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

CLAY SHENTRUP clay at electopia.org
Thu Jan 3 02:55:59 PST 2008

```On Jan 3, 2008 12:44 AM, Jobst Heitzig <heitzig-j at web.de> wrote:

> 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.

it's a proof that intensity of preference, not just order, exists.  if you
and i both prefer A>B>C, but I score them 10/9/0 and you score them 10/1/0,
then I would take the guarantee of B over the 50/50 chance of A-C.  You
wouldn't - unless you sucked at math.

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.

It does meet all those things.  Here's the first major error I see at that
link, which is perhaps one of many.

>If (Archi) would be true, there would have to be a lottery in which
>your child is shot dead with some positive probability p, in which you
>receive 1 cent otherwise, and which lottery you prefer to nothing
>happening. It's obvious that we cannot expect every rational
>individual to have such preferences. (In my personal view, I expect
>*no* rational individual to have such preferences!)

well, you're just wrong.  every time someone drives or flies with his child,
or even leaves the house, or takes the family to dinner at jack-in-the-box,
he's taking a probabality p that his child will be killed by a wreck or a
crash or an illness, or what have you.  we board airplanes because that
lethal chance of dying is so small.

you've used a misleading alternative with the 1 cent.  clearly people will
put their childrens' lives at risk to have the benefit of, say, driving to
the ice cream shop.  but that's a "substantial" benefit, whereas 1 cent
seems so insubstantial as to be negligible.  the problem is that there are
so many other ways a person could come by 1 cent, that don't involve risking
his child's life.  so of _course_ it seems like the knee-jerk reaction for
someone to say he would never risk his child's life for 1 cent - but that's
only because he doesn't have to.  tell a person he will only have
subsistance living, but can have earn an additional dollar ONLY by putting
his child's life at a small risk, p, and he'll do it.  every parent in the
world proves this by putting his children in small-risk situations because
the perceived benefit is greater than the small chance of getting his kid
killed.  that's just undeniable reality.

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.

no it's not at all.  if you see one person in the E.R. with a urinary tract
infection, and another with his arm hanging on by a tendon after getting
into a car wreck, it's obvious who is in "more pain".  the problem in real
life is that we can't measure utility with some kind of mind probe.
computer simulations fix that.

CLAY
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