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

[Abd ul-Rahman Lomax]

At 01:59 PM 3/1/2007, Michael Poole wrote:

>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.

What I stated was that the entire procedure, which is a Range poll 
followed by a runoff between the Range and Condorcet winners, 
satisfied the criterion. I did not claim that Range, alone, satisfied 
the criterion. If the runoff is Range, theoretically, it would not 
satisfy the criterion.

However, if we have a two-candidate election, and it *is* Range, the 
majority would allow a minority to prevail only if it votes weak 
votes. That would be a deliberate decision, I'd suggest, to allow 
such a victory, and thus majority rule, it could be argued, would be 
satisfied. This was my point.

But I did not think, nor would I advocate, that the runoff be Range. 
I *assumed* that it would be understood that a "runoff" between two 
candidates would represent an ordinary choice. There would seem to be 
no reason to have the runoff as Range, since the Range data has 
already been collected.

But, as usual, I can think of something. Perhaps the original Range 
election was distorted by strategic considerations. In the runoff, 
there is no motive to vote "strategically," there are only two 
candidates involved and only if the voter desires to weaken the vote 
would one vote other than the extremes. If enough voters did this, 
then the preference of the majority could be passed over. Deliberately.

But this is not at all what I was thinking.

>(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.)

The kind of runoff specified was not a "top two" runoff, but rather a 
contest between the Range winner and a Condorcet winner or plurality winner.

How would this work if the election were Approval?

Presumably the majority preference would be approved by the majority. 
So the only case in which the majority preference would not be in the 
top two would be a case in which more than two candidates were 
approved by a majority.

We should be so lucky....

So if we apply this to Approval, we would have to specify that the 
runoff is not top-two, rather it is between all candidates approved 
by more than a majority. In this case, I'd think, it *would* be an 
Approval election. So couldn't it theoretically still leave the 
majority preference unelected?

That's right, because I'm suggesting it be such on public policy 
grounds, not on the grounds of trying to satisfy the Majority Criterion.

If the runoff were a simple plurality election, it would 
unconditionally satisfy the majority criterion.

Again, I'm applying the criterion to the whole process, the 
combination of two polls, not to either poll singly. Certainly one 
may claim that this is a misapplication of the criterion, and I would 
say to such a person:

bug off. I can apply the criterion to whatever I please. Unless, of 
course, you can show your Criterion Police card, showing that you 
have the authority to regulate the application of election criteria.

Nobody is obligated to accept anything I write, unless, of course, it 
happens to be the truth, and, to be sure, that may only happen 
occasionally.... :-)