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From: carnes@gargoyle.UUCP (Richard Carnes)
Newsgroups: net.politics.theory
Subject: The Pareto criterion
Message-ID: <212@gargoyle.UUCP>
Date: Fri, 11-Oct-85 19:20:14 EDT
Article-I.D.: gargoyle.212
Posted: Fri Oct 11 19:20:14 1985
Date-Received: Sat, 12-Oct-85 20:06:50 EDT
Reply-To: carnes@gargoyle.UUCP (Richard Carnes)
Organization: U. of Chicago, Computer Science Dept.
Lines: 44

The Pareto criterion was devised by Vilfredo Pareto to get around the
problem of the interpersonal comparison of utilities (satisfactions)
that was faced by classical Bentham-Mill utilitarianism.  If you
satisfy X at the expense of Y, is it meaningful to say that the
increase in X's utility is greater than the decrease in Y's?  The
Pareto criterion provides a way of choosing among social outcomes
without having to make such comparisons.

Let there be a set of possible social states {A,B,...,Z} (e.g.,
income distributions).  Each individual in the society is assumed to
have a preference ordering of these states.  A social state A is
*Pareto-optimal* just in case there is no other state in the given
set which is unanimously preferred to A.  Example:

Assume a two-person society composed of individuals X and Y, and
assume that each ranks social states solely according to how much
income he receives.  Let the possible income distributions be the
following:
		X		Y
 A		$0		$0
 B	     $1000	     $2000
 C	     $2000	     $4000

In this case, C is Pareto-optimal, and A and B are not.  Neither A
nor B is unanimously preferred to C.  If we add another state D to
the set

 D           $3000           $3000

then both C and D are Pareto-optimal, and A and B are not.  Now if we
consider a new set of income distributions

	      X               Y
 A_k          $k  	$(1,000,000 - k)

where k ranges over the integers from 0 to 1,000,000, then *all* the
the income distributions in the set are Pareto-optimal.

Amartya Sen has shown in essence that Libertaria cannot make
collectively rational social choices without violating either the
Pareto principle or libertarian principles from time to time.  If
there is great popular demand I will post his example to the net.
-- 
Richard Carnes, ihnp4!gargoyle!carnes