[EM] Score Sorted Margins + Sequential Monroe Voting (python code)

[Ted Stern]

After a bit of thought, I modified ssmpr.py to use a different sort of
scaled reweighting.

first, let's define some terms:

S[r] = ballots giving the seat winner a score rating of r

v = the rating at which S[v] + S[v+1] + ... S[MAX] is greater than the quota

TS[v,mm] = S[v] * (mm - MAX + v) + ... + S[MAX] * mm        (a total of
MAX-v terms)

Then, if   MAX * quota is greater than TS[v,mm=MAX], we increment mm until
we find a new max rating for which

mm * quota < TS[v,mm]

Then the reweighting factors for ratings r >=v are

Factor[r] = 1 - (r + mm - MAX) * Quota / TS[v,mm]

This treats the scores a bit more like Borda ranking, automatically
rescaling the ballot in order to get proportional reweighting.

I don't have any mathematical justification for one reweighting method over
another, other than the sense that it "feels right" to reweight in some
proportion to the rating when you are using a rating ballot, and if you
fully deweight *all* ballots over the threshold rating, you create an
incentive for Hylland free riding.


On Fri, Jun 5, 2020 at 6:42 PM Rob Lanphier <robla at robla.net> wrote:

> Hi Ted,
>
> This looks really interesting.  I haven't (yet) followed the details
> of all of this, but I *may* dig into this at some point.
>
> BTW, you have a typo in the URL to the Github repo you cited (with
> ssmpr.py in it)  The correct URL:
> https://github.com/dodecatheon/approval-sorted-margins/
>
> At *some* point, I would love to build a language-agnostic test suite
> for election methods. I'm pretty comfortable with Python, but I also
> have dreams of reviving Electowidget in Lua and hosting it on
> electowiki.org (and I have many ideas I could keep writing about here
> but I'll try not to threadjack).
>
> Ted, I think there's an email that you sent a year or so ago that I
> *meant* to respond to.  My backlog of emails and wiki edits and forum
> postings that I want to make is pretty long.  I hope you get traction
> with ^that approval-sorted-margins project.  Like I said: interesting.
>
> Rob
>
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