 
nomination, you could get something analogous to surplus redistribution 
anyway. If the A-voters consider D to be close to A, then some of them 
could vote for D, after which the fixed council size would push C off. 
The benefit of reducing C's strength to zero could then make up for A's 
relative power being reduced in the council.

A stronger strategy would involve cloning A into A1 and A2 and, instead 
of redistributing votes to D, distributing them between A1 and A2. That 
produces a more party list-like outcome -- but that strategy would also 
be possible under an unweighted multiwinner system.