[EM] Bayesian Regret analysis of Bucklin, Top-Two-Runoff, and other methods

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> Various factors that affect real elections have been neglected in the 
> simulations which have been done to compare performance of various 
> voting systems. The analysis which has been done, so far, is quite 
> valuable and represents the best data we have on voting system 
> performance, but the neglect of real voting patterns and factors has, I 
> suspect, produced warped comparisons of systems.
> 
> The technique of simulating underlying absolute preferences has too 
> quickly moved into an assumption that preferences can be normalized and 
> that all members of the simulated population will actually vote. In 
> fact, real voter behavior can be predicted to vary with preference 
> strength.
> 
> As an example, if I'm correct, analysis of Bucklin made the assumption 
> that all voters would rank all candidates, which is actually preposterous
> Further, with Top Two Runoff, a assumption has been made that all of the 
> original voters will then vote in a runoff, so the simulation, of 
> course, simulates a Contingent Vote that accomplishes the same thing 
> with a single ballot, unless, of course, voters truncate, and truncation 
> hasn't been simulated, to my knowledge.

If that is true, then it should be relatively simple to make a 
simulation to take the fact into account. Assign every voter-candidate 
pair a certain utility, then for each voter, equal-rank candidates that 
are close enough as far as utility goes. Remove a random number of 
candidates from each rank, leaving at least one.

In terms of a runoff, if both candidates are close enough, the voter 
votes randomly for one of them, which evens out. If they're both also 
close to status quo (which would have to be assigned some utility, as 
well), then the voter wouldn't bother to vote at all, his ballot 
effectively empty.

> It is a common assumption that low turnout in an election is a Bad 
> Thing. However, I've seen little analysis that does anything more than 
> make partisan assumptions; allegedly, low turnout favors Republican 
> candidates. If so, then the source of the problem would be large numbers 
> of voters who might otherwise favor a Democrat, but who have, in fact, 
> low absolute preference strength, and Baysian regret analysis of the 
> whole population would likely reveal that the Republican would be the 
> social utility winner.

Low turnout is a problem if its reason is that voters are saying "makes 
no difference, they're equally bad". It's not as much a problem if its 
reason is that voters are saying "makes no difference, they're equally 
good", except to the extent that makes voters as used to low turnout 
that they don't bother voting - good candidates or not.

If you look at that from a Majority perspective: if a majority doesn't 
care which way the election goes, then the minority who actually bothers 
to vote may have disproportionate power - from a Majority "a democracy 
is rule by the people - /all/ the people" point of view. From this POV, 
low turnout is bad because it makes the democratic process less 
democratic: the decision hinges on fewer people, and these fewer are not 
a random sample of the population.

 From a social utility point of view, you want a minority with strong 
views to be able to overturn a majority with weaker opinions (as long as 
it's worth it, for some definition of that measure); but that is not the 
Majority perspective usually considered when talking about "democracy".