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

[Dave Ketchum]

On Feb 8, 2010, at 12:35 PM, Kristofer Munsterhjelm wrote:
> 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

Sounds correct.
>>
>> 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.

Does not seem to me to be that easy.  Easy enough to throw rocks, but  
not so easy to know where to aim for better results.
>
>
> 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.

Low turnout is an expectable reasonable response to candidates being  
about equal.  Why should it matter for that whether they are good or  
bad?

Voters seeing bad candidates getting elected SHOULD be looking into  
how to make the next election better.
>
> 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.

If the voters could and did see that it mattered little which  
candidate won, there would be little value in their bothering to  
vote.  If it was difficult to know this it sounds like time to prepare  
for a better election next time.
>
> 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".

Seems debatable.  How do you judge whether a particular minority  
should have that power?
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