[EM] When and how can we speak of "individual utility" and "social utility"?

[Abd ul-Rahman Lomax]

At 07:57 AM 2/28/2007, Michael Poole wrote:
> > Aggregating utilities, however, is obviously not such a simple thing.
> > But we should not let this distract us from the fact that utility
> > analysis is really the *only* approach to judging how well election
> > methods perform, it is not like we have other methods competing with it.
> >
> > Election criteria might be considered such methods, but they are
> > clearly indirect. Even the most basic of them, such as the Majority
> > Criterion as usually defined, is clearly flawed in that we can easily
> > propose election scenarios, and not rare ones but common ones, where
> > it requires results that by any reasonable definition of election
> > success are defective. As I've mentioned, if we can't use an election
> > method for a group of people to pick a pizza, how can we expect the
> > same method to work well with picking officers? Picking officers is a
> > *more* difficult problem, not a simpler one.
>
>You may not like those criteria, or the results reached by methods
>that satisfy them.  That does not mean the criteria are "clearly
>indirect" or the methods "defective".  Kindly stop confusing your
>preferences with what is reasonable.

This is a variation on "Kindly stop beating your wife." No, I'm not 
confused about this. Note that incorporated in Mr. Poole's remark was 
the assumption that my preferences aren't reasonable.

Now, what I expressed here refers to a whole series of posts that 
consider how various election criteria, which may seem totally 
reasonable at first sight, produce preposterous results *under some 
conditions.* That is, the claim that the result is a desirable one, 
or that there is no better alternative choice, is preposterous, and I 
have found no reasonable person to disagree about this. If Mr. Poole 
*does* disagree, I'd invite him to explain why. And I'm not repeating 
the examples at this time, I'll leave that to someone else. There is 
a clue in the paragraph quoted. Pizza.

>It is ludicrous to claim that a criteria based on ballot markings is
>less direct than one based on utility.  No useful definition of
>"direct" permits such a claim.

Is the goal of an election method to have marked ballots? No, that is 
a means to the goal. The definition of utility is difficult if we 
insist on precision, particularly with intermediate utilities and a 
social utility that is more or less balanced or controversial. But 
there are situations aplenty that we can posit that clearly violate 
one or another of the "reasonable" election criteria while being 
totally clear that the violating result is optimal. Again, if Mr. 
Poole does not understand this, he's not been paying attention. Not a 
fault in itself, as nobody is obligated to read what I write. But 
please don't assert that it is ludicrous if you haven't read it (or, 
as in this case, that one has not read the foundation that has been 
laid for it.)

The goal of an election is to make choices in a manner which 
satisfies the intentions of those who arrange or participate in the 
election, and in a democracy, we assume that these intentions are to 
satisfy society in general. The satisfaction of society in general is 
meaningless apart from the aggregated satisfaction of individuals. 
It's clear that if everyone is dissatisfied with an election result, 
that result is not optimal. It is even clear to me, though it could 
be argued without being "ludicrous," that if a majority is 
dissatisfied, the method has failed to find a winner, if another 
candidate or possibility *would* have satisfied this majority.

Conversely, if everyone is satisfied, if no member of the society 
would say, after the election, "I wish that a different choice had 
been made." Presumably, of course, this is before subsequent 
consequences have arrived.

>Among other problems, the only utility you can collect before an
>election is estimated prior utility, and people are notoriously bad
>predictors of the future.

But they don't need to predict the future. Yes, if we wanted to study 
election methods in maximum depth, we'd want to look at ultimate 
consequences, and occasionally I speculate on such. For example, I 
note that sometimes the Majority Criterion will suggest a winner who 
will lead to a civil war. In my view, this objection to the criterion 
disappears if the majority goes ahead and selects its preference 
*with sufficient knowledge of the condition of the electorate.* This 
is impossible, however, with single-stage methods, for there must be 
some aggregation of the data on which this knowledge rests.

I claim that Range, or some variation on it, is the most direct 
method of maximizing social utility; Range is excellent for use in 
polls, and, in spite of the oft-repeated claim that Range isn't being 
used currently, it *is* used in polls, and frequently. But, of 
course, the polls aren't deciding results, rather they are used to advise.

Now, if you submit a Range result as a proposed winner, and the 
electorate votes on this, the Majority Criterion is satisfied. But 
not in a single step, which is often a burden we place on election 
methods. Indeed, it is this which distinguishes pure aggregative 
methods with deliberative ones.

>   What you really want to measure is
>posterior utility (after the term being voted upon).  For reasons like
>that, I think social utility is a poor metric by which to judge an
>election method, but you will not catch me claiming it is an invalid
>metric.

The context would lead me to think that Mr. Poole thinks I've claimed 
that, for example, the Majority Criterion is an "invalid metric." 
That is, of course, a confusion. My claim is that it is "defective" 
if applied to a single stage method, which is quite equivalent to a 
claim that it is a "poor" method.

However, assuming that Mr. Poole is *not* confused on this, I 
conclude that he *has* claimed that social utility is an invalid 
metric in claiming that it was "poor." Denial of that would be, I'd 
expect, a quibble. So,

Caught you! :-)

Seriously, Mr. Poole may claim that social utility is a "poor 
metric," but it is a "direct" metric in that it claims to study 
election results *without regard to process*, whereas election 
criteria *assume* the benefit of various process aspects, including 
the Majority Criterion, which is generally the simplest one to 
approach in this way, and it is also the strongest of the criteria in 
the sense that satisfying it *does* connect with social utility. That 
is, the foundation of the Majority Criterion is that it is desirable 
that the majority, where possible, be pleased with an outcome. But it 
goes a little further than that. It requires that the outcome be the 
*first preference* of the majority, without any reference to 
preference strength, and it is this that leads, quite simply and 
easily, to preposterous results, such that I can claim that any 
election method which satisfies the Majority Criterion (without 
incorporating a step that proves majority approval) is seriously defective.

(Majority approval of a result satisfies the Majority Criterion 
because, presumably, the majority has the option of rejecting the 
result, so the *overall process* satisfies the criterion. 
Essentially, if a compromise is made where the majority accepts less 
than its first preference, it is being made with the knowledge and 
consent of the majority, presumably because a higher order of 
preference is involved, one now better informed.)

By the way, it's my opinion that if a majority, in a single-question 
poll, rejects a candidate, that candidate should become ineligible to 
run in any replacement election. The majority, in rejecting the 
candidate, is deciding that there is a better option, and it would 
prefer to seek this option than the previous subject of ratification. 
This, by the way, is standard deliberative process. One cannot 
ordinarily bring up a rejected motion for Reconsideration, without 
the consent of at least some members who voted against the original motion.

Now, if a process includes a top-two runoff, and the top two are the 
Range winner and the Condorcet winner, where they differ, does the 
method satisfy the Majority Criterion? I'd claim that it does, quite 
clearly. While it is already true that Range and Approval *do* 
satisfy that Criterion, in my opinion, on the argument that the 
majority has consented to a different outcome, it is also quite 
reasonable to argue that this "consent" was constrained, whereas it 
is not so constrained with top-two added. It becomes explicit. It is 
full preference, without debate, if the first election is a 
presentation of either the Range winner or the Condorcet winner for 
ratification. Which assumes, then, a third election if the first one 
presented is not approved. And a back-to-the-drawing board process if 
neither is approved.