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

Michael Poole mdpoole at troilus.org
Thu Mar 1 10:59:09 PST 2007

```Abd ul-Rahman Lomax writes:

> 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.

You did not specify a method for the runoff election.  There are two
candidates in the result set I specified; it might itself be the
runoff.  If the method for the runoff cannot be Range Voting, it is
inappropriate to claim that Range satisfies the Majority Criterion,
since Range Voting is not the method being evaluated.

I omitted the rest of your sentence because I could not parse it in
any other way than a desire to redefine the criterion -- and even
then, the meaning was unclear to me.  I refer you to our discussion
from last November as to whether substantially redefining well-known
criteria is acceptable.

(A two-candidate Approval election satisfies MC, but it is fairly easy
to construct a three-candidate Approval case where the Majority winner
is not in the top two results, so I do not think it is appropriate to
say that Approval satisfies MC either alone or with a ratification
step.)

Michael

```