[EM] [CES #3586] How to measure somebody's utilities

[Jameson Quinn]

The problem is, what if Joe doesn't understand?

In a separate thread, Dodeca proposes a definition of utility that is
intuitively easy. The problem is, it's probably not the perfect definition
of "utility" for range voting... especially when you consider that you'd
have to rescale strategically to vote in range.

That's one of the reasons why I like MJ. As long as the voters agree on what
the numbers/grades mean, it works, even if nobody is rescaling and the scale
isn't even linear.

JQ

2011/9/9 Warren Smith <warren.wds at gmail.com>

> 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)
>
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