[EM] A New Multi-winner (PR) Method

[Forest Simmons]

One thing I forgot: as each ballot is added to a candidate's pile, it must
be scaled by the favorability of the ballot to that candidate. That reduces
the max total for each pile from ten thousand

[messages referred to]

> Today's Topics:
>
>    1. A New Multi-winner (PR) Method (Forest Simmons)
>    2. Re: A New Multi-winner (PR) Method (Abd ul-Rahman Lomax)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 10 Apr 2019 14:08:37 -0700
> From: Forest Simmons <fsimmons at pcc.edu>
> To: EM <election-methods at lists.electorama.com>
> Subject: [EM] A New Multi-winner (PR) Method
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> B8UrDg at mail.gmail.com>
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>
> As near as I know the following PR method based on Range/Score style
> ballots is new.
>
> This method is based on maximizing a measure of "goodness" of
> representation to be specified later.  Slates of candidates are nominated
> individually for consideration, because in general there are too many
> possible slates to consider every one of them (due to combinatorial
> explosion).  Among the nominated slates, the one with the best measure of
> "goodness" of PR is elected.
>
> To reduce the abstraction, suppose that there are only 100 candidates and
> that only five vacancies to be filled.   Suppose further, that there are
> ten thousand ballots (one for each of ten thousand voters).
>
> Given a subset S of five candidates, we decide how good it is as follows:
>
> Order the set S according to their Range totals, so that the highest to
> lowest score order is c1, c2, ...c5.  This order only comes into play to
> determine the cyclic order of play as the candidates "choose up teams" so
> to speak.
>
> Ballots are assigned to each of the candidates cyclically so that the
> ballot most favorable to c1 goes to c1's pile, of the remaining, the one
> most favorable to c2, goes to c2's pile, etc. like the way we used to
> choose teams when we were in grade school.
>
> (Eventually we'll get to how to automate judgment of favorability.  Be
> patient)
>
> After 2000 times around the circle, each pile will contain exactly 2000
> ballots. (Thanks for your patience.)
>
> For our purposes the relative favorability of ballot V for candidate C is
> the probability that V would elect C if it were drawn in a lottery; i.e.
> V's rating of C divided by the sum of all of V's ratings for the candidates
> in S including C.
>
> What happens when one of more of the candidates is not shown any
> favorability by any of the remaining ballots?  The other candidates
> continue augmenting their piles until they reach their quotas (two thousand
> each in this case), and the remaining ballots are assigned by comparing
> them to the official public ballots of the candidates whose piles are not
> yet complete. (We won't worry about the details of that for now.)
>
> For each candidate C in S add up all of the ratings over all of the ballots
> in the pile, but not the ratings for candidates outside of S.  Divide this
> number by the total possible, which in this case is two thousand times five
> or ten thousand.
>

Because of the scaling by favorability, the max possible total is only two
thousand, not ten thousand.

>
> We now have five quotients, one for each candidate.  Multiply these five
> numbers together and take the fifth root.  This geometric mean is the
> "goodness" score for the slate.
>
> Among the nominated slates, elect the "best" one, i.e. the one with the
> highest "goodness."
>
> It is easy to show that this method satisfies proportionality requirements.
> And (I believe) it takes into account "out-of pile" preferences as much as
> possible without destroying proportionality.
>
> No time for proofs or examples right now, but first, any questions about
> the method?
>
>
>
>
>
>
>
>
>
>
> ****
> >
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> Message: 2
> Date: Wed, 10 Apr 2019 18:30:26 -0400
> From: Abd ul-Rahman Lomax <abd at lomaxdesign.com>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] A New Multi-winner (PR) Method
> Message-ID: <be0d97ba-67e4-4982-f916-ba8208cf4b41 at lomaxdesign.com>
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
> I continue to be amazed that someone like Forest Simmons, who was an
> early writer about what later was called Asset Voting, as named by
> Warren Smith, and was simply a tweak on STV when invented by Charles
> Dodgson in the 1880s, which can produce *perfect* representation,
> beyond? mere "proportional representation," still works on complex
> single ballot deterministic methods that must compromise and prevent
> true /chosen/ representation in favor of some sort of theory of
> "optimised goodness."
>
> Asset Voting can very simply produce unanimous election of seats, where
> the seat represents a quota of voters who have */unanimously/*
> consented, directly or, probably much more commonly in large-scale
> elections, through chosen "electors," I call them, who becomes a proxy
> for the anonymous voters, for the election of the seat. Asset allows the
> electors --- those who become public voters -- to cooperate and
> collaborate for the selection of seats.
>
> The "Electoral College," fully and accurately, represents *all* the
> voters. But it might be very large, possibly too large to even meet
> directly. But all that is needed is a way for electors to communicate
> and to register their vote assignments for the creation of seats. They
> could use delegable proxy to advise them how to transfer.
>
> Asset was actually tried once, and it produced a result that most would
> have considered impossible. 17 voters, five candidates for a three-seat
> steering committee. A rather sharp division, but the final result was
> the election of the three seats *with every vote represented directly or
> by proxy*. Before the third seat was elected, nevertheless two seats
> were elected, so the steering committee, if needed, could have made any
> decision by unanimous vote (two agreeing) through the representation of
> two-thirds of the electorate. It could, in theory, have decided to elect
> the third seat by using the Droop quota. (the quota had not actually
> been specified, and the one who called the election and created the
> process was not totally sophisticated on Asset, which does not need to
> specify an election deadline, it can, instead, leave that last seat or
> seats open, and consider the rest of the electorate as Robert's rules
> considers unrecognizable ballots: they count for determining "majority"
> but not as a vote for or against any candidate.
>
> So, say, there is a jurisdiction with a million voters. It is decided
> that an optimal assembly would be 49, so the basis for a quota could be
> 50, and thus the quota would be 2% of the votes cast. This allows that
> if all electors assign their votes in exact measure to seats, 50 seats
> could be elected, but that outcome is improbable. (But if it happens,
> whoopee!), so, normally, 49 seats might be elected. Instead of electing
> the last seat by plurality, depending on some deadline for vote
> assignments, I have suggesting leaving the election open. Further, those
> electors could be consulted by the Assembly. This is the power of having
> public voters who, collectively, represent the entire electorate.
>
> Unanimous election of seats. Bayesian regret, zero. No losers. Minimal
> damage to the dregs. No expensive or extensive campaigning necessary. (I
> expect that the tradition would develop rapidly that one would only vote
> for people one could meet face-to-face, because how else can they truly
> represent? But this would be voluntary, not coerced. Basically, anyone
> who registers as an elector may participate further, the only
> requirement being a willingness to vote publicly (which is already
> required of elected representatives!)
>
> The U.S. Electoral College was a brilliant invention, knee-capped by the
> party system. It did not, however, represent the people, but
> jurisdictions, specifically states. It could have been reformed to
> represent the people, but it went, instead, toward representing the
> party majority in each state, in effect, becoming a rubber stamp and
> creating warped results.
>
> Asset is simple, close to tradition, but actually revolutionary, a
> dramatic shift from the entire concept of "elections" as contests. The
> voters would be 100% represented in the College, though voluntary
> choices, no need to consider "electability," hence no need for "voting
> strategy." Choose the available person, from a large universe, you most
> trust. As Dodgson noticed, that was relatively easy for ordinary voters,
> much easier than sensibly ranking many candidates. That complexity is
> completely unnecessary with Asset. No votes are wasted.
>
> The only tweak I see as needed involves making it difficult to coerce
> votes, by making it impossible to know that a specific person did *not*
> vote for one. This would not be needed for small NGO elections. In
> public elections, I'd have a set of known candidates who received
> substantial votes in a prior election, or something like that, and when
> electors register, they would assign their own vote to another
> candidate. If they receive less than N votes, their vote would be
> transferred as directed. If they receive N votes, they become an
> elector. Electors would not vote in the election, so, if they receive N
> votes, they get their own declared vote back and so they have N+1 votes
> to transfer. N should be the minimum size necessary to ensure that they
> cannot know that a specific person did not vote for them. If they do not
> receive N votes, their received votes are privately added to the total
> for the candidate they chose when registering. So N might be two, but if
> it is a bit higher, it could provide increased security. 3 might be
> completely adequate, together with it being very illegal to coerce votes.
>
> *No more original content below.*
>
> On 4/10/2019 5:08 PM, Forest Simmons wrote:
> > As near as I know the following PR method based on Range/Score style
> > ballots is new.
> >
> > This method is based on maximizing a measure of "goodness" of
> > representation to be specified later.? Slates of candidates are
> > nominated individually for consideration, because in general there are
> > too many possible slates to consider every one of them (due to
> > combinatorial explosion).? Among the nominated slates, the one with
> > the best measure of "goodness" of PR is elected.
> >
> > To reduce the abstraction, suppose that there are only 100 candidates
> > and that only five vacancies to be filled. Suppose further, that there
> > are? ten thousand ballots (one for each of ten thousand voters).
> >
> > Given a subset S of five candidates, we decide how good it is as follows:
> >
> > Order the set S according to their Range totals, so that the highest
> > to lowest score order is c1, c2, ...c5.? This order only comes into
> > play to determine the cyclic order of play as the candidates "choose
> > up teams" so to speak.
> >
> > Ballots are assigned to each of the candidates cyclically so that the
> > ballot most favorable to c1 goes to c1's pile, of the remaining the
> > one most favorable to c2, goes to c2's pile, etc. like the way we used
> > to choose teams when we were in grade school.
> >
> > (Eventually we'll get to how to automate judgment of favorability.? Be
> > patient)
> >
> > After 2000 times around the circle, each pile will contain exactly
> > 2000 ballots. (Thanks for your patience.)
> >
> > For our purposes the relative favorability of ballot V for candidate C
> > is the probability that V would elect C if it were drawn in a lottery;
> > i.e. V's rating of C divided by the sum of all of V's ratings for the
> > candidates in S including C.
> >
> > What happens when one of more of the candidates is not shown any
> > favorability by any of the remaining ballots?? The other candidates
> > continue augmenting their piles until they reach their quotas (two
> > thousand each in this case), and the remaining ballots are assigned by
> > comparing them to the official public ballots of the candidates whose
> > piles are not yet complete. (We won't worry about the details of that
> > for now.)
> >
> > For each candidate C in S add up all of the ratings over all of the
> > ballots in the pile, but not the ratings for candidates outside of S.?
> > Divide this number by the total possible, which in this case is two
> > thousand times five or ten thousand.
> >
> > We now have five quotients, one for each candidate. Multiply these
> > five numbers together and take the fifth root. This geometric mean is
> > the "goodness" score for the slate.
> >
> > Among the nominated slates, elect the "best" one, i.e. the one with
> > the highest "goodness."
> >
> > It is easy to show that this method satisfies proportionality
> > requirements. And (I believe) it takes into account "out-of pile"
> > preferences as much as possible without destroying proportionality.
> >
> > No time for proofs or examples right now, but first, any questions
> > about the method?
> >
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