The basic idea of PR methods is to create an assembly that represents
the voters. While voters don't neatly fall into categories, we can
measure the performance of the systems as if they did. In the end,
the only category that matters is who the voter trusts most to represent them.
So if there is an assembly with N seats, and V voters, and there are
V/N voters who prefer, out of all possibilities, a candidate, we can
define a Proportionality Criterion. That candidate must be elected if
the voters express this preference on the ballot.
Asset Voting satisfies this, so does Candidate Proxy. Both are simple
methods; Candidate Proxy (which has been used to refer to a method
where candidates state a preference order, before the election, and
this order is used with the counting system to apply to the voter's
ballot, it essentially substitutes for the voter's ballot. Asset
Voting is more flexible and could theoretically allow for a candidate
to be chosen who wasn't on the ballot and received no votes in the
election at all.
"Win" must be interpreted as "has the right to unconditionally
declare a person elected, which could be the candidate himself or
herself, or anyone else eligible for the office."
And then more detailed criteria could be defined, like the
Distributed Proportionality Criterion. If there is a set of M
candidates who received together a sum of V/N votes as
most-preferred, those candidates, by cooperating, could
unconditionally elect a winner. This, to my mind, satisfies the
intention of proportional representation even where no candidates, by
themselves, gain a quota.
To try to simulate this with a single-ballot method can get tricky,
but it could be done.
However, I'll suggest this simple method:
Bucklin ballot. For simplicity, I'm not going to allow multiple votes
in each rank, but it would be improved if multiple votes are allowed,
it simply complicates the counting and calculations.
First rank choices are counted. If any candidate gains a quota (for a
single-ballot method, it must be a Droop quota, not the Hare quota
that makes more sense with pure Asset Voting), that candidate is
elected. This is done for all candidates who are direclty elected
with a quota in the first round. The ballots with that candidate in
first preference position are segregated. By the condition, the total
vote count, T(C1), is at or over the quota. If only one seat were
elected with these votes, it would be disproportionate, the voters
would be underrepresented. So there must still be effective votes
left to be exercised of T(C1) - Q. So each ballot is devalued by the
ratio of (T(C1 - Q)) / T(C1). These ballots are then counted
separately to examine the next rank listed, and those votes are
multiplied by the devaluation factor and added in to the totals, and
this is repeated as needed until no more ranks are available. At each
point, the number of remaining votes to be distributed are V minus Q
times the number of candidates elected thus far. It may be easier to
understand than to describe!
If a ballot has a candidate in first position who is not elected,
when all candidates which can be elected as described are elected,
the ballot is opened to the next rank, and those votes are added in
(from all ballots except those that are completely exhausted -- which
is unlikely, for it to happen an candidate would have to be elected
by an exact quota of votes.)
While your second rank choice may "harm" your first rank choice, it
never actually reduces the chance of that candidate being elected
unless the candidate wasn't going to gain a quorum of votes. The
possibility that your ballot might elect your lower-ranked choice is
balanced by the fact that your favored candidate might be elected by
a lower-ranked choice of another. And because there are no
eliminations, except of elected candidates, the "harm" would only
occur at the very end of the process, and with one seat at stake,
and, yes, Virginia, if you want to be represented by the best
possible representative, you must be willing to make compromises.
Hopefully, they are not large ones.
If voters voted in blocks, and each block wanted their favorite to be
elected, and the block was Q in size or larger, all preferring the
same candidate, the candidate would be elected provided they vote
their sincere preference. As well, if a block places two candidates
at the top of their preference lists, and votes the preference, and
is 2 * Q in size, both candidates would be elected. If two blocks
exist, one voting A>B>all others, and one voting B>A>all others, and
the two blocks together are 2 * Q in size, then both A and B will be elected.
Has this method been described by anyone? If forget how Proportional
Approval Voting is run, but I'd guess it would look like this, with
just one Approval stage, i.e., as if all ballots in the Bucklin
system I described were collapsed at once.
I described a method that depended on ballot patterns, it's possible
to consider opening up the second rank simultaneously with all
ballots, in which case individual ballot data is no longer needed.
And I don't have time at the moment to review the details, so aspects
of this may be incorrect or incomplete.
If write-ins are allowed, or there are a very large number of
candidates and a lot of seats to be elected, there might be votes
that end up unused. Lewis Carroll suggested a solution, and it's
Asset Voting. Candidates get the leftover votes to recast at their
discretion. So a bunch of candidates with vote counts, as devalued,
at the end, less than a quota, could cooperate to name a seat. Asset
Voting was invented and published in 1884 as a tweak on STV, and STV
would be far more effective and far less dependent upon party
affiliations, had this tweak been noticed and adopted.
If no votes are wasted, and Asset makes wasted votes unlikely, with a
particular known individual being responsible for wasting *your*
vote, you can vote accordingly in the future, and if voters aren't
artificially constrained to listed candidates affiliated with
empowered parties, then parties must necessarily become less
important. They would still serve other functions, I'm sure. However,
this situation sets up a conflict of interest between political
parties and those vested within them, and the voters themselves, so I
wouldn't hold my breathe for political parties to rush to support
something like this. It is pure voter benefit, so it will probably
have to be the voters themselves to make it happen, which will
require direct voter organization for that purpose.
That is probably true for any truly major reform of the system. The
people who have accumulated power under the present system are not
likely to rush to support reforms that make their accumulated power
less relevant. They wouldn't lose their natural influence, but who
will stop to think like that? In fact, a party leader who did push
for and successfully implement an Asset system would probably thereby
be creating independent support, and would maintain effective power
or influence even without needing to please a party elite or needing
to satisfy wealthy donors.
But I'm not holding my breath.
I'm simply applying the organizational principles wherever and
whenever I have a chance. Others can imitate if they choose.
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