[EM] Soliciting feedback for a modification of Allocated Score
Andy Dienes
andydienes at gmail.com
Tue Apr 12 08:28:57 PDT 2022
Hi Kristofer,
> You'll get quota proportionality anyway, as long as you reweight
everybody who contributes to getting a candidate elected, in such a way
that their total weight afterwards is equal to the surplus.
As long as voters vote along party-lists, this is true, and most such
"quota spending" methods degenerate to Hamilton. However for an arbitrary
approval profile only Proportional Justified Representation (PJR) is
guaranteed. PJR is quite weak and there are often many committees
satisfying it for a given ballot set, and some of these committees are
substantially less fair / quality than others. I have found theoretically
and empirically that the way the support is spent can matter a lot in terms
of outcome quality.
I agree that the modification of AS might reduce free-riding hopefully!
Although I find it somewhat hard to analyze strategic incentives generally
when not isolated to single examples.
> which maximally delays the decision of just what ballot weights to
attenuate.
Looks quite interesting, and related to the Maximin Support method
[1609.05370] which I already have implemented, so I can compare when I get
some more time in a few weeks. I would be worried that this is not always
resolute, in that if many voters truncate their ballots not every candidate
can achieve a quota. Maybe it can be rephrased to be more immediately
similar to Maximin Support, this could be done just by changing the
objective to
maximize (over support distributions): minimum_{1 <= j <= n+1}: sum
over all voters v: support[v][j]
On Tue, Apr 12, 2022 at 4:30 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:
> On 07.04.2022 01:56, Andy Dienes wrote:
> > Hi all,
> >
> > I have recently come up with a small change to the way surplus handling
> > is performed on Allocated Score (AS). It is inspired by the way MES
> > (which you can read about
> > here
> https://proceedings.neurips.cc/paper/2021/hash/69f8ea31de0c00502b2ae571fbab1f95-Abstract.html
> > <
> https://proceedings.neurips.cc/paper/2021/hash/69f8ea31de0c00502b2ae571fbab1f95-Abstract.html
> >)
> > operates on ranked ballots, which is also related to the Expanding
> > Approvals rule by Aziz.
> >
> > Basically, the way it works in the reweighting step of AS is:
> > Set a threshold d such that the total ballot weight of voters who scored
> > the candidate >= d is at least one quota (using Hare for now, but other
> > choices are fine). Then, find the minimal amount of voting power that
> > can be subtracted equally from each ballot such that the total amount
> > taken is exactly one quota. Note that some ballots may have less than
> > this amount remaining, so they will be fully exhausted.
> >
> > It is very similar to the original surplus handling, but rather than
> > exhausting fully all ballots with score > d and then fractionally
> > ballots with score = d, it chooses to subtract an equal amount of power
> > from all ballots above the threshold.
> >
> > When all scores are 0,1 (i.e. approval ballots) it does not satisfy EJR
> > (in the same way that AS doesn't), but it does satisfy PJR.
> >
> > I have already done some simulations and found favorable results, so
> > what I am mostly looking for is if there are any sneaky ways this can go
> > very wrong? Of course, every voting method has pathological examples so
> > it's never good to put too much stock in specific bad scenarios, but
> > I've already looked at this proposed modification from many other
> > perspectives so pathological examples are exactly what I'm after here :)
>
> I don't think there should be a problem as long as you make sure to
> never elect more than one candidate in one go. E.g. if both A and B are
> above the quota, apply the tiebreaker of your choice (say it picks A),
> then elect A, deweight the voters, and *then* check if there's a quota
> for B. Otherwise a majority might get too many candidates elected.
>
> Your change might also reduce free-riding. Let's say my honest vote is
> A: 5, B: 4. I know some other voters are also voting A:5, so it's
> tempting for me to vote A: 4 instead so that my voting weight is only
> exhausted fractionally. With the original reweighting (as you describe
> it), I may get exhausted fully with A: 5 but only partially with A: 4.
> But with your change, I would get exhausted equally.
>
> In general, as long as you reasonably fairly reweight the votes, then
> just how you distribute the surpluses shouldn't matter much. You'll get
> quota proportionality anyway, as long as you reweight everybody who
> contributes to getting a candidate elected, in such a way that their
> total weight afterwards is equal to the surplus.
>
> For instance, I constructed a more strategy resistant variant of EAR,
> https://electowiki.org/wiki/Maximum_Constrained_Approval_Bucklin, which
> maximally delays the decision of just what ballot weights to attenuate.
> So although it's very hard to reason about just whose votes will count
> less, it still passes Droop proportionality, because it does the
> reweighting as soon as a candidate is backed by a quota.
>
> -km
>
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