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

[Abd ul-Rahman Lomax]

At 12:35 PM 2/8/2010, 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
>>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.

I don't think so. It's not random, truncation depends on preference 
strength, probably absolute preference strengths, to some degree.

The assignment of utilities should be realistic; that is, it should 
predict voter behavior reasonably well in situations where we know 
the votes. Random assignment doesn't cut it. Issue space simulations 
are interesting, but I'm not sure at all how realistic they are. Many 
voters vote based on name recognition and affect.

>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.

No, turnout should be simulated. This is not a simple piece of work, 
Kristofer. And it's important, because simulations based on 
unrealistic models of voter preferences and behavior may produce very 
misleading results.

>>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.

The point, though, is that the remedy to the bad situation isn't to 
eliminate the runoff! There would be a number of approaches, if we 
think government is important (Some don't!). While better voting 
systems to produce better results initially, if terminating, or 
better candidates for runoffs, could help, they won't necessarily 
improve runoff turnout. What if they *do* choose the two best 
candidates, so that voters don't care very much? My point is that 
runoff turnout is *not necessarily* a bad thing.

But there is a general voter despair that is the cause of *overall* 
low turnout, and to fix this I suggest Asset Voting, to create 
proportional representation, where every vote counts and is 
effective, in a well-designed system. If they system is hybrid, as 
I've suggested, between direct and representative democracy, every 
vote *continues to count* until the next election. It's exercised by 
the candidate who received it, perhaps, or by someone to whom the 
candidate has transferred it. That a primary elector might vote 
directly, when the elector chooses to do so, means that the choice of 
the voter is unconditionally respected! Compromise is only on 
representation in deliberation, speaking on the floor of the 
Assembly, and, of course, in setting up default voting rights in the Assembly.

>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

This is standard in democratic process. "Majority" does not 
ordinarily mean "majority of all those eligible to vote," but 
"majority of those voting on a question." Yes, they have 
"disproportionate power," but only as permitted by the actual 
majority. Consider it a form of delegation.

>  - 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.

That's correct that they are not a random sample. They are a sample 
of those *concerned.* That's *better* than a random sample. Much better.

What I'd agree is bad is differential access to voting. If election 
officials make it difficult for some voters to vote, but not others, 
this is truly harmful. And that's certainly happened.

> 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".

It is what happens in direct democratic process, all the time. What 
"the majority perspective" is on this I care little about, most 
people haven't spent ten minutes thinking about this stuff.

But, just to be clear, I do *not* want what was stated. I've stated 
again and again that the majority has the right of decision. I do not 
*ever* want a minority to "overturn a majority" unless the majority 
consents, and I prefer, greatly, for that consent to be explicit. But 
it does mean "a majority of those voting on the question," not some 
vague "majority of all eligible voters" or, worse, "majority of those 
who vote because they will be tossed in gaol if they don't." 
Nevertheless, however they got there, a majority of voters has the 
right to make a decision, no matter what the minority think.

However, that's strictly on a Yes/No question. It gets very tricky 
when it's a multiple-choice question. If a Range ballot is used, with 
approval cutoff, and we have a majority assenting to, say, two 
results, and one has higher range sums than the other, should we go 
ahead and award the result purely to the highest approval? Or to the 
range winner, if that's different? That's a possible ambiguous 
situation, and which way it should go could depend on more detail 
than I'm presenting.

But what if only one candidate gets majority approval, but by a small 
margin, and another candidate has very significantly higher range 
scores? I'm saying that it might be worth a runoff!

But to get there, we'd need quite a bit of election history to 
analyze. When in doubt, I'd say, hold a runoff! If there is no 
majority approved winner, the result is in doubt, and no direct 
democratic organization accepts *any* election without a majority -- 
and they use vote-for-one, normally!

The enemies of Approval and Bucklin claim that voters will truncate, 
bullet voting, because of fear of "harming" their favorite. Fine! 
That will cause majority failure, sometimes, and a runoff. If voters 
like this better than being a little looser with their approvals, 
that's quite okay with me. But start collecting the data!

Bucklin in the primary in a runoff system can't do *worse* than top 
two runoff, not if voters are at all educated. Even then, I'm not 
sure it would be worse. (Uneducated voters may over-approve, but this 
may indeed not be harmful in the end.)