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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Thu Mar 1 10:20:50 PST 2007

```At 05:28 PM 2/28/2007, Michael Poole wrote:

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

I'm glad. Which is not at all an incentive to reread what Mr. Poole
wrote.... I did not intend what I wrote to be a commentary on his
writing, but simply to be what occurred to me in a context which was
developed out of what he wrote.... and enough on this irrelevancy.
One matter to confront:
[...]

> > 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.

There is a top-two runoff, after this Range election. The top-two
runoff is a simple election, the ballot says "vote for one," and the
candidates are A and B. Who will be the victor in this election?

Mr. Poole, I'd imagine, thinks that it can be inferred from the Range
poll. It cannot.

Looking at those numbers, and knowing nothing else about the context,
I'd assume that A, indeed, was the best winner of the election. Thus
the *single step*, the Range election, clearly does not satisfy the
Majority Criterion. *However,* if the result is a runoff, as would
happen under the stated conditions -- which is that the Range winner
and the Condorcet winner differ -- A can only win if those voters who
prefer B change their preference once they know how strongly the
single voter prefers A. In other words, they have a higher
preference, presumably based on now understanding the position of the
other voter. If, on the other hand, they continue to prefer B, *B wins.*

There remains the last sentence quoted. As stated, it would seem to
be incorrect. However, we can thank Mr. Poole for indicating that the
quotation was not complete with his ellipses. The remainder of the
statement showed that it was a statement of opinion, based on an
implied consent of the majority, and also acknowledged the weakness
of this opinion. Mr. Poole, in his response, showed that he did not
understand the claim, since it incorporated an understanding of the
kind of example that he gave.

In that example, the majority *allows* A to prevail, by rating A
highly enough. Had they voted A=0, B=99, B would have been both the
Range and Condorcet winner. Their weaker vote essentially said, "I
don't care strongly." And so the strong preference of the A voter prevails.

Another way of looking at this is that those voters elected to cast
one-tenth of a vote each. That is what those ratings mean. Naturally,
if they do this, a voter who votes full strength has more influence
on the outcome. Range gives the majority *more* power of expression,
not less. It does not weaken the majority, but it *allows* voters,
including the majority, more flexibility. If a voter thinks that it
is silly to cast a weak vote, Range does not require it.

However, with a top-two runoff as described, this is all moot. If A
wins that runoff, there is no violation of the Majority Criterion,
nor if B wins it. The Criterion, on the overall process, is fully satisfied.

(Only if you insist that the "preference of the majority" means the
"uninformed preference of the majority" could you claim that the
Criterion fails. As long as *at the end of the election*, the
*ultimate* preference of the majority has prevailed, the Criterion is
satisfied. And the top-two runoff makes that fully explicit, and does
not constrain it. The majority only changes its preference freely,
without constraint.)

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