[EM] A possible solution to SNTV vote-splitting

[Kristofer Munsterhjelm]

Raph Frank wrote:
> On Mon, Feb 8, 2010 at 3:23 PM, Kristofer Munsterhjelm
> <km-elmet at broadpark.no> wrote:
>> So why not have the method devise its own strategy?
> 
> This is what PR-STV was designed to do.
> 
>> The trick, of course, is to have the strategy transformation preserve
>> monotonicity.
> 
> Well, that is an an issue with PR-STV, but abusing the
> non-monotonicity is hard without accurate polls and comes with risks.
> 
> Vote management is an example of it in operation.

I don't think vote management is an example of nonmonotonicity; rather, 
it's an observation that PR methods "punish" you if you get what you 
voted for (so it won't have a majoritarian result), therefore, it's a 
good strategy to only vote for someone if you make a difference by doing 
so. Upranking X doesn't hurt X, but if X wins, it hurts others you prefer.

>> The mechanics of the method is then: for every elimination that has a
>> positive improvement score, check if those that would benefit could, by
>> acting alone, change the old outcome into the new outcome. The point of that
>> check is to prevent the effective withdrawal of a winner just because some
>> very small minority would benefit. Among those where the voters that would
>> benefit could pull it off by themselves, pick the one with the greatest
>> improvement score, then restart. Continue until there is no move that can
>> improve the outcome.
> 
> I really doubt that this method is monotonic and it seems dependent on
> initial seed council arrangement.

I'll try to experiment with it, see if I can find nonmonotonicity, but 
the gradient of SNTV (that it only has vote-splitting problems, not 
teaming problems) seem to suggest, at least at first glance, that it 
shouldn't be that nonmonotonic. However, my point is to find a PR method 
that is monotone (period), so almost won't cut it. Again, we'll see...

> It is similar to CPO-STV in that it searches for a condorcet-like
> winner at the council level, rather than at the individual candidate
> level.
> 
> Presumably, you start with the standard SNTV result and proceed?
> 
> So, anyway, the method is something like:
> 
> 1) Each voter submits a range ballot.
Each voter submits a continuous cumulative ballot. These are like range 
ballots, only the sum is fixed. It can be done at the "back end" by 
rescaling range ballots so the sum of the points given is fixed.

> 2) This is used to determine the initial council somehow.
Count up the points allocated to each candidate and run Sainte-Lague. If 
some candidate gets more than one "seat", redistribute according to my 
other post (but I'm ignoring that case for now - more important is to 
find out whether this is monotone before trying to integrate it with the 
nonlinearity of my redistribution idea).

The idea here is that in the limit of many seats, the method becomes 
Webster party list PR, which we know is PR; and that when no candidate 
has an excess of votes, it's simple SNTV, which is also PR (under 
strategy, hence "devise its own strategy").

> 3) When comparing 2 councils, the (sum) range votes are used.
For all possible coalitions (sets of candidates) that are not in the 
current council: determine if some group of voters would benefit by 
rating the candidates of this coalition as zero. If they do, then alter 
their votes so that they do rate these candidates as zero, and start 
from the beginning. The outcome is stable when there's no such 
coalition. If there's more than one such coalition in a single round, 
pick the one that provides the best benefit.

Here, the reasoning is that since SNTV's problem is vote-splitting, 
strategists would try to get greater proportionality by zero-rating 
candidates "on their side" that can't win anyway (i.e. not in the 
current council).
In the classical "one conservative versus two liberals", the liberal 
voters (where the two liberal candidates are splitting the vote) would 
strategize to not vote for one of them (presumably the one they consider 
weaker).

> 3b) If enough voters agree to force the change, then that becomes a
> valid change.
If the voters who would benefit from excluding (zero-rating) some 
candidates can change the outcome (council) to their benefit by 
unilaterally doing so, then they do so and the process restarts, yes.

> 4) Make the valid change to the council that has the highest sum of range scores
> 
> However, what condition 3b means is that there must be near unity
> agreement to make a change.
> 
> If there are N seats, then you need N/(N+1) of the votes in order to
> guarantee that the new council will be elected.
Hm, not necessarily, I think. Say you have something similar to:

10: A1 A2 A3 ... A10 >> B1 B2 B3 ... B20
10: B1 B2 B3 ... B20 >> A1 A2 A3 ... A10

Where >> means those above are rated highly, those below low. The B 
voters are spreading their power too thin, and so there will be a lot 
more A-candidates on the council; but the B-voters can decide 
(unilaterally) to zero-rate all B-candidates but B1...Bn (where there 
are n*2 seats). Then the A-voters do the same (exclude all A but 
A1...An), and the outcome is stable, because at that point, neither the 
A-voters nor the B-voters can improve the outcome.

The improvement score is considered on the basis of the new council, not 
of the candidates eliminated. Say there are 2 seats and you have

10: A1 (9.1) A2 (9) >> B1 (1) B2 (1) B3 (1) B4 (0.9)
10: B1 (5.1) B2 (5) B3 (5) B4 (5) >> A1 (1) A2 (0.9)

The council will be {A1, A2}. By eliminating B3 and B4, the latter 
faction can get the council to become {A1, B1}, which they prefer (since 
they value {A1, A2} 2 points each, and {A1, B1} 7 points each). Hence 
they do so.

You would be right if the council changes completely, but in the example 
above, A1 remains; only one seat changes hands.

(Hm, it might be beneficial to some factions to exclude candidates that 
are already on the council... although here, the B-voters can't get more 
B candidates on the council by zero-rating the A-candidates.)

> It is unclear if it is a PR method.  However, as long as the initial
> council is PR, then I think it would be OK.  A Droop quota of voters
> can guarantee their candidates gets a seat on the initial council and
> can then block any other changes.

Being based on Sainte-Lague, the method might not be PR in the Droop 
quota sense, since divisor type party list PR may fail quota (though 
such occurrences are rare).

> CPO-STV says that if your first choice has a seat, then you can't vote
> for any of the other seats (subject to surplus transfers)

Ordinary STV doesn't go beyond first choices, either, which I think 
amplifies its chaos.