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

[Juho Laatu]

One interesting question is, if you want proportional representation, should you use the proportional ranking approach. The simplest example in maybe the following one.

40: A>B>C
10: B>A>C
10: B>C>A
40: C>B>A

B is the Condorcet winner, so it would be a good choice if we will elect one winner. But if we elect two winners, then electing A and C could be a good choice. B would not be elected although B was elected if the number of elected candidates was one lower.

One thus needs to decide if one wants to have an ordering of the candidates (e.g. if one picks them one by one without possibility to change the already elected candidates), or if one wants the proportionality to be accurate (in the way described above). One can not have both.

Juho


> On 05 Oct 2016, at 12:16, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
> 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
> (http://m-schulze.9mail.de/schulze2.pdf).
> 
> 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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