*Post by Marijn Stollenga*Thanks for all the suggestions. I'll briefly describe my method to make

I want to avoid aggregating all votes in a tally, because I think that

loses information. Specifically, I would like a method that can find a

representative ranking. I.e. if I want the top 10 songs, it should

reflect the preferences of everyone, but not only contain electronic

music because a majority likes that.

When I you do the simple Schulze ranking (not STV) I find it

over-represents certain groups because they essentially can vote more

than once.

I think once their preference is (partially) included their voting

strength should lessen, but with a tally their vote can not be removed

(reduced) since it's all agglomerated.

Schulze, like other single-winner Condorcet methods, is intended for

determining a best single choice given the preferences of the

electorate. This means that if a majority all place the candidates in a

particular preference order, then that order will show up as the social

order. Clearly, that's not a good outcome if you want proportional

representation.

For that, you could use STV or Schulze STV. Or, if you have continuous

ratings (like it seems you have), I would suggest Monroe's method:

- Let each ballot be fractionally or fully assignable to a candidate.

When the ballot is assigned to a candidate, that candidate gets a number

of points equal to his rating on the ballot.

- Let the system assign ballots to candidates so that the sum of scores

is maximized, subject to that each candidate either gets zero ballots or

v/s ballots, where v is the number of voters and s is the number of seats.

For small elections, this can be solved by integer programming. For

larger elections, approximations exist: see

http://arxiv.org/pdf/1301.6400.pdf for example.

I would prefer no quadratic constraint, but it should be relatively easy

to fit it to Monroe if you want it. When the voter submits his (rated)

ballot, just check that the sum of the squares of the ratings is less

than or equal to his budget.

Of course, that suggests a DSV approach where the system rescales the

ratings so that the voters don't waste budget points on candidates they

can't get elected anyway. Doing that might be trickier; you could

probably make a quadratically constrained programming version of

Monroe's method to handle it, but finding a PTAS for that is... well,

harder.

*Post by Marijn Stollenga*- Everyone has a voting budget of 1.0

- They spread their budget over their preferences: So if you have A > B

C you spread your budget over three preferences A > B, B > C and A >

C. With quadratic voting this means spending .333 on each preference,

each gets a voting strength of sqrt(.333)

- All votes are averaged.

- Everyone has a policy, which is to have an equal avg. voting strength

for their preference, and taking the resulting average into account,

they adjust their votes (using a simple gradient step).

- This is repeated until convergence.

The result is a preference matrix, which has to be turned into a

ranking. I think this is possible by eliminating the weakest preference,

and re-vote and rebalance, until a ranking is obtained. But it is not

clear that this works, it could result in a broken graph, so I'm not

sure about what to do there.

What do the numbers in the matrix denote?

*Post by Marijn Stollenga*The advantage would be that no structure is lost by tallying. It also

avoids the problem of Quadratic Voting where it assumes people have an

adequate estimate of what others will vote (unrealistic in my opinion),

instead the policy is enacted by the algorithm and the user just

presents a ranking.

I'm not sure if the 'averaging policy' is the best approach, maybe there

are other policies that are more fair. Also, instead of voting on

preferences, the votes can be done directly on candidates, but it is

unclear to me how to take ranking preferences into account there.

Any thoughts?

Marijn Stollenga

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