[EM] PR-SODA? Try 2 (and 3)

[Jameson Quinn]

The intent is to make a proportional version of SODA, which preserves SODA's
principal advantages. These are, as I see them: (1) ballot simplicity, (2)
relative counting simplicity, (3) good results, and (4) acceptability from
the point of view of an existing plurality-winner politician.

The resulting system will not reduce to SODA in the single-winner case,
although it will come close. The tactical concerns in an "order of play"
system are too different between mulit- and single-winner. For instance,
single-winner has no free-rider strategy.

So here's the base system. As with SODA, ballots are approval-style, with
bullet votes counting as delegated to the candidate for further use. The
Droop quota is used and reweighting is "quota-style".

Unlike SODA, candidates pre-declare, not a delegation ranking, but an
approval-style ballot for delegation. One can imagine that many candidates
would simply approve all "nominated" members of their party.

The election proceeds by first electing candidates with a Droop quota and
re-assigning overvotes, from most "total votes" on down; then eliminating
candidates and transferring, from least "unique votes" up, electing any
candidates who attain a Droop quota during the transfers; and finally,
electing all un-eliminated candidates when there are only enough to fill the
remaining seats. The pseudocode is at the end of this message; and it's
simpler than it looks at first glance. Basically, it defines "total votes"
and "unique votes", and implements the procedure I just explained in one
(compound) sentence.

This system, I believe, satisfies my first three criteria for a good
PR-SODA. To make it satisfy the fourth — acceptability from the point of
view of an existing plurality-winner politician — I would simply redesign
the ballots by district. All candidates from the district where the ballot
is cast would be listed first, in large type; all candidates from the
closest two other districts (by some simple metric - it doesn't matter)
would be listed later, in smaller type; and all other candidates would be
available only as write-ins.

Why would this be acceptable to existing politicians? Well, if you assume
"no changes to voting patterns", and a state gerrymandered "fairly" such
that results are already two-party proportional, it would give the same
results as districted FPTP. That is, if all voters vote for one of two
"nominated" major-party candidates from their district, and all candidates
approve the one "nominated" candidate per district from their party, then
this system is just a proportional adjustment to FPTP.

It would be important, in this system, that both main parties and third
parties would allow "fusion" main-party candidates. If not, a fringe party
could "spoil" the election of too many sympathetic major-party candidates,
and thus counterproductively push the major party (although not the
legislature) away from their position. This is a matter of intraparty rules,
not election rules, but I think it could be worked out satisfactorily.

JQ

ps. Here's the pseudocode I promised:

subroutine recalculate totals:

for each candidate:

total votes T(C) <- sum(ballots approving candidate * ballot weight)
delegated votes D(C) <- sum(ballots delegating to candidate * ballot weight)
unique votes U(C) <- sum(ballots approving candidate * ballot weight /
number of uneliminated candidates approved on the ballot)

subroutine elect C and reweight ballots:

add C to elected candidates, remove C from uneliminated candidates, reduce
remaining seats by 1

for each ballot B which was delegated to C:

ballot now approves of all candidates approved by C
ballot weight W(B) <- W(B) * min(0, (D(C)-d)/D(C)) [that is, use up
delegated votes first]

for each ballot B approving but not delegating to C:

ballot weight W(B) <- W(B) * min(0, (T(C) - max(0, d-D(C)))/T(C)) [that is,
use up the remainder of the Droop quota which wasn't used up in delegated
votes]

subroutine eliminate C:

remove C from set of uneliminated candidates

 for each ballot B which was delegated to C:

 ballot now approves of all candidates approved by C



Main procedure:

Droop Quota d <- V / (N+1) [this is really the non-integer whatstheirname
quota, but whatever]
All ballots start with weight W(B) <- 1
uneliminated canidates <- all candidates
recalculate totals
while there are more uneliminated candidates than remaining seats:

while there are any candidates with T(C) > D:

elect candidate with highest T(C) and reweight ballots

recalculate totals

eliminate candidate with lowest U(C)

elect all uneliminated candidates
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