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

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.

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

Should you believe in the Shanghai ranking?

This paper proposes a critical analysis of the "Academic Ranking of World Universities", published every year by the Institute of Higher Education of the Jiao Tong University in Shanghai and more commonly known as the Shanghai ranking. After having recalled how the ranking is built, we first discuss the relevance of the criteria and then analyze the proposed aggregation method. Our analysis uses tools and concepts from Multiple Criteria Decision Making (MCDM). Our main conclusions are that the criteria that are used are not relevant, that the aggregation methodology is plagued by a number of major problems and that the whole exercise suffers from an insufficient attention paid to fundamental structuring issues. Hence, our view is that the Shanghai ranking, in spite of the media coverage it receives, does not qualify as a useful and pertinent tool to discuss the "quality" of academic institutions, let alone to guide the choice of students and family or to promote reforms of higher education systems. We outline the type of work that should be undertaken to oer sound alternatives to the Shanghai ranking.Shanghai ranking; multiple criteria decision analysis; evaluation models; higher education.

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

A characterization of two disproportionality and malapportionment indices : the Duncan and Duncan index and the Lijphart index

Disproportionality indices aim at measuring to what extent the composition of a parliament differs from the distribution of the votes among parties. Malapportionment indices measure to what extent the number of parliament seats attached to each district differs from the distribution of the population among districts. Since there exist many different such indices, some conditions have recently been proposed for assessing the merits of the various indices. In this paper, we propose a characterization of two disproportionality and malapportionment indices: the Duncan and Duncan index (also called Loosemore-Hanby) and the Lijphart index

A theoretical look at ELECTRE TRI-nB and related sorting models

ELECTRE TRI is a set of methods designed to sort alternatives evaluated on several attributes into ordered categories. The original ELECTRE TRI-B method uses one limiting profile per category. A more recent method, ELECTRE TRI-nB, allows one to use several limiting profiles for each category. We investigate the properties of ELECTRE TRI-nB. When the number of limiting profiles used to define each category is not restricted, ELECTRE TRI-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature. We extend this result in various directions.Comment: 40 page