[EM] How to measure somebody's utilities

[Warren Smith]

It is often erroneously claimed that utilities are "unmeasurable."

Here is a way to do it. This kind of idea was one ingredient in F.W.Simmons's
invention of various honesty-inducing voting methods,
such as "double range voting," but it is worth isolating this ingredient since
it is of interest by itself.

We suppose there are N items, alternatives, events, candidates, or
whatever you want to call them.
We want to know Joe's N utilities for those N events.
We make a machine to carry out the following

UTILITY-REVELATION ALGORITHM:
STEP 1. Machine tells Joe:
"Please tell me your utility values (real numbers U_1, U_2, ..., U_N)
for the N events,."

STEP 2. [Joe tells.]

STEP 3. Machine chooses 3 events A,B,C at random from the N
with (say) U_A <= U_B <= U_C

STEP 4. Machine now chooses a random real p with 0<=p<=1.

STEP 5. Machine now GIVES to Joe, either B, or {A with probability p
and C with probability 1-p},
whichever of these two has greater utility according to the U-values
Joe had told us in step 2.
The utility of the former is U_B and of the latter is p*U_A + (1-p)*U_C.

The end.

THEOREM:
No matter what the random processes are in steps 3 and 4 (provided they
cause positive probability for each triple {A,B,C}, and no subsegment of the
real p-interval [0,1] has probability=0, and the randomness is not
predictable by Joe),
Joe's uniquely best (expected-utility-maximizing) strategy is
to give honest (perhaps rescaled) utility values in step 2.

(Certain weaker conditions on the triples also would be acceptable.)


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)