# Ed Green’s personal web page

## 1 Research

The papers linked below reflect my current interests. Also, I have linked a paper (“Lending and the smoothing of uninsurable income,” 1987) from an out-of-print book. My CV on the PSU Economics Department website lists other, published research. If copyright restrictions and lack of library access prevent you from reading an article, then you are welcome to contact me to obtain it for your personal, noncommercial use.

### 1.1 Decision theory and game theory

• “Identifying the presence or absence of cognitive bias in situations resembling the Monty Hall problem” (with Fatemeh Borhani) 2019.04.05. 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.

• “A parsimonious theory of evidence-based choice” (with Fatemeh Borhani) 2018.02.21. 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.

• Presentation slides for “A peculiar coin-tossing model” 2015.09.18. A purely atomic measure on infinite sequences of observations, such as is constructed in the preceding paper to rationalize consistent plans in a restricted class of evidential structures with respect to expected utility, is shown to be implied by an intuitively describable—albeit peculiar—coin-tossing experiment.

• “Events concerning knowledge” 2012.04.17. Common knowledge of a Borel event is shown to be a co-analytic event, and is therefore universally measurable. An extension of Aumann’s “agreement theorem” regarding common knowledge of posterior probabilities is proved in the framework of a measure space defined on a complete, separable, sigma-compact metric space.

### 1.2 Mathematics

• “Semi-decidable equivalence relations obtained by composition and lattice join of decidable equivalence relations” 2019.04.21. 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.

• “Embedding an analytic equivalence relation in the transitive closure of a Borel relation”[Journal of Logic and Analysis 5:4 (2013)]. The transitive closure of a reflexive, symmetric, Borel 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. The Baire space is homeomorphic to an open subset of itself, X, that has an open complement. It is shown that any analytic equivalence relation E on the Baire space can be embedded homeomorphically in the transitive closure of a reflexive, symmetric, closed relation on X. Specifically, the relation can be constructed as the union of two closed equivalence relations. This result shows that Aumann’s common-knowledge operator can map individuals’ information partitions of low complexity to a considerably more complex common-knowledge partition.

• “Individual-level randomness in a nonatomic population” is unpublished research that provides a set-theoretic construction of a continuum of i.i.d. random variables, such that the integral of each sample path with respect to a measurable subset of the indexes is the product of the measure of the index subset and the expectation of the random variable. The construction is an alternative to a construction by nonstandard analysis. (Cf. Robert M. Anderson, ”Non-standard analysis with applications to economics,” in W. Hildenbrand and H. Sonnenschein, editors, Handbook of Mathematical Economics, volume 4, chapter 39, pages 2145–2208. Elsevier, 1991.) This paper was rejected for publication, but all of the referees (4 reports were received in total) judged that the results are mathematically sound.

## 3 PSU Economics Department web page for Ed Green

Go to the Penn State Economics Department web page for Ed Green.

## 4 Personal information

### 4.1 GPG public key

GPG public key (0x8BEC8D37) and fingerprint.

### 4.2 POLST form and Healthcare advance directive

In case of medical emergency, here is my

• POLST form. It is digitally signed with this GPG detached digital signature executed on 2017-10-15.

• The original, signed documents from which these PDF files were scanned, are on file in my home. (The power of attorney is notarized. The POLST form is signed by a licensed physician, Dr. Timothy Doberstein, M.D.) By uniform state law (including Pa. Stat. tit. 73 2260.101 et seq.) and federal law (15 U.S.C. 7001), doctors and hospital administrators can rely directly on this scanned, digitally signed document. In order to verify the signature, use my GPG public key (provided above) and follow the instructions provided in the relevant GPG Handbook chapter.

Revised 2019-05-05