Related papers: An axiomatic approach to diversity
Diversification is a useful tool for exploring large collections of information items. It has been used to reduce redundancy and cover multiple perspectives in information-search settings. Diversification finds applications in many…
In many countries and at European level, research policy increasingly focuses on 'excellent' researchers. The concept of excellence however is complex and multidimensional. For individual scholars it involves talents for innovative…
In this article we consider alternative definitions-descriptions of a set being Infinite within the primitive Axiomatic System of Zermelo.
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
Understanding functional diversity, the range and variability of species' roles and actions within their communities, is key to predicting and preserving the functions that sustain both nature and human well-being. In this paper, we provide…
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
Topic models extract representative word sets - called topics - from word counts in documents without requiring any semantic annotations. Topics are not guaranteed to be well interpretable, therefore, coherence measures have been proposed…
We provide a formal framework accounting for a widespread idea in the theory of economic design: analytically established incompatibilities between given axioms should be qualified by the likelihood of their violation. We define the degree…
Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Selection under category or diversity constraints is a ubiquitous and widely-applicable problem that is encountered in immigration, school choice, hiring, and healthcare rationing. These diversity constraints are typically represented by…
Magnitude, obtained as a special case of Euler characteristic of enriched category, represents a sense of the size of metric spaces and is related to classical notions such as cardinality, dimension, and volume. While the studies have…
In this paper, we propose a novel fairness framework grounded in the concept of happiness, a measure of the utility each group gains fromdecisionoutcomes. Bycapturingfairness through this intuitive lens, we not only offer a more…
We present some applications of the notion of numerosity to measure theory, including the construction of a non-Archimedean model for the probability of infinite sequences of coin tosses.
Although hypothesis tests play a prominent role in Science, their interpretation can be challenging. Three issues are (i) the difficulty in making an assertive decision based on the output of an hypothesis test, (ii) the logical…