[EM] A New Multi-winner (PR) Method

[Warren D Smith]

Hi Forest, this is in reaction to your new "card dealing" PR multiwinner
voting method.

> "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)."

--My belief is, either
(a) a computer can enumerate all binomial(C,W) possible W-winner subsets
of the C candidates, or
(b) too many for the computer.
In case (b), I have arguments that virtually any multiwinner method is
inherently ridiculously
ultra-vulnerable to strategy.  Suggesting none should be used in this regime.

> "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."

--this measure seems suspicious if there could be many cloned candidates.
If we had ballots of the form "you (the voter) have 100 points to distribute to
the candidates in any way you please" it would be less suspicious.  But then
voters would likely be strategically motivated to give one 100 & all others 0.

> 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.)

--sounds like a freaking major "detail" to me.  And if the candidates,
or the voters, produce
low-information ballots (such as plurality style voting) then seems
likely there will just not be enough information in there to allow any
intelligent way of deciding how to assign them.

> 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.
  Actually, because of the nature of the favorability factor by which
each ballot has already
been scaled, no ballot can contribute more than one unit...

--I am not seeing that.  Favorability is in [0,1].  Ratings are
nonnegative integers.
The product can be any nonnegative rational, not upperbounded by 1.

> 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.
  Among the nominated slates, elect the "best" one, i.e. the one with the
highest "goodness."

--you could have omitted taking the 5th root, and just used the product as
the goodness.  And also, you could have avoided multiplying things,
and instead summed the logs of things, and just used that sum-of-logs
as the goodness.
These are equivalent restatements.  As I daresay you already knew.

> I believe it takes into account "out-of pile" preferences as much as
possible without destroying proportionality.

--that sounds like it could be the beginning of some interesting train
of thought.
But I don't know what it is.

> any questions about the method?

--I have not figured out what it is.  Pseudocode might help.




-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
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