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

[Warren D Smith]

There is a flaw (perhaps merely aesthetic?) in the Simmons "data compression"
idea: discontinuity.

That is, suppose I am a voter.  I rate candidates X and Y high.
I gradually lower my X-rating
while gradually raising my Y-rating.  Kaboom! -- Suddenly,
when they cross, my ballot flies into the Y-bin instead of the X-bin.
This yields a discontinuous change in the "quality of the winner set" function
(if our voting method were based on such a function).

However, if this is considered a flaw, it is one that is easily repaired.
Split each ballot into C weighted copies in a C-candidate election (instead
of the simpler Simmons course of usually making all weights 0 except
for one that
is 1).   The weight for copy J is
    K / (E + (maxscore - score[J])^2)
where the constant K>0 is chosen to make all the C different weights sum to 1,
and the constant E>0 is arbitrary and Simmons' original approach arises in the
limit E --> 0+.

Or other formulas also may be used, of course.  You may prefer one
which becomes 0 when score[J]=0.  Anyhow, when anything of this ilk is done
the quality function becomes smooth and continuous everywhere, no
discontinuities.


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