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

[Jobst Heitzig]

Dear Clay,
> On Jan 3, 2008 6:18 AM, <heitzig-j at web.de <mailto:heitzig-j at web.de>> 
> 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.
>
>
> i already did.  it mentioned various fruits.
Seems we have different concepts of "proof". If so, I can't help it.
>
>     > It does meet all those things.
>
>     Nice claim again, but where is the evidence? 
>
>
> every facet of human existence, like the examples of taking trips in 
> planes and cars.
Uhu, let's leave it to others to judge whether the observation that 
people take trips is evidence for specific properties of preferences 
over lotteries.
>
>     I'm very curious how you prove that my preferences fulfil the
>     conditions without knowing anything about me or my preferences :-)
>
>
> because preferences are just a scaler quantity, and so they have to.
I get the impression that you confuse reasoning with axiomatics. Let me 
assure you that your announcing that my preferences "have to" fulfil 
certain conditions doesn't change the fact that they simply don't :-)
>
>     > 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.
>
>
> yes, my style of discussion is to point out errors when i see them.  
> ever heard of peer review?  same concept.
So you're a peer of mine? What qualifies you as such?
>
>     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. 
>
>
> of course they do.  you're confused or lying if you say otherwise.
Thank you very much. Yes I must be confused, thinking a fruitful 
discussion with you was possible...
>
>     > 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? 
>
>
> what i mean is that the reason people won't put their child's life at 
> risk for 1 cent because they can get 1 cent in safer ways.  but say 
> you took away that alternative, and forced them to live at home at a 
> subsistence level, and then told them that for every amount p by which 
> they'd let us increase the odds of their child's being killed, we'd 
> give them 1 cent, then if we made X low enough, they'd do it.  they'd 
> take 1 million pennies for p*1,000,000 probability of having their 
> child die.
I don't force anybody to do anything. I just gave an example of 
lotteries about which your theory claims people must havec certain 
preferences and about which my theory claims not all people do.
> this is an undeniable fact based on the real choices of every human 
> being in existence, without exception.
If you're not laughing at that sentence, I surely do.
>
>     > 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. 
>
>
> but you missed the point!  the point isn't just that the cent in 
> negligible.  because we can also make p infinitesimal to the point 
> that 1 cent should be worth risking the child's life.  the point is 
> that the 1 cent can so easily be earned in safer ways than risking 
> your child's life.
Again, when discussing an example, keep to the facts stated in the 
example. And although I don't believe in infinitesimal *probabilities*, 
we could safely introduce them into the model since when p is 
infinitesimal that just shows that the utility of the 1 cent is 
infinitesimal, too, instead of a real number as required by your version 
of utility theory.
>
>     > 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! 
>
>
> this comment was in response to your claim that we cannot compare 
> utilities between people, not the part about whether utility is 
> additive.  the point is, yes, we can compare utility between people.  
> that's what it proves.
A single example can never prove a general claim. I did not question 
that in some cases we can compare utilities when they are obviously far 
apart. I just question the general claim that this be always possible, 
since there is no evidence whatsoever that this must always be so.
>
>     > 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.
>
>
> yes we can measure it in real life, but not with a perfectly accurate 
> mind probe.  instead we have to use imperfect voting methods.  and 
> computer simulations tell us how close these election methods come to 
> the accuracy of a mind probe.
Voting methods, as long as they are subject to strategic behaviour, are 
not a good measure of utility. Perhaps the one artificial method posted 
about a year ago which was proved to be strategy free would be a way to 
measure utilities, but that method was extremely inefficient.

Yours, Jobst