[EM] Arrow's axioms

[Philippe Errembault]

Hi Forest,

> But Arrow does require transitivity in the partial orderings,
> which excludes ballots of the form A > B > C > A,
> which is quite compatible with human nature.

Just try to order all your friends by preference, and you will see that human nature preferences are not transitive by essence.

> One way to break the cycle is to try to quantify location along with
> price and size, and then assign weights according to the relative
> importance of price, location, and size to you, the potential buyer.

Yes, this is one way to do it. but this is nothing natural. this is just a way to force taking a decision. that's all.

This is precisely because Arrow requires thing that are non-natural to people that I believe that he also can't require it from
group of people.

Philippe

----- Original Message ----- 
From: "Forest Simmons" <fsimmons at pcc.edu>
To: "Ernest Prabhakar" <drernie at mac.com>
Cc: "Philippe Errembault" <phil.errembault at skynet.be>; <>
Sent: Saturday, March 06, 2004 2:20 AM
Subject: Re: [EM] Arrow's axioms


On Fri, 5 Mar 2004, Ernest Prabhakar wrote:

>
> On Mar 5, 2004, at 5:45 PM, Philippe Errembault wrote:
>
> > Arrow's axioms do NOT apply to real world, since he wants to make
> > ranked results from ranked individual choices, while strict ranking of
> > preferences is incompatible with human nature.
>
> Hi Philippe,
>
> I'm not sure I understand your point.  My impression was that Arrow's
> theorem also applied to systems with partial orderings, i.e., where I
> could say A > B = C > D.

But Arrow does require transitivity in the partial orderings, which
excludes ballots of the form A > B > C > A, which is quite compatible
with human nature.

>
> > We all would find very difficult to make a strict and fixed order of
> > preference between different choices. All preference are based on
> > multidimensionnal criterions, and to order them you must choose
> > a ponderation, which are by the human nature NOT fixed.

Let's see what is meant by "choosing a ponderation" in this interesting
posting:

Suppose that you are in the market for a house.  You have narrowed it down
to three houses A, B, and C.  House A beats house B in price and location.
House B beats house C in location and size.  House C beats house A in both
size and price.

So far we have A beats B beats C beats A, all by two to one margins.

One way to break the cycle is to try to quantify location along with price
and size, and then assign weights according to the relative importance of
price, location, and size to you, the potential buyer.

"Choosing a ponderation" means this process of assigning weights.

Forest

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