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

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Oct 5 02:16:57 PDT 2016

On 10/03/2016 04:29 PM, Paul Smits wrote:
> Dear election enthusiasts,
> First of all I would like to congratulate you on the great wealth of
> works and ideas you brought into the world of voting/election methods.
> Even though it may be out of the scope of your focus, I have a
> consideration I would like to consult you on. If I came to the wrong
> place, let me know.
> In my organisation we are implementing the Schulze method to all
> situations where a single winner or sorted list of winners has to be
> chosen from more than two options. We basically did a straight
> implementation from the wikipedia pseudocode into our own online voting
> system.
> Now the question arose how we could use the Schulze method in a decision
> where the amount of winners is also up for debate. We used to make this
> decision by conducting an approval vote with a certain threshold for
> winners. I was not happy about this slightly arbitrary choice of
> threshold. Now some colleagues wish to again see some value by which the
> quantity of support for all the candidates can be understood.

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. If it's just an ordinary multiwinner
situation (you know the assembly will be, say, 12 seats), see below.

If your scenario can handle repeated balloting, I would suggest
something like this:

Produce a list by the Schulze proportional ranking

Then, starting with one winner, repeatedly hold a majority vote of
whether the assembly size should be increased to two seats, three seats,
etc. When the motion fails, the assembly size is set.

If you can't do repeated balloting, something like this should work:

On the ballot, have two questions. The first asks for the voter's
ranking of the candidates, and the second asks for how large an assembly
he wants to have.

Once you have the ballots, determine the median value of the second
question: this is the value where just as many voters want a larger
assembly as a smaller one, so in a sense there's a balance there.

Then use either a proportional ranking method (like the Schulze
proportional ranking) or an STV method (like Schulze STV) to elect that
many candidates.

The greatest problem with these proposals, I think, is that both Schulze
STV and the Schulze proportional ranking are very complex systems. You
might have a problem getting them accepted to begin with.

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