A simple test of Richter-rationality

We propose in this note a simple non-parametric test of Richter-rationality which is the basic definition of rationality used in choice functions theory. Loosely speaking, the data set is rationalizable in the Richter' sense if there exists a complete-acyclic binary relation that rationalizes the data set. Hence a data set is rationalizable in the Richter' sense if there exists a variable intervals function which rationalizes this data set. Since an acyclic binary relation is not necessary transitive then the proposed Richter-rationality test is weaker than GARP. Finally the test is performed over Mattei's data sets.GARP ; choice functions ; Richter-rationality ; variable intervals functions.

Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way Relationship

This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness, and its natural extensions; and two consequences that only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.Comment: 47 pages, 4 figure

Rationality in a general model of choice

In this paper we consider choice correspondences which may be empty-valued. We study conditions under which such choice correspondences are rational, transitively rational, partially rational, partially almost transitive rational, partially almost quasi-transitive rational.choice correspondence, rational, almost transitive, almost quasi-transitive

A Revealed preference analysis of solutions to simple allocation problems

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy-maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii)representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational;and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function

The World According to GARP* : Non-parametric Tests of Demand Theory and Rational Behavior

The purpose of this paper is twofold. We first point out that violation of rationality axioms (SARP, GARP, WARP) do not necessarily lead to a non-rational behavior. Second, our tests of axioms SARP, GARP and WARP over a Polish panel data (1987-90) show that over the 3630 households only 240 violate the three axioms. However these 240 violations are not caused by the non-respect of demand theory axioms but by the changing of preferences over the period. A logistic regression confirms the robustness of the test since the more the real expenditure increases in absolute value, the more the probability of violating the axioms increases (the respect of the axioms by the 3390 households is not due to an increase of the real expenditure). Moreover, changing in the composition of the family structure increases the probability of being inconsistent. It seems therefore that the 240 apparent violations are due to the appearance of new constraints, which increase the shadow prices of the goods. In order to explain these 240 households' preference changes, we build an econometric model of prices including an observed monetary component and an unobserved non-monetary component expressing the constraints faced by the agent. The estimation of this econometric model shows that the agents who apparently violate the axioms have these complete price changes superior to those of the agents who respect the axioms. Thus the agents who apparently violate the axioms faced during the period a change of their non-monetary resources and the appearance of new constraints.Rationality, GARP, Non-parametric tests, Shadow prices.

On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else

We prove that defining consumers’ preferences over budget sets is both necessary and sufficient to make every fully informative and finite set of observed consumption choices rationalizable by a collection of preferences which are transitive, complete, and monotone with respect to own consumption. Our finding has two important theoretical consequences. First, assuming that preferences depend on budget sets is illegitimate under the scientific commitments of revealed preference theory. Second, as long as consumers’ preferences are not defined over budget sets, we can assume that preferences depend on observable objects other than own consumption without compromising the logical possibility to reject the model against observation. We however point out that, despite this logical possibility, in practice it can be almost impossible to reject a model where preferences are defined over objects that depend on budget sets. As an example of this we show that if preferences are defined over consumption choices of other individuals then rationalization fails only in cases of negligible practical interest.Revealed Preferences, Budget Sets, Rational Preferences, Rationalizability

Consumer theory with bounded rational preferences

The neoclassical consumer maximizes utility and makes choices by completely preordering the feasible alternatives and weighing when indifferent. The consumer studied in this paper chooses by weighing when indifferent and also when indecisive, without necessarily preordering the alternatives or exhausting her budget. Preferences therefore need not be complete, transitive or non-satiated but are assumed strictly convex and "adaptive". The latter axiom is new and parallels that of ambiguity aversion in choice under uncertainty.preferences: incomplete, intransitive, convex, adaptive; representation; demand.

GARP violation, Economic Environment Distortions and Shadow Prices : Evidence from Household Expenditure Panel Data

This paper contributes to the discussion of the compatibility of consumers' behavior in "real" life with GARP. Within expenditure panel data we observe a relatively low rate of violation (240 out of 3630 households). We show that these violations do not imply an "irrational" behavior of the agents, but can be attributed to a change in the agents' choice conditions during a period of time, which includes a shift from a centrally planned towards a market oriented economy.GARP, shadow prices.