[EM] Voting Benchmark

[Marijn Stollenga]

Thanks for all the suggestions. I'll briefly describe my method to make 
my goal clear:

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.

My idea is to combine Quadratic Voting with ranking. The setup is this:
- 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.

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

On 01/10/15 22:14, Markus Schulze wrote:
> Hallo,
>
> > Thank you for the reply. So it seems pretty essential
> > to get these nice properties. I wonder if there are
> > other ways to get them, i.e. it's not proven to be
> > the only way to get these properties I guess?
>
> Well, you could calculate the Schwartz set and then
> eliminate all those candidates who are not in the
> Schwartz set and then apply the Schulze method with
> "pairwise opposition" to the remaining candidates.
> But this would violate monotonicity because it could
> happen that, by ranking the candidate A higher, some
> other candidate B, who was in the strongest path from
> candidate A to some other candidate C, is kicked out
> of the Schwartz set.
>
> You could use the Schulze method with "pairwise
> opposition" to calculate a complete ranking of all
> candidates and then declare the highest ranked
> candidate elected who is in the Schwartz set.
> This would satisfy monotonicity, but violate
> independence of Smith-dominated alternatives.
>
> Markus Schulze
>
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