# [EM] Soliciting feedback for a modification of Allocated Score

Richard, the VoteFair guy electionmethods at votefair.org
Thu Apr 7 15:00:57 PDT 2022

```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
> 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
>
>
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>
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