# [Election-Methods] utility theory lesson for a very confused rob brown

Jobst Heitzig heitzig-j at web.de
Thu Jan 3 00:44:23 PST 2008

```Dear Clay,

you wrote:
>  the point is that we know it
>  exists. a very simple economic concept called "revealed preference"
>  demonstrates this. it works like this.
>
> say you prefer apples to oranges to bananas. i give you a guarantee
>  of having to eat an orange, or a 50/50 chance of having to eat an
>  apple or a banana. if utility_apple-utility_orange is less than
>  utility_orange-utility_banana, then you'll choose the orange - because
>  you like it more than the average of the other two fruits. but say we
>  change those odds to 60/40. well, then you have to ask whether orange-
>  banana is at least 60% as much as apple-banana. if so, stick with
>  orange, otherwise take the gamble.
>
> by offering you enough different options, we can force you to reveal
>  your true magnitude of preference (unless you get more utility out of
>  lying to us about your preference than you do out of the fruit
>  outcome, but that is obviously besides the point).
>
> so it's clear that utility exists, and has levels of intensity that
>  are empirical reality.

Are you aware that this is no existency proof at all? Assuming one can urge individuals to answer to certain questions about preferences between a sure outcome and some lottery does not prove anything about what those answers will look like and on what reasoning they will be based.

I urge you to read this posting which makes absolutely clear under what conditions one could infer some "additive utilities" from those answers about preferences:
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2007-February/019584.html

So, unless you can somehow show that the answers the individuals will give to your questions will always meet the conditions (Tot), (Trans), (Comp), (Decomp) and (Archi) of the posting, you will not have proved anything. Even if those conditions are met, one can only speak of *individual* utilities. It is even more problematic to argue that they be comparable amoung different individuals.

We had this discussion before on this list, of course...

Yours, Jobst

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