Making a Virtue of Necessity

The Pareto principle can be read as a positive hypothesis, reconciling theory with reality, or as a normative hypothesis, standing for a behavior that might be nudged or not, depending on the desirability of its consequences. The behavioral underpinnings of the Pareto principle are reviewed, together with its ethical foundations. In particular, the thesis of adaptive preferences is critically examined, and an axiomatic characterization of such preferences is proposed. Their likeliness is explored in light of the duality between persons and groups, a classic notion of theoretical sociology. Finally, a contribution to the reflection on group agency and corporate social responsibility is provided. It is argued that environmental and social responsibility can emerge from collective decision-making of selfish individuals depending on the governance adopted.

Risk aversion for losses and the Nash bargaining solution

We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses.

Boolean-Valued Set-Theoretic Systems: General Formalism and Basic Technique

This article is devoted to the study of the Boolean-valued universe as an algebraic system. We start with the logical backgrounds of the notion and present the formalism of extending the syntax of Boolean truth values by the use of definable symbols, internal classes, outer terms and external Boolean-valued classes. Next, we enrich the collection of Boolean-valued research tools with the technique of partial elements and the corresponding joins, mixings and ascents. Passing on to the set-theoretic signature, we prove that bounded formulas are absolute for transitive Boolean-valued subsystems. We also introduce and study intensional, predicative, cyclic and regular Boolean-valued systems, examine the maximum principle, and analyze its relationship with the ascent and mixing principles. The main applications relate to the universe over an arbitrary extensional Booleanvalued system. A close interrelation is established between such a universe and the intensional hierarchy. We prove the existence and uniqueness of the Boolean-valued universe up to a unique isomorphism and show that the conditions in the corresponding axiomatic characterization are logically independent. We also describe the structure of the universe by means of several cumulative hierarchies. Another application, based on the quantifier hierarchy of formulas, improves the transfer principle for the canonical embedding in the Boolean-valued universe.