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

[Michael Poole]

Abd ul-Rahman Lomax writes:

> 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.

This is proof that you are confused between preferences and
reasonability.  I disagree with your preferences.  I do not think that
they are unreasonable.

> 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.

That "various election criteria [...] produce preposterous results
*under some conditions*" is neither new nor interesting.  One may
contrive a number of examples for any criteria that are (arguably)
preposterous in their results.  This is precisely why so many criteria
for election systems have been defined through the ages.  The post to
which I responded asserted that most of those criteria were flawed
because they can sometimes reach preposterous results.

We had this argument over your pizza allergy example before.  My
position now is the same as it was then.

>>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.)

I suggest you re-read what I wrote.  This rambling has nothing to do
with what I wrote.

> 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.

I suggest you re-read what I wrote.  This rambling has nothing to do
with what I wrote.

> 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.

I suggest you re-read what I wrote.  This rambling has nothing to do
with what I wrote.

>>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.

I am struggling to see what any of this has to do with the directness
of criteria or the validity of results based on those results.  My
initial impulse is to scream "hire an editor".

> 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.

Again, this has nothing to do with the point I made.

>>   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.

You cannot reasonably expect us to understand your initial post to
contain qualifications that you add later.  Your earlier post made no
reference to single-stage versus multi-stage methods.  Let me remind
you what you wrote earlier:

>> 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.

Your next paragraph mentioned and dismissed the Majority Criteria as a
competitor to social utility.  If you think that is not an implication
that MC is an invalid metric -- in the domain that you specified,
which is "judging how well election methods perform" -- you really
need an editor.

> 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! :-)

I believe this is a new record in how few posts it took you to
convince me (and probably the rest of the list) that you are still an
idiot.

[snip]

> 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 [....]

They do not satisfy that criterion.

  1 person votes A=99, B=0
  2 people vote A=50, B=60

The Majority Criterion demands the election of B.  Range elects A.

Michael Poole