10,763 research outputs found
The Axiomatic Structure of Empirical Content
In this paper, we provide a formal framework for studying the empirical content of a given theory. We define the falsifiable closure of a theory to be the least weakening of the theory that makes only falsifiable claims. The falsifiable closure is our notion of empirical content. We prove that the empirical content of a theory can be exactly captured by a certain kind of axiomatization, one that uses axioms which are universal negations of conjunctions of atomic formulas. The falsifiable closure operator has the structure of a topological closure, which has implications, for example, for the behavior of joint vis a vis single hypotheses.
The ideas here are useful for understanding theories whose empirical content is well-understood (for example, we apply our framework to revealed preference theory, and Afriat's theorem), but they can also be applied to theories with no known axiomatization. We present an application to the theory of multiple selves, with a fixed finite set of selves and where selves are aggregated according to a neutral rule satisfying independence of irrelevant alternatives. We show that multiple selves theories are fully falsifiable, in the sense that they are equivalent to their empirical content
Social choice of convex risk measures through Arrovian aggregation of variational preferences
It is known that a combination of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preferences with the Föllmer-Schied (2002,2004) representation theorem for concave monetary utility functionals provides an (individual) decision-theoretic foundation for convex risk measures. The present paper is devoted to collective decision making with regard to convex risk measures and addresses the existence problem for non-dictatorial aggregation functions of convex risk measures - in the guise of variational preferences - satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). We prove an impossibility result for finite electorates, viz. a variational analogue of Arrow's impossibility theorem. For infinite electorates, the possibility of rational aggregation of variational preferences (i.e. convex risk measures) depends on a uniform continuity condition for the variational preference profiles: We shall prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. Methodologically, we adopt the model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). In an appendix, we apply the Dietrich-List (2010) analysis of logical aggregation based on majority voting to the problem of variational preference aggregation. The fruit is a possibility theorem, but at the cost of considerable and - at least at first sight - rather unnatural restrictions on the domain of the variational preference aggregator.variational preference representation, convex risk measure, multiple priors preferences, Arrow-type preference aggregation, judgment aggregation, abstract aggregation theory, model theory, first-order predicate logic, ultrafilter, ultraproduct
Set-Rationalizable Choice and Self-Stability
A common assumption in modern microeconomic theory is that choice should be
rationalizable via a binary preference relation, which \citeauthor{Sen71a}
showed to be equivalent to two consistency conditions, namely
(contraction) and (expansion). Within the context of \emph{social}
choice, however, rationalizability and similar notions of consistency have
proved to be highly problematic, as witnessed by a range of impossibility
results, among which Arrow's is the most prominent. Since choice functions
select \emph{sets} of alternatives rather than single alternatives, we propose
to rationalize choice functions by preference relations over sets
(set-rationalizability). We also introduce two consistency conditions,
and , which are defined in analogy to and
, and find that a choice function is set-rationalizable if and only if
it satisfies . Moreover, a choice function satisfies
and if and only if it is \emph{self-stable}, a new concept based
on earlier work by \citeauthor{Dutt88a}. The class of self-stable social choice
functions contains a number of appealing Condorcet extensions such as the
minimal covering set and the essential set.Comment: 20 pages, 2 figure, changed conten
Aggregation theory and the relevance of some issues to others
I propose a general collective decision problem consisting in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. Aggregate decisions should respect the mutual constraints, and be based on relevant information only. This general informational constraint has many special cases, including premise-basedness and Arrow''s independence condition; they result from special notions of relevance. The existence and nature of (non-degenerate) aggregation rules depends on both types of connections. One result, if applied to the preference aggregation problem and adopting Arrow''s notion of (ir)relevance, becomes Arrow''s Theorem, without excluding indifferences unlike in earlier generalisations.mathematical economics;
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