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6 - Characterizing Pareto Optimality: Introduction and Preliminary Ideas

Published online by Cambridge University Press:  19 August 2009

Julius B. Barbanel
Affiliation:
Union College, New York
Alan D. Taylor
Affiliation:
Union College, New York
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Summary

We now turn our attention to characterizations of Pareto optimality. Suppose that P is a partition. How can we determine whether or not P is Pareto maximal or Pareto minimal? We have seen that P is Pareto maximal if and only if m(P) is on the outer Pareto boundary of the IPS and that P is Pareto minimal if and only if m(P) is on the inner Pareto boundary of the IPS. However, the relevant IPS is not always available to us. Our goal is to find other ways to make this determination. We begin by considering Pareto maximality.

Of course, if P is not Pareto maximal, the presentation of a Pareto bigger partition establishes this. But it may not, in general, be clear how to find such a Pareto bigger partition and, of course, our inability to find such a Pareto bigger partition is not a proof that there is none. The methods presented in Examples 6.3 (where we show that a certain partition is not Pareto maximal) and 6.6 (where we show that a certain partition is Pareto maximal) are rather ad hoc. We wish to develop general characterizations for Pareto maximality (and, of course, Pareto minimality too).

Chapters 7, 8, and 10 each focus on a different approach.

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Publisher: Cambridge University Press
Print publication year: 2005

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