MMP can be quite clunky with its two different ways of electing representatives. There was a discussion of MMP that allowed independent candidates to stand properly, and I even did a video on it.
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RE: Some political groups within Slovenia are pushing for MMP with runoff election

RE: Best cardinal PR method(s)?
There's also a discussion of different PR philosophies on the wiki. It doesn't really cover all the ground though, as COWPEA or COWPEA Lottery wouldn't be included, for example. But perhaps nondeterministic methods deserve their own entry on there.
Optimised PAV Lottery is another nondeterministic method. In this you work out the optimum amount of weight each candidate should have (by e.g. infinitely cloning all candidates and running an election with a very large number of seats), and then elect candidates probabilistically according to these weights. (Though you would have to work out the distribution again every time a candidate is elected). Unlike deterministic PAV, it is thought (though not known) to be proportional by passing the Perfect Representation In the Limit criterion.
I also think that sequential methods generally fail participation (for a suitable multiwinner definition), whereas optimal electallatonce methods are computationally infeasible. However, I think nondeterministic sequential methods can get around this failure. Optimised PAV Lottery is computationally infeasible anyway, but COWPEA Lottery is easily runnable.

RE: Good simple semiPR methods?
@matija Is Sequential Ebert simpler to administrate than SPAV? It's also nonmonotonic though, which could be seen as a problem.

RE: Voting by Compendium
@cfrank, I don't know how to calculate a probability distribution over a collection of rankings. Maybe someone who knows statistics can understand your proposal and maybe critique it.
In regard to "tragedy", I judge that too broad a word, as it includes accidents, and "past", not fully accurate, because, among other reasons, Mr. Biden is killing children by the minute with US resources.
I ask you to join me in mourning the death of Layan Mohammed Sayed AlAker, who was two years old, a girl.
I ask you to join me in spending a minute and a few tears on Samir Mahmoud Hassan Abu AlHawa, who was a man, aged 62.
I received the suggestion to "hold space" from an organization, the "US Campaign for Palestinian Rights". Is this organization a grift? Yes, to an extent, they probably are, as indicated by the fact that they have an "executive director", which usually means a person drawing pay out of donations. Nevertheless, I judge the message of this organization more honest than the official story, which "happy Thanksgiving" ties into. This organization suggests for thingstaking day, among other practices (which I admit to not having followed):
When you gather with your loved ones, hold space for mourning the mass killing of Indigenous people from Turtle Island to Palestine. Hold a mourning ritual based in your community’s traditions. You may read the names and stories of our beloved people killed by colonial violence (for example, see here).
So I'm endorsing this organization's request, the one that I repeated above, in the context of your having wished me a happy Thanksgiving at this fraught time.

RE: Voting by Compendium
@jackwaugh the position measure would essentially be determined by the probability distribution over the basis rankings, so it would be a discriminant measure between distributions.
I agree the past is full of tragedy, and every day of the year could easily commemorate some horrible thing. Some of them are excuses to take off work and see friends and family for a potluck

RE: Voting by Compendium
Ballot sets could be normalized to have a sum of coefficients of +1, and a metric can be defined over this space in many ways, including a simple Euclidean distance, or a Wasserstein distance.
To what arguments will you apply the distance measure?
And as for the day of the year, please join me in mourning for Indigenous victims of genocide as well as those in Palestine. Now someone will say I went off topic and should have to apologize or get kicked out, but I did not initiate the foray into the meaning of the day. And someone who promotes a political or social position can expect a response from adherents of the other side, or multiple other sides.

RE: Voting by Compendium
@jackwaugh in the space I’m considering above as an example, a ballot set like
10abc+7bcd+2acd
is just a representation for
10: a>b>c>d
7: b>c>d>a
2: a>c>d>bso no information is thrown away. The letters are candidates and the product terms like “abc” and “acd” represent rankings of candidates, so the “product” here between candidates to produce rankings is not commutative.
You can also represent score ballot sets as polynomials. For example,
5 a^5 b^4 c^1 + 2 a^1 b^5
could represent a score ballot set of
5: a[5] b[4] c[1] d[0]
2: a[1] b[5] c[0] d[0]and the product could be commutative.
And happy Thanksgiving!

RE: Leastsquares  Is This Just A Complicated Restatement Of Score Voting?
@jackwaugh I don't think this would work for PR, not in its current guise anyway. It wouldn't be proportional for party voting. If everyone scored 0 to candidates of their favourite party and 1 to everyone else, then a voter's pain for each candidate is just 0 or 1. The most popular party would win all the seats.

Leastsquares  Is This Just A Complicated Restatement Of Score Voting?
Let each voter submit a Scorestyle ballot. Assume normalization from 1 to 0. Then define the square of a score as the pain that voter will experience should that candidate be elected. For each candidate, calculate the sum over the pains experienced by the voters should that candidate win. Elect the least painful candidate.
Yes, this is just Score with the elements of the range being expressed in a strange notation. But maybe an extension of a leastsquares idea to the multiwinner context can get you multiwinnercognoscenti (among whom I don't include myself) somewhere interesting.