[OPE-L:29] [OPE-L:252] Re: RE: Re: Re: Chapter 1

Stephen Cullenberg (Stephen.Cullenberg@ucr.edu)
Thu, 29 Oct 1998 09:43:09 -0800 (PST)

>Kia ora Stephen.
> >Here are two references from economics which are very
>influential. The
>> first is Gerard Debreu's _Theory of Value_, Chapter I, pp 1-26. The
>> other
>> is Amartya Sen's _Collective Choice and Social Welfare_., the first
>> couple
>> of chapters.
> [...]
>> The two examples from economics where a relation is characterized by
>> an
>> equivalence class are equality, and indifference. As you are pointing
>> out
>> from Russell and Tarski, equality does indeed satisfy RST. So, too
>> does
>> the relation of indifference satisfy RST. So too would a relation
>> defined
>> as follows: "at least as tall as". That is, John is at least as tall
>> as
>> John (Refelexivity). John is at least as tall as Bill and Bill is at
>> least
>> as tall as John (Symmetry).....Obviously, there are many more such
>> relations, but I doubt very few that have economic interpretation.
>In fact "is at least as tall as" is not an equivalence relation, because
>it is not symmetric. That is, the fact that John is at least as tall as
>Bill does not imply that Bill is at least as tall as John. If fails if
>John is taller than Bill. But a relation like "is the same height to the
>nearest whole centimetre" would be an equivalence relation.
You're right about "at least as tall as", I meant to write "as tall as".
Sorry about the slip. But this doesn't alter the other points I made.
I'll respond to your other resposnes later when things are slower.

Stephen Cullenberg
Department of Economics office: (909) 787-5037, ext. 1573
University of California fax: (909) 787-5685
Riverside, CA 92521 http://www.ucr.edu/CHSS/depts/econ/sc.htm