[EM] Fwd: Soliciting feedback for a modification of Allocated Score

[Ted Stern]

Sorry, forgot to Reply All to the list.

Also, there is a correction to my original message, italicized


---------- Forwarded message ---------
From: Ted Stern <dodecatheon at gmail.com>
Date: Fri, Apr 8, 2022 at 4:53 PM
Subject: Re: [EM] Soliciting feedback for a modification of Allocated Score
To: Richard, the VoteFair guy <electionmethods at votefair.org>


Hi Richard,

Please read the Allocated Score page to get an idea of the original method:

https://electowiki.org/wiki/Allocated_Score

There's also a page on the Method of Equal Shares:

https://electowiki.org/wiki/Method_of_Equal_Shares

(the same page is also on Wikipedia).

In the original AS method, the winner of each seat is the candidate with
highest weighted score sum.
Then the threshold score delta is found by finding the maximum score at and
above which a quota of weighted ballots support the seat winner, at ballots
with score >= delta are called delta-supporting ballots.

If the winner has support exceeding the quota, AS then deweights ballots
above delta *completely, *then reweights ballots at delta *proportionally *to
remove any quota left over.

In AS*, the proposed change is to remove a quota of support *subtractively*,
removing the same amount from delta-supporting-ballots to the extent
possible until a ballot is exhausted. To do this, AS* does everything that
AS does before reweighting, including finding the threshold score delta. If
the minimum weight on delta-supporting ballots exceeds the average price ==
quota / weighted-support, then quota/weighted-support is removed from all
delta-supporting ballots.

If some delta-supporting ballots would be exhausted at the average price,
the delta-supporting ballots are sorted in ascending order of weight, and
are successively exhausted until the remaining ballots can each pay the
same price for the remainder of the quota. This is the same budget-spending
step as in MES *for ranked ballots*, which, please note, is *not* the same
as how MES *for ranked ballots *chooses the seat winner.

That should explain what you wanted to know in your first question: When a
candidate is seated, top-quota supporting ballots all lose the same amount
of weight. But AS* distributes the pain equally across all ballots at and
above the threshold score, instead of deweighting ballots above the
threshold score completely.

Overall, a candidate will win when it has broad support among voters who
have not previously been represented with high preferences.

Compared to STV, AS* will always elect a consensus winner first, if there
is one, instead of the strongest candidate in a faction.

On Thu, Apr 7, 2022 at 3:01 PM Richard, the VoteFair guy <
electionmethods at votefair.org> wrote:

> On 4/6/2022 4:56 PM, Andy Dienes wrote:
>  > I've already looked at this proposed modification from many other
>  > perspectives so pathological examples are exactly what I'm
>  > after here :)
>
> How does your version of "surplus handling" handle a ballot on which,
> say, 3 candidates are ranked at the same ranking level, and the excess
> beyond the quota would give each of the fully supporting
> (non-shared-preference) ballots, say, 0.25 (one quarter) of a vote
> toward electing the next winner?
>
> Specifically:
>
> * How much of that shared-preference ballot's influence is lost by
> electing a candidate?  In other words, how much of that ballot's
> influence remains available for electing a second, and even third,
> candidate?
>
> * How are the two kinds of reduced influence interact? How is that
> calculated?
>
> I'm interested in your answer because the same concepts are relevant to
> any well-designed variation of the single transferable vote (STV).
>
> Thanks!
>
> Richard Fobes
> The VoteFair guy
>
>
> On 4/6/2022 4:56 PM, 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
> )
> > 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 :)
> >
> > Best,
> > Andy Dienes
> >
> >
> > ----
> > Election-Methods mailing list - see https://electorama.com/em for list
> info
> >
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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