Axiomatic Characterizations of a Proportional Influence Measure for Sequential Projects with Imperfect Reliability

We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If, in a certain task group, a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.

The Efficient Proportional Myerson Values for Hypergraph Games

This study deals with a class of efficient extensions of Myerson value for games with hypergraph communication situations in which the surplus is allocated proportionally. We introduce w -fairness of surplus and provide axiomatic characterizations of the new allocation rule. Furthermore, we give an example of research fund distribution amongst researchers, compare the numerical results with several values, and realize other efficient extensions of Myerson value can be obtained depending on the different measure function w on the hypergraph.

Explication as a Three-Step Procedure: the case of the Church-Turing Thesis

In recent years two different axiomatic characterizations of the intuitive concept of effective calculability have been proposed, one by Sieg and the other by Dershowitz and Gurevich. Analyzing them from the perspective of Carnapian explication, I argue that these two characterizations explicate the intuitive notion of effective calculability in two different ways. I will trace back these two ways to Turing’s and Kolmogorov’s informal analyses of the intuitive notion of calculability and to their respective outputs: the notion of computorability and the notion of algorithmability. I will then argue that, in order to adequately capture the conceptual differences between these two notions, the classical two-step picture of explication is not enough. I will present a more fine-grained three-step version of Carnapian explication, showing how with its help the difference between these two notions can be better understood and explained.

Credibility-limited Base Revision: New Classes and Their Characterizations

In this paper we study a kind of operator —known as credibility-limited base revisions— which addresses two of the main issues that have been pointed out to the AGM model of belief change. Indeed, on the one hand, these operators are defined on belief bases (rather than belief sets) and, on the other hand, they are constructed with the underlying idea that not all new information is accepted. We propose twenty different classes of credibility-limited base revision operators and obtain axiomatic characterizations for each of them. Additionally we thoroughly investigate the interrelations (in the sense of inclusion) among all those classes. More precisely, we analyse whether each one of those classes is or is not (strictly) contained in each of the remaining ones.

Characterizing NTU-bankruptcy rules using bargaining axioms

This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility, by using properties from bargaining theory in order to characterize bankruptcy rules. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule, using properties which concern changes in the estate or in the claims.