[EM] Using Schulze Election Method to elect a flexible amount of winners

[Kristofer Munsterhjelm]

On 10/07/2016 06:29 AM, VoteFair wrote:
> On 10/5/2016 2:16 AM, Kristofer Munsterhjelm wrote:
>> On 10/03/2016 04:29 PM, Paul Smits wrote:
>>> ...
>>> Now the question arose how we could use the Schulze method in a decision
>>> where the amount of winners is also up for debate.
> ...
>> The way I'm reading this is that you're wondering how you might extend a
>> Condorcet method to a situation where you want "how many winners to
>> elect" to also be up to vote, and not just to a situation where you know
>> the number of winners to elect.
> 
> In my previous reply I focused on the importance of using a proportional
> method rather than a single-winner method, and I forgot about this part
> of the question.
> 
> The answer for this part depends on the answers to these questions:
> 
> * What is the range for the number of seats?
> 
> * Is the number voted on at the same time as the candidates are ranked?
>  Or are there two rounds of voting such that the voters know which
> candidates will get elected when they vote on increasing the number of
> winners?
> 
> As an extreme case, the transition from 1 to 2 seats likely would not
> get majority support -- because the majority chooses the first winner,
> who gets total control.
> 
> A similar but more complex effect can occur going from 2 to 3
> candidates, or going from 3 to 4 candidates.

That's a very good point, at least when using a proportional ranking
method. Thus, I'll revise my suggestion. If you're using a proportional
ranking method and a majority vote for each transition, you should
probably replace the majority vote with a consensus one, using something
like Jobst's random ballot fallback. A majority may want to be in
complete control, but presumably a consensus method would want a more
proportional assignment.

The main danger is that it would go too far in the other direction, and
you'd get an assembly more like what minimax approval would produce: one
where each faction, no matter how large or small, gets a representative
because each faction (no matter how large or small) can block consensus.

So perhaps the best option is the median voting plus STV-like proposal.
Suppose that we have a worst case scenario, where everybody knows how
everybody else voted, and the process is like this:

1. Everybody submits their ranked ballots (first round)
2. Everybody votes for assembly size, and the median wins.

Then if there's an LCR situation, the majority might be indifferent to
whether they want a one-seat or two-seat. On the one hand, with a
smaller assembly, the majority has greater control because there are
fewer people on the assembly. On the other, in an LCR, the power will be
diluted because the winner is pushed towards the center to compensate
for the loss of representation that the smaller assembly gives.

(In contrast, the house monotonicity restriction makes this balance less
effective for proportional ranking methods.)

The incentive to strategically choose the assembly size is still
present, however, for non-LCR situations. So perhaps it would be better
to ask for the optimal assembly size first? I'm not sure. The incentive
would be weaker the less the voters know about each other's votes.