Date: Nov 13, 2012 11:07 PM
Author: Paul
Subject: "Strategically equivalent utility functions" involve two lotteries
My apologies if this appears twice. Cross-posting to a moderated

group seems to have held up the appearance of this post.

I'm following the definition of "strategically equivalent utility

functions" in Keeney et al, "Decisions with Multiple Objectives...":

http://tinyurl.com/anrxytj

It says that "u1~u2" if they imply the same preference ranking for any

two lotteries. "Lotteries" is not defined, but the definition I've

found on the web is that a lottery is a complete set of mutually

exclusive outcomes (or "consequences"), along with associated

probabilities that add to 1. Usually, the implication is that there

are different lotteries for the same set of consequences depending

from a decision or action i.e. the probabilities of the consequences

depend on the decision/action, but (I assume) the set of consequences

are the same for the two lotteries.

"Preference ranking" is not defined. In the above definition for

strategically equivalent utitility functions, I assume that the

preference ranking is the ranking of the set of outcomes by the

decision maker. This is determined solely by the utility function,

and not by the probabilities of the consequences. Hence, utilities

that are monotonically related should yield the same rank, regardless

of what specific lottery is being considered (since the lottery

differs from the set of consequences only in that probabilities are

associated with the consequences). Therefore, I am confused by the

the specification of "any two lotteries" in the above definition.

Can anyone please clarify this?