Stefano Vannucci

Filtral Preorders and Opportunity Inequality

We compare opportunity set distributions by means of set-inclusion filtral preorders (SIFPs). Some significant results of the classic theory of income inequality are reproduced in the SIFP-framework.

On the Volume-Ranking of Opportunity Sets in Economic Environments

We provide a characterization of the volume-ranking of opportunity sets as defined on the set of all polyconvex sets, i.e. finite unions of convex, compact, Euclidean sets. In fact, such a domain is large enough to encompass most of the opportunity sets typically encountered in economic environments, including non-linear or even non-convex budget sets, and opportunity sets arising from production sets. Our result relies on a valuation-based volume-characterization theorem due to Klain and Rota (Introduction to Geometric Probability, Cambridge University Press, Cambridge, 1997) and helps to highlight some quite unusual conditions under which the volume-ranking can be justified as a freedom-ranking of opportunity sets. Therefore, it may also help to understand why the latter has been so conspicuously ignored in welfare analysis.

Effectivity Functions and Stable Governance Structures

Stability properties of several governance structures are studied by means of their effectivity functions. It is shown that (strong) stability of a governance structure is mainly determined by the collegial nature of the underlying assemblys decision rule.

Effectivity Functions and Parliamentary Governance Structures

Several parliamentary governance structures based upon a directly elected premier are analyzed through their effectivity functions.lt is shown that only collegial governance structures which provide a tight connection between the premier and her prefixed majority enjoy strong stability.

GAME FORMATS AS CHU SPACES

It is argued that when morphisms are ignored virtually all coalitional, strategic and extensive game formats as currently employed in the extant game-theoretic literature may be presented in a fairly natural way as (concrete categories over) discrete subcategories of Chu(Set,2). Moreover, under a suitable choice of coalitional morphisms, coalitional game formats are shown to be (concrete categories over) full subcategories of Chu(Set,2).

Choice Overload and Height Ranking of Menus in Partially-Ordered Sets

When agents face incomplete information and their knowledge about the objects of choice is vague and imprecise, they tend to consider fewer choices and to process a smaller portion of the available information regarding their choices. This phenomenon is well-known as choice overload and is strictly related to the existence of a considerable amount of option-pairs that are not easily comparable. Thus, we use a finite partially-ordered set (poset) to model the subset of easily-comparable pairs within a set of options/items. The height ranking, a new ranking rule for menus, namely subposets of a finite poset, is then introduced and characterized. The height ranking rule ranks subsets of options in terms of the size of the longest chain that they include and is therefore meant to assess menus of available options in terms of the maximum number of distinct and easily-comparable alternative options that they offer.

Diversity as Width

It is argued that if a finite partially ordered population is given, and incomparability is taken as the relevant type of dissimilarity, then diversity comparisons between subpopulations may be conveniently based on widths namely on the maximum number of pairwise incomparable units they include. We introduce two width-based rankings. The first one is the plain width-ranking of subposets as induced by width computation. The second one is the undominated width-ranking of subposets namely the ranking induced by the sizes of undominated subposets. Simple axiomatic characterizations of the foregoing rankings are provided.

Effectivity Functions, Opportunity Rankings, and Generalized Desirability Relations

Generalized individual desirability relations are defined relying on a) effectivity functions (EFs) b) Galois lattices of EFs and c) opportunity rankings as defined on EFs. It is argued that such desirability relations enable an enlargement of the scope of gametheoretic approaches to the analysis of power allocation far beyond the narrow domain of voting procedures.

Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules

It is shown that simple and coalitional strategy-proofness of an aggregation rule on any rich weakly unimodal domain of an idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including–but not reducing to–trees and Euclidean convex spaces. Therefore, strategy-proof location problems in a vast class of networks fall under the scope of that proposition.

The Cardinality-based Ranking of Opportunity Sets in an Interactive Setting: A Simple Characterization

It is argued that if opportunity sets are properly embedded in an interactive environment then the lattice of set-inclusion order filters of opportunity sets is the most suitable domain for opportunity rankings. A simple characterization of the cardinality-based preorder in terms of certain invariant valuations on the foregoing lattice is provided and contrasted with the well-known Pattanaik-Xu characterization.