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

[Jan Kok]

Kevin Venzke wrote:
> Hi all,
>
> I've been sitting on this for a while, but I'm thinking I'll post it now:
>
>
> Here are some results from the simulation I recently wrote about:
>
> (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.

> 2. The sincere Schulze winner is found.  The complete rankings are derived
from the utilities.
> (Sincere ties in utility are very rare.)
> 3. The Approval winner is found according to several methods for
generating odds.  Every voter
> uses "better than expectation" strategy.  This means that they approve
every candidate for whom
> their utility is greater than their expectation for the election.  A
voter's expectation is the
> sum of (voter's utility for J)*(odds of J winning) for every candidate J.
> 4. Both Schulze and Approval ties are resolved in favor of candidates with
earlier letters.
> 5. The simulation reports which of Schulze and Approval elected a
candidate with higher average
> utility, or whether they picked the same candidate.  It keeps track of
this information, as
> well as the average absolute gain in utility over the Schulze result.
>
> 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.

> "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.

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

Cheers,
- Jan