[EM] Simmons' brilliantly simple "data compression" idea for large multiwinner elections

[Warren D Smith]

I think this whole "data compression" idea by Forest Simmons for
multiwinner elections is brilliantly simple.

The obvious first worry about Forest Simmons' idea is that averaging
too-large sets of ballots
as step 1, destroys all hope for proportional representation voting.

E.g. imagine we averaged ALL the ballots as step 1, then we'd only
have one amalgamated ballot, and from it we clearly would be unable to
elect a PR parliament.

But Simmons is being smarter about it, he is reducing everything down
to C amalgamated ballots, if C is the number of candidates -- not one.
I.e. he amalgamates all
the ballots that score X highest, for each candidate X.

And that actually seems acceptable, in the sense that with 100%
"racist" voters in
a situation with "colored" voters and candidates,
you would not lose any information in this way!
Thus, you could still do proportional representation in "racist"
situations, which
by some reckonings is all you need -- i.e. if the definition of PR is "yields
color-proportionality in racist situations."

However, there would be a problem if we sort of had "2-level racism."
E.g. suppose every voter had both a "color" and a "secondary color."
Ditto for candidates.  Voters give candidates score 7 if agree on
color, and bonus score
3 if  agree on secondary color.

In that kind of situation, Simmons' "data compression" method would lose
information and presumably lose the ability to deliver (the more
clever sort of) PR
that it ought to.

Also, Toby Pereira and (at his urging) me too, like to think about
elections in which there are 2 kinds of candidates -- colored and
uncolored -- and voters
give same-color candidates score 10, other-color candidates score 0,
and uncolored candidates get a score that depends only on the candidate not
on the voter.  But it seems to me Simmons' data compression technique
already is lossless for these elections.

And it seems to me we can devise other "data compression methods"
which do not lose information in the Color+SecondaryColor scenarios.
For example we could amalgamate all ballots which both score X highest,
and score Y highest among candidates getting a lower score than X;
put all those ballots into bin(X,Y), then amalgamate all ballots
within any one bin.
This results in at most (C-1)*C ballots after compression -- and at most
(C-1)*C^2 approval-style ballots after both the compression
and a Pereira transform -- in a C-candidate election.

The other brilliant thing about Simmonsesque data compression is,
this permits multiwinner PR elections to be "counted in precincts."

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)