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

heitzig-j at web.de heitzig-j at web.de
Thu Jan 3 06:18:35 PST 2008

```Dear CLAY SHENTRUP,

you wrote

> it's a proof that intensity of preference, not just order, exists.

Well, if you claim to have such a proof, then please just post it.

> It does meet all those things.

Nice claim again, but where is the evidence? I'm very curious how you prove that my preferences fulfil the conditions without knowing anything about me or my preferences :-)

> Here's the first major error I see at that link, which is perhaps one of many.

Is that your style of discussion? It's not mine, though. I try to take you serious, so please do likewise.

> >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.

This is an argument which Warren gave, too. But you seem to confuse the fact that many people supposedly *behave as if* their preferences met the conditions with the false fact that *everybody's* preferences *do actually* fulfil them. Mine certainly don't.

> you've used a misleading alternative with the 1 cent.

What do you mean by that? Would you or would you not enter such a lottery when p is small enough? And if so, how small must p be for you to put the life at that risk?

> 1 cent seems so insubstantial as to be negligible.

Exactly! It is negligible compared to the child's life. Mathematically speaking: It is infinitesimal. That's just what non-archimedean arithmetics is all about.

> 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".

Is that so? And what does that prove? Only that most of us will prefer to have a urinary tract infection instead of having one's arm hanging on by a tendon after getting into a car wreck. But the question was not whether preferences exist but whether they are based on additive utilities!

> the problem in real life is that we can't measure utility with some kind of mind probe.  computer simulations fix that.

Now finally you admit at least this: One can't measure utility in real life. And therefore it cannot be used in elections.

Yours, Jobst

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