[EM] Before Voting Methods and Criteria: Outcome Design Goals (long)

[Kristofer Munsterhjelm]

On 06/30/2013 10:19 PM, Benjamin Grant wrote:
> I’ve been coming at understanding better the options and choices, merits
> and flaws of various approaches to holding votes – mostly with the kind
> (and sometimes not-so-kind) help of the people on this list.
>
> However, a (I assume) basic thought occurred to me, which may be so
> obvious no one need ever discuss it, but I want to double check my
> thinking on some of this.
>
> The rest of this post will NOT be concerned with any one particular
> voting method or criteria.  Instead I will be comparing different
> scenarios of voter preference with thoughts about who “should” win. If I
> am not making sense quite yet, come along and hopefully it will make
> more sense in practice. If not, you can ask me questions or delete the post.
>
> Let’s assume that we have a magical gift – a super power, if you will.
> We can know exactly what each voter thinks about each candidate.  Now,
> because this comes from magic, it cannot unfortunately be used as a part
> of the election process, but it will be useful for our examination of
> attitudes of the voters.

Welcome to utilitarianism!

But note that there's a subtle distinction. Either this magical gift 
gives you the *opinions* of the voters, according to some scale, or it 
gives you a number that tells you how much voter X would come to like 
the choice being Y, were Y to be elected. These may be different - if 
for no other reason than that many politicians lie - and I'm going to 
assume you mean the first one.

Some claim that with experience, the two will converge. The voters will 
see through the lies, and if there's any bias in the voting method, it 
will be included in the judgement. But that takes time and may or may 
not happen.

> I am going to posit a series of two candidate comparisons, and ask who
> “should” win. The point here is to ignore the methods for a bit, and
> just see what our gut says, given the absolutely magically accurate
> information we have about the voter’s preferences.
>
 > [...]
>
> This brings me to my main thought.  As we compare candidates using
> perfect knowledge of how the voters favor them (or disfavor them), at
> what point does our guts, intuition, and instinct for fairness cause us
> to flip our support from one candidate to another? Are our transition
> points naturally similar, or fundamentally different, based on perhaps a
> different valuing of compromise or partisanship?

If you assume that the voter automatically takes second order effects 
into account, then there's no problem. You can just use a method like 
Range and say that the voter will report expected value rather than his 
opinion of the candidate. Such an approach would be more like assuming 
that the magical method provides how much voter X would come to like the 
choice being Y.

However, if the effects are based on the distribution of candidate 
scores - for instance that that the voter's perceived it'll be better to 
elect X if X's score is closer to the scores of the other candidates - 
then the method will have to find equilibrium, and that requires running 
it repeatedly. To show this, let's take another example where the voter 
starts off really liking X, but also likes fairness. At the outset, the 
voter doesn't know where Y will end up, so he rates X according to his 
opinion of X alone. If there's only one round (and no polling), that's 
the best that voter can do; but if there are more, he can take the 
results from the previous round (or poll) into account and then adjust 
his scores.

On the other hand, if the voters don't report expected value, but rather 
their opinion according to some well-defined scale, then the method has 
to either clean up for them or make them aware that they should factor 
more into their scores.

When you look at it like this, what you're seeing is really the same 
question that I've mentioned before: whether processing should be done 
at the front end (in the method itself) or the back end (in the minds of 
the voters). And that question can be answered in many ways, all of 
which are self-consistent.

The extreme back-end answer would be to just have a very large 
discussion and then a majority vote. The majority vote decides very 
little; the discussion is where everything happens, but it is not a 
voting method, it is just a way for the "voters" to communicate among 
themselves. But that answer is not scalable. In contrast to such an 
extreme, the idea of voters reporting expected value is not so 
"back-end-centric" at all. There are certainly methods that are between 
the two, also: like an exhaustive runoff under the assumption that the 
voters will adjust their strategies to reach an equilibrium and thus 
that the (honest) Condorcet winner will never be eliminated.

I *think* that those who advocate rated voting (particularly Approval) 
lean towards prioritizing the back end. Not as much as the extreme I've 
given, but Approval pretty much needs some of the processing to happen 
in the minds of the voters when there's a three-way contest.

MAV and median methods in general lean further towards front end than do 
Range and Approval. For instance, it automatically satisfies Majority 
instead of requiring a majority to actually exaggerate the votes. This 
simplification has a cost: that the method is no longer as good as Range 
when voters are honest and optimal (that is, take into account dynamics 
to produce an expected value estimate).

But to return to your subject of designing fairness into a method. It 
would be possible to do so, but as you put it, different people may have 
different ideas of what fair is. I also think a problem is that you need 
a consistent reference in order to do it, and it's hard to establish 
consistent reference points under rated voting.

Let's explain that a little further. A consistent reference point says 
what a score of 100 (or 0, for that matter) *means*. If you don't have a 
consistent reference point, then it's very hard to make the decision of 
whether A should win by raw support or B should win by fairness, because 
you don't know if the 0-100 scale goes from "Stalin" to "savior of the 
world" or from "bumbling but harmless" to "the most we've come to 
expect".I would imagine fairness to be much more important when the 
scale goes from Stalin to savior than when it goes from bumbling to 
okay-good.

The back-end focus of some rated voting methods just unasks the 
question: the logic goes that the voters will factor in all they need to 
factor in and then be done, so the method shouldn't interfere. It's 
about as well as you can do without an established reference, and (I 
think) this is related to Arrow's disregard of rated methods in general.

Then there are methods like MAV (MJ). These do try to establish a 
consistent reference point. But the reference point is still quite vague 
- it's just that the vagueness doesn't matter to the method. I can 
explain that in detail if you wish :-)

And finally, you have ranked methods. These are generally very front-end 
based (or at least I prefer to look at them in this way). But a ranking 
doesn't contain any strength of preference information, so it's hard to 
do any sort of fairness adjusting there. It is *possible*, but only in 
very general terms. For instance, Borda can elect a compromise candidate 
even when some other candidate has a majority of first preference votes. 
But it can't make the fine-grained sort of call you seem to be seeking.

So to sum all of that up: Range-style ratings are very detailed (contain 
very specific information), but their meaning is left in the air. 
Rankings are just the opposite. In the former case, it's difficult to 
see how the method would know where to trade fairness for raw support. 
In the latter, it's difficult to see how the method would know the 
distribution of support precisely enough to trade one for the other in 
the first place.

(But, just to contradict myself at the very end: you could consider some 
criteria to be ways of establishing fairness. The majority criterion 
could be said to be about fairness to a majority. The Condorcet 
criterion could be said to be about fairness to a candidate that would 
beat every other one-on-one. But that's just one way of interpreting 
those criteria. The Condorcet criterion could just as easily be 
considered an efficiency criterion, based on the jury theorem or on 
statistical grounds that probably also explain why Condorcet does as 
well as it does in Olson's simulations.)

And in closing, I'd say that it is late here (again!) so I may be wrong 
somewhere in here. Feel free to ask if I passed by something too 
quickly, or if something just doesn't seem right.