[EM] New simple kind of party-based proportionality, avoiding deweighting, and using range-style ballots

[Jameson Quinn]

I like the concept. However, it is especially subject to Range Voting's
greatest flaw - that a coherent group of strategic voters beats a coherent
group of unstrategic voters. In normal Range, this flaw is by-candidate, and
so can really be said to be the voters' choice (if I choose to be
unstrategic on a given candidate, instead of ranking them approval-style, I
could be simply saying that I do not care enough to do so; that's my right).
However, consider the following honest preferences:
Candidates
Party A: Alice and Al; party B, Berenice

Voters:
5 A voters: Alice 100, Al 40, Berenice 0
2 independent voters: Alice 0, Al 100, Berenice 90
3 B voters: Alice 0, Al 10, Berenice 100

Totals: Alice 500, Al 430, Berenice 480. Party averages: A 465, B 480.
Winners, Al and Berenice

So the independent voters would be best-served by dishonestly ranking Alice
above Berenice, so as to give party A an extra slot and elect Al. In other
words, you're forcing the straitjacket of party loyalty onto them.

I understand that the situation is somewhat contrived. But the strategy is
generally applicable: if all you care about is getting a certain candidate
elected, you should rank all co-party-members at max, even if you hate them.

The response from the candidate selection point of view is simple: one
candidate per "party". That way, a solid, strategic 51% coalition can elect
their whole slate. I guess you'd call this failing the "party-clone-proof"
criterion - instead of cloning the candidates, you clone the parties.

I do like the simple, polynomial check, and the summability. I think,
though, you need two-way correlations. For instance, you could have a matrix
M(m,n); for m=n this would be the average score, and for m<>n it would be
the average (by ballot) of (score m*score n). Choose best candidate w (that
is, M(w,w) is higher than next-place M(l,l)). Adjust the matrix as follows:

M(k,k) := M(k,k)-M(k,w)/M(l,l)   (use M(l,l) instead of M(w,w) to not punish
overvotes - it's w's minimum winning score)

for j<>k: M(j,k) := M(j,k)-M(j,w)*M(k,w)/(M(l,l)^2)

I think that this works out as a pretty standard elect-and-punish scheme;
or, to put it another way, ballots "still count" in proportion to the amount
they are "still unrepresented".

OK, I don't have time to go over all the math, and there's still issues - if
the ratio of adjusted average scores between the winner and the second-place
is different between rounds, the "not punishing overvotes" will give
supporters of different already-elected candidates different deweightings in
later rounds. But hopefully, you get what I'm trying for here. Once you have
the matrix, choosing the winners is polynomial time in number of candidates
(almost linear, but you have to find the new best candidate each step.)

It's certainly less clean than your suggestion, though.

Jameson

2009/10/9 Warren Smith <warren.wds at gmail.com>

> As input, every voter submits a rating-type (range-voting-style) ballot
> scoring
> all N candidates on some fixed allowed-score-interval say [0, 999].
> (It will be important that the min score be 0.)
> Also, each candidate has a publicly-known party affiliation.
>
> The goal is to produce W "winners" (0<W<N) in a "proportional
> representation" manner.
>
> Compute the average rating for each candidate, which (via sorting)
> yields an ordering of all candidates. Scan through it from top to
> bottom, declaring each candidate a "winner" or "not" as you go; a
> candidate is a winner unless prevented from being so by a
> proportionality condition (in view of the previously-declared
> winners).
>
> Note that this is fast (low order polynomial time)
> and simple.  And "precinct summable" too.
> Also note that there is no ballot "deweighting" going on.  Every
> ballot is used with
> "full weight."
>
> The problem is the proportionality condition -- what should it be?  If
> we know party affiliations this is no problem:  each party is granted
> a share of the number of seats.
> You can't get (much) more than your share (that's our definition of
> "violation of proportionality").
>
> Party X's share could be proportional to score for a party-X candidate
> summed over all voters, and averaged over all candidates in X.  This
> definition has the property that if voters score their party's
> candidates max and all other parties min, then party X's share will be
> proportional to the voter-population that wants party X.
>
> Parties will have incentive to run their best candidates and ONLY their
> best
> (since otherwise their avg score and hence share decreases), but not so few
> they
> cannot win all the seats they will deserve.  That ought to control ballot
> bloat.
> There are senses in which the method is "cloneproof" and "monotonic."
>
> Voters who wish not to provide a score for some candidate (e.g. they
> feel ignorant about him) can do so, and then only his genuine scores
> affect his average (and ditto for the party-wide average).   There
> could be a fixed initial number of artificial all-0 votes to
> bias averages a little toward 0 (or all-K to bas toward K).
>
> I dislike all methods (including this) that use party-affiliations as
> input, but aside
> from that it looks good to me
> (pending all the criticisms and comments that may soon arrive :)
>
> --
> Warren D. Smith
> http://RangeVoting.org  <-- add your endorsement (by clicking
> "endorse" as 1st step)
> and
> math.temple.edu/~wds/homepage/works.html
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
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