Ranking authors using fractional counting of citations : an axiomatic approach

This paper analyzes from an axiomatic point of view a recent proposal for counting citations: the value of a citation given by a paper is inversely proportional to the total number of papers it cites. This way of fractionally counting citations was suggested as a possible way to normalize citation counts between fields of research having different citation cultures. It belongs to the “citing-side” approach to normalization. We focus on the properties characterizing this way of counting citations when it comes to ranking authors. Our analysis is conducted within a formal framework that is more complex but also more realistic than the one usually adopted in most axiomatic analyses of this kind

Subjective expected utility without preferences

This paper proposes a theory of subjective expected utility based on primitives only involving the fact that an act can be judged either "attractive" or "unattractive". We give conditions implying that there are a utility function on the set of consequences and a probability distribution on the set of states such that attractive acts have a subjective expected utility above some threshold. The numerical representation that is obtained has strong uniqueness properties.Subjective Expected Utility ; Conjoint Measurement

Ranking scientists and departments in a consistent manner

The standard data that we use when computing bibliometric rankings of scientists are just their publication/citation records, i.e., so many papers with 0 citation, so many with 1 citation, so many with 2 citations, etc. The standard data for bibliometric rankings of departments have the same structure. It is therefore tempting (and many authors gave in to temptation) to use the same method for computing rankings of scientists and rankings of departments. Depending on the method, this can yield quite surprising and unpleasant results. Indeed, with some methods, it may happen that the "best" department contains the "worst" scientists, and only them. This problem will not occur if the rankings satisfy a property called consistency, recently introduced in the literature. In this paper, we explore the consequences of consistency and we characterize two families of consistent rankings.Bibliometrics, ranking of scientists, ranking of departments

Multiattribute preference models with reference points

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the in- duced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature.

Cooperative phenomena in crystals and the probability of tied Borda count elections

AbstractIn 1960, C. Domb published a paper entitled On the Theory of Cooperative Phenomena in Crystals in which he presented an expression for the number of cycles of length l in a triangular lattice. This expression was erroneous. We present a correct expression and we show that it is linked, in social choice theory, to the probability that all candidates are tied in an election with the Borda rule

Utilitarianism without individual utilities

We characterize anonymous utilitarianism in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand

An axiomatic characterization of the ranking based on the h-index and some other bibliometric rankings of authors

In the last few years, many new bibliometric rankings or indices have been proposed for comparing the output of scientific researchers. We propose a formal framework in which rankings can be axiomatically characterized. We then present a characterization of some popular rankings. We argue that such analyses can help the user of a ranking to choose one that is adequate in the context where she/he is working

Separability and aggregation of equivalence relations

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto+ and Pareto-. If we drop Pareto-, then conjunctive separability and Pareto+ characterize the family of meet aggregators along with a trivial aggregator

An axiomatic approach to bibliometric rankings and indices

This paper analyzes several well-known bibliometric indices using an axiomatic approach. We concentrate on indices aiming at capturing the global impact of a scientific output and do not investigate indices aiming at capturing an average impact. Hence, the indices that we study are designed to evaluate authors or groups of authors but not journals. The bibliometric indices that are studied include classic ones such as the number of highly cited papers as well as more recent ones such as the h-index and the g-index. We give conditions that characterize these indices, up to the multiplication by a positive constant. We also study the bibliometric rankings that are induced by these indices. Hence, we provide a general framework for the comparison of bibliometric rankings and indices