[EM] PR with weighted rep. power

[Kristofer Munsterhjelm]

On 2024-11-15 03:24, Etjon Basha wrote:
> I will ask a potentially very silly question and I own up to this: in 
> which way would this setup be superior to allocating singe-seat 
> districts with separate candidate pools and electing a random winner 
> from each? Is it the issue of variable voter participation?

Strategyproof methods usually aren't good in practice; in my case I'm 
just using it to show you can have some kind of proportionality and not 
be susceptible to free riding, even though Droop proportionality implies 
some vulnerability to free riding.

Your method is probably superior in the sense that there's no need for 
weighted representative power and it's still strategyproof. But it 
relies on candidates not being able to run in multiple districts, which 
means part of the problem has already been solved (compared to a 
multiwinner PR method).

In a multiwinner PR method, a candidate A might have near-unanimous 
support, and this could lead to free riding problems because some of A's 
supporters would be better off ranking some other candidate first. But 
in a single-member district system, A can only be elected in one of the 
districts; in a sense, the free-riding problem is solved by that only 
one district can vote for A.

If each district has a clone of A, then SMD random ballot and my system 
produces pretty much the same result, except SMD random ballot embodies 
A's voting weight in how many of his clones are elected.

Your idea could be used to make (also strategyproof) generalizations of 
random pair, though. Say there are n seats and at least 2n candidates. 
Establish a random order of these candidates. Pick 1/n of the ballots at 
random, and elect the candidate of the first two that they prefer to the 
other. Throw the ballots away and repeat for the next 1/n fraction of 
ballots (and next two candidates in the established order). But, like 
random pair, this fails Pareto.

-km