arXiv subjects

Edward J. Green

Publications and source records attributed to Edward J. Green.

6 recordsLinked to original sources

arXiv2019

Individual-level randomness in a nonatomic population

This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) a sample is a measurable function from the index space, and (b) an idealization of the Glivenko-Cantelli theorem holds exactly with respect to the measure on that space. That is, samples possess a.s. the distribution from which they are drawn. Moreover, any subspace of the index space with positive measure inherits the same property. This homogeneity property is important for applications of the construction in economics.

math.PR↗

arXiv2019

J. S. Mill's Liberal Principle and Unanimity

The broad concept of an individual's welfare is actually a cluster of related specific concepts that bear a "family resemblance" to one another. One might care about how a policy will affect people both in terms of their subjective preferences and also in terms of some notion of their objective interests. This paper provides a framework for evaluation of policies in terms of welfare criteria that combine these two considerations. Sufficient conditions are provided for such a criterion to imply the same ranking of social states as does Pareto's unanimity criterion. Sufficiency is proved via study of a community of agents with interdependent ordinal preferences.

econ.TH↗

arXiv2018

A parsimonious theory of evidence-based choice

That an agent's possible evidential states form a Boolean algebra (on which it is natural to define a probability measure) is an assertion that ideally should be proved, rather than assumed, in justifying rational choice as a representation of expected utility. A more parsimonious, axiomatic characterization of evidence is provided here. Two primitive entities are evidential states and a relation, more specific than, between evidential states. The axioms specify that more-specific-than is a partial order, there is a minimally specific e-state, and more-specific-than is a separative order. Choice alternatives are another primitive entity. A plan is an assignment of a choice alternative to each evidential state. In general, plans satisfying a version of the sure-thing principle cannot be rationalized by expected utility. But there is such a rationalization if the evidential structure is a tree.

math.ST↗

arXiv2018

Identifying the occurrence or non occurrence of cognitive bias in situations resembling the Monty Hall problem

People reason heuristically in situations resembling inferential puzzles such as Bertrand's box paradox and the Monty Hall problem. The practical significance of that fact for economic decision making is uncertain because a departure from sound reasoning may, but does not necessarily, result in a "cognitively biased" outcome different from what sound reasoning would have produced. Criteria are derived here, applicable to both experimental and non-experimental situations, for heuristic reasoning in an inferential-puzzle situations to result, or not to result, in cognitively bias. In some situations, neither of these criteria is satisfied, and whether or not agents' posterior probability assessments or choices are cognitively biased cannot be determined.

econ.EM↗

arXiv2018

Semi-decidable equivalence relations obtained by composition and lattice join of decidable equivalence relations

Composition and lattice join (transitive closure of a union) of equivalence relations are operations taking pairs of decidable equivalence relations to relations that are semi-decidable, but not necessarily decidable. This article addresses the question, is every semi-decidable equivalence relation obtainable in those ways from a pair of decidable equivalence relations? It is shown that every semi-decidable equivalence relation, of which every equivalence class is infinite, is obtainable as both a composition and a lattice join of decidable equivalence relations having infinite equivalence classes. An example is constructed of a semi-decidable, but not decidable, equivalence relation having finite equivalence classes that can be obtained from decidable equivalence relations, both by composition and also by lattice join. Another example is constructed, in which such a relation cannot be obtained from decidable equivalence relations in either of the two ways.

math.LO↗

arXiv2012

Embedding an analytic equivalence relation in the transitive closure of a Borel relation

The transitive closure of a reflexive, symmetric, analytic relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. Every analytic equivalence relation on an arbitrary Polish space is Borel embeddable in the transitive closure of the union of two smooth Borel equivalence relations on that space. In the case of the Baire space, the two smooth relations are closed and the embedding is homeomorphic.

math.LO↗