18,484 research outputs found
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
The shape of incomplete preferences
Incomplete preferences provide the epistemic foundation for models of
imprecise subjective probabilities and utilities that are used in robust
Bayesian analysis and in theories of bounded rationality. This paper presents a
simple axiomatization of incomplete preferences and characterizes the shape of
their representing sets of probabilities and utilities. Deletion of the
completeness assumption from the axiom system of Anscombe and Aumann yields
preferences represented by a convex set of state-dependent expected utilities,
of which at least one must be a probability/utility pair. A strengthening of
the state-independence axiom is needed to obtain a representation purely in
terms of a set of probability/utility pairs.Comment: Published at http://dx.doi.org/10.1214/009053606000000740 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Representation of strongly independent preorders by sets of scalar-valued functions
We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization
Utilitarianism with and without expected utility
We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single âindividual preorderâ. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyiâs utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a âlocal expected utilityâ condition popular in non-expected utility theory, then the social preorder has a âlocal expected total utilityâ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity
The Arbitrage Pricing Theorem with Incomplete Preferences
This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where the individual's preferences may be incomplete or intransitive. This extends existing results to a more general set of individual preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [1986]. These preferences model Knightian uncertainty by allowing for the possibility that preferences are incomplete.Incomplete Preferences, Equilibrium Existence, Arbitrage Pricing Theorem, Knightian Uncertainty
Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version
Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a âGrand State Spaceâ, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.Decision making, Bayesian, Behavioral Economics
Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version
Economic theory reduces the concept of rationality to internal consistency. The practice of economics, however, distinguishes between rational and irrational beliefs. There is therefore an interest in a theory of rational beliefs, and of the process by which beliefs are generated and justified. We argue that the Bayesian approach is unsatisfactory for this purpose, for several reasons. First, the Bayesian approach begins with a prior, and models only a very limited form of learning, namely, Bayesian updating. Thus, it is inherently incapable of describing the formation of prior beliefs. Second, there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.Decision making, Bayesian, Behavioral Economics
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