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<p>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 <i>chosen</i> representation in favor
of some sort of theory of "optimised goodness."</p>
<p>Asset Voting can very simply produce unanimous election of seats,
where the seat represents a quota of voters who have <b><i>unanimously</i></b>
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.</p>
<p>The "Electoral College," fully and accurately, represents <b>all</b>
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.<br>
</p>
<p>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 <b>with every
vote represented directly or by proxy</b>. 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.</p>
<p>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.</p>
<p>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!)<br>
</p>
<p>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.<br>
</p>
<p>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.<br>
</p>
<p>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.</p>
<p><b>No more original content below.</b><br>
</p>
<div class="moz-cite-prefix">On 4/10/2019 5:08 PM, Forest Simmons
wrote:<br>
</div>
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<div>As near as I know the following PR method based on
Range/Score style ballots is new.<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>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).<br>
<br>
</div>
<div>Given a subset S of five candidates, we decide how good it
is as follows:<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>(Eventually we'll get to how to automate judgment of
favorability. Be patient)<br>
</div>
<div><br>
</div>
<div>After 2000 times around the circle, each pile will contain
exactly 2000 ballots. (Thanks for your patience.)<br>
<br>
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.<br>
</div>
<div><br>
</div>
<div>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.)<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>Among the nominated slates, elect the "best" one, i.e. the
one with the highest "goodness."<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>No time for proofs or examples right now, but first, any
questions about the method?<br>
</div>
<br>
</div>
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