- An agent knows the complete list of choices from which they must select.
- Given any two elements from this space of choices, the agent knows whether one of these elements is not preferred to the other.
- Any element from this space is not preferred to itself.
- The ranking obtained from the preference relation is transitive.
- If the space of choices is a continuum, a certain continuity assumption must hold for the preference relation so as to rule out lexicographic preferences.
Economists have transcended this framework. I have previously pointed out models of agents as consisting of multiple selves. I think this approach exhibits a consilience with theories in, for example, cognitive psychology. I have recently stumbled upon two other ways of modeling choice, generalizing the textbook view to an approach more consistent with empirical evidence from behavioral economics and that cannot be justifiably characterized as "irrational".
Nadeem Naqvi has developed an approach of incorporating tertiary information into choice. In the outdated neoclassical theory, one might represent the relationship y is not preferred to x for agent i by:
x Ri yNaqvi and his colleaques introduce the relation Ri(Vij), where Vij is the background set for agent i. Parametric variation in the agent’s background set can alter the agent’s preferences. That is, one can have, for l ≠ m:
x Ri(Vil) yand
y Ri(Vim) xOne interesting consequence of this modeling strategy is that racial discrimination is formally consistent with Pareto optimality. This "is a surprising, though serious, indictment of relying exclusively on the Pareto principle in social evaluation."
Gul and Pesendorfer consider choice among menus. They consider an agent who is a vegetarian for health reasons, but who is tempted to choose hamburgers, if available. In choosing a restaurant at noon, they would prefer a restaurant with hamburgers on the menu. But in choosing in the morning a restaurant to visit at noon, they will select one with an all-vegtable menu. I hope you can see how this approach allows one to analyze time-consistency of choices.
How long do you think before such approaches are presented in mainstream textbooks in widespread use?
1 Nominal, ordinal, interval, and ratio are well-known measurement scale level, where a level is defined up to a set of transformations. I find curious the claim that the expression of the marginal rate of transformation as a ratio of marginal utilities is consistent with an ordinal scale. Mirowski, in More Heat Than Light has also raised questions about the claim that utility only attains an ordinal scale level. I recently stumbled upon Mandler (2006), where he suggests, not necessarily for related reasons, utility be considered to attain a measurement scale level between ordinal and interval.
- George A. Akerlof and Rachel E. Kranton (2010) Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being, Princeton University Press (TO READ).
- Arian Berdellima and Nadeem Naqvi (2011) "Existence of a Pareto optimal social interaction with non-binary preferences".
- Frank Gul and Wolgang Pesendorfer (November 2001) "Temptation and Self-Control", Econometrica, V. 69, N. 6: 1403-1435.
- Michael Mandler (September 2006) "Cardinality versus Ordinality: A Suggested Compromise", American Economic Review, V. 96, N. 4: 1114-1136.
- Nadeem Naqvi (2010) "On Non-binary Personal Preferences, Economic Theory and Racial Discrimination".