[EM] PR with weighted rep. power

[Etjon Basha]

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?

Regards,



On Fri, 15 Nov 2024, 12:21 pm Kristofer Munsterhjelm, <
km-elmet at munsterhjelm.no> wrote:

> In a post in September, Toby Pereira said the following about the
> "Random Ballots" method I had implemented in quadelect:
>
> > This is very interesting. Thank you for doing this analysis. Random
> > ballots, as I understand your implementation, I think would not be
> > strategyproof. If there are c candidates to be elected, then every
> > voter ranks their top c. And then you sequentially pick c ballots at
> > random, electing the top-ranked unelected candidate on each ballot.
> > Is that correct? In that case, I think if a voter is fairly confident
> > that their favourite candidate will be elected anyway, it makes sense
> > for them to put other candidates above them that might not get
> > elected anyway. If my second favourite candidate is not very popular
> > among other voters, and my favourite is, I am likely to put my second
> > favourite top.
>
> And I responded that that too is interesting, because that looks like
> vote management (Hylland free riding), and I hadn't expected vote
> management to be that robust a strategic feature.
>
> But a few days ago I had a thought. Suppose we change the method to the
> following:
>
> - Pick c random ballots. For simplicity, disallow equal-rank.
> - Let each candidate's voting power be the fraction of these ballots on
> which he is the favorite.
> - Elect every candidate with positive voting power. (Note that there may
> be fewer than c distinct winners.)
> These candidates are the winners, and their votes have the given weight
> in the assembly.
>
> This turns the method into a sort of randomized party list. Is it
> strategyproof?
>
> The voting stage seems to be, at least, because in effect each candidate
> has an infinite number of clones, and if you prefer A to B, you would
> rather want to give an assembly seat to A (or a clone of A) than to B.
> Note that the number of seats need to be variable, otherwise there would
> be an incentive to vote for separate candidates to push opposition
> candidates out of the assembly.
>
> If there's an incentive to strategy for this method, it would be in how
> voter weights add up to majorities (power indices being nonlinear). But
> I'm not sure there's an incentive there either.
>
> So if it is strategyproof, we have a weighted variable seat method that
> is proportional without vote management/free riding; and we also have
> results that say that Droop proportionality is incompatible with
> complete immunity to free riding. The natural question then is: how
> close to DPC can we go and have immunity to free riding? Is it possible
> by just having a variable size assembly, or do we need some amount of
> weighted representative power too?
>
> I don't know what the answers would be, but they're interesting thoughts.
>
> -km
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