Capabilities and Equality of Health II: Capabilities as Options

The concept of capabilities, introduced originally by Sen, has inspired many researchers but has not found any simple formal representation which might be instrumental in the construction of a comprehensive theory of equality. In a previous paper (Keiding, 2005), we investigated whether preferences over capabilities as sets of functionings can be rationalized by maximization of a suitable utility function over the set of functionings. Such a rationalization turned out to be possible only in cases which must be considered exceptional and which do not allowfor interesting applications of the capability approach to questions of health or equality. In the present paper we extend the notion of rationalizing orderings of capabilities to a dynamical context, in the sense that the utility function is not yet revealed to the individual at the time when the capabilities are ordered. It turns out that orderings which are in accordance with such probabilistic utility assignments can be characterized by a smaller set of the axioms previously considered.Capabilities; characteristics; equality of health

A note on rationalizability and restrictions on beliefs

Rationalizability is a widely accepted solution concept in the study of strategic form game with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality. Battigalli and Siniscalchi extend rationalizability and derive the solution concept called Δ-rationalizability. Their analysis is based on the following assumptions: (a) players are rational; (b) their first-order beliefs satisfy some restrictions; and (c) there is common belief of (a) and (b). In this note I focus on games with complete information and I characterize Δ-rationalizability with a new notion of iterative dominance which is able to capture the additional hypothesis on players' beliefs.rationalizability, strategic form game, complete information

Rationalizing Choice with Multi-Self Models

This paper studies a class of multi-self decision-making models proposed in economics, psychology, and marketing. In this class, choices arise from the set-dependent aggregation of a collection of utility functions, where the aggregation procedure satisfies some simple properties. We propose a method for characterizing the extent of irrationality in a choice behavior, and use this measure to provide a lower bound on the set of choice behaviors that can be rationalized with n utility functions. Under an additional assumption (scale-invariance), we show that generically at most five "reasons" are needed for every "mistake."Multi-self models, Index of irrationality, IIA violations, Rationalizability

Weighted Voting Via No-Regret Learning

Voting systems typically treat all voters equally. We argue that perhaps they should not: Voters who have supported good choices in the past should be given higher weight than voters who have supported bad ones. To develop a formal framework for desirable weighting schemes, we draw on no-regret learning. Specifically, given a voting rule, we wish to design a weighting scheme such that applying the voting rule, with voters weighted by the scheme, leads to choices that are almost as good as those endorsed by the best voter in hindsight. We derive possibility and impossibility results for the existence of such weighting schemes, depending on whether the voting rule and the weighting scheme are deterministic or randomized, as well as on the social choice axioms satisfied by the voting rule

Stable Matching under Forward-Induction Reasoning

A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning. This approach leads to a new definition of stability. The main result shows an equivalence between this notion and “incomplete-information stability”, a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014), for markets with one-sided incomplete information. The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions. In addition, it provides an epistemic foundation for incomplete-information stability. The paper also shows new connections and distinctions between the cooperative and the epistemic approaches in matching markets

A theory of reference-dependent behavior

Extensive field and experimental evidence in a variety of environments show that behavior depends on a reference point. This paper provides an axiomatic characterization of this dependence. We proceed by imposing gradually more structure on both choice correspondences and preference relations, requiring increasingly higher levels of rationality, and freeing the decision-maker from certain types of inconsistencies. The appropriate degree of behavioral structure will depend on the phenomenon that is to be modeled. Lastly, we provide two applications of our work: one to model the status-quo bias, and another to model addictive behavior.Individual rationality, reference-dependence, rationalization, path independence, status-quo bias, addiction, habit formation, LeeX