[EM] Simulation results (Approval, utility, Schulze efficiency)

[Kevin Venzke]

Jan,

Thanks for responding.

 --- Jan Kok <kok at surfbest.net> a écrit : 
> > (Description of it:)
> > 1. It generates randomly-sized factions, and their sincere utilities for
> every candidate.
> 
> It sounds like you assume that all voters in a faction vote identically.  I
> would suggest that you generate 1000 individual voters and a few candidates,
> assign them random positions (Gaussian distribution?) in a multidimensional
> issue space, and then determine how each voter would vote.

I do assume that.  I could certainly run simulations with more than five factions,
but I don't see why factions make less sense than individual voters.

Also, I'm hesitant to use issue space, with distance as a measure of utility,
1. because I'd have to make some assumptions just to get there (for instance,
how many dimensions there are), 2. because in turn this would make the simulation
less general, and 3. because it seems that using distance as the measure of
utility would lead to the "median candidate" winning consistently, at least by
Schulze.  It doesn't seem to me that this would demonstrate much, since real utility
is based on more than distance in issue space.

> > Here are the methods for generating Approval ballots:
> > "Two Evils": Every voter believes that candidates A and B have 50% odds
> each of winning, and that
> > every other candidate has 0%.
> > "First Preference Proportion": Every voter knows every other voter's
> sincere favorite, and
> > believes that each candidate's odds of winning are equal to the proportion
> of voters whose
> > favorite they are.
> > "Utility Maximizer Known": Every voter knows which candidate has the
> highest average utility, and
> > believes that this candidate has a 90% chance of winning, with the other
> 10% divided evenly among
> > the other candidates.
> > "Schulze Winner Known": Every voter knows which candidate is the sincere
> Schulze winner, and
> > believes that this candidate has a 90% chance of winning, with the other
> 10% divided evenly among
> > the others.
> > "Zero-Info": Every voter believes that every candidate has an equal chance
> of winning.
> > "Acceptables": No odds.  Every voter votes as though their expectation is
> equal to 50 (the maximum
> > being 100).  This means they could approve all or none of the candidates.
> 
> I think not many people will vote for none (unless they don't care about the
> election at all) or all.  I would suggest that if a voter would vote for
> none or all, have him vote for one, or for all but one.

I would consider this, except that I doubt it would make much difference in
the performance; I don't want to make the "Acceptables" method less general;
and I don't think the "Acceptables" method is realistic, anyway.

> > "Bullet-Voting": Every voter bullet-votes for their favorite.  (Donald
> Davison's recommended
> > Approval strategy.)
> > "Random Candidate": A candidate wins at random.  (Not really Approval.)
> 
> This class of methods simulates the effect of polls in an Approval election:
> 
> XYZ Approval Winner Known: Every voter knows which candidate would win with
> approval ballots generated by the XYZ (e.g. Zero-Info or Acceptables)
> method.

As far as my simulation's framework goes, that definition isn't complete unless
you add "and every voter believes that this candidate has a 90% chance of winning,
with the other 10% divided equally among the others."

That is, unless you are suggesting that the voters use something other than
"better than expectation" strategy.

I am interested in simulating the "max power" or "max information" strategy that
Forest has brought up, where voters aim not to maximize expectation, but to
maximize the odds of their ballot being "positively pivotal."  However, this still 
requires odds predictions to come from somewhere, and I'm not sure what method
is best.

> Those suggestions might possibly result in more true-to-life election
> simulations.

They could, but it would be hard to demonstrate either way.  Are you thinking
that there is some method of voting in Approval that would bring a considerable
utility gain, on average, over Schulze?

Kevin Venzke
stepjak at yahoo.fr



	

	
		
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