Related papers: Classification aggregation: a quantitative impossi…
In many real-life situations that involve exchanges of arguments, individuals may differ on their assessment of which supports between the arguments are in fact justified, i.e., they put forward different support-relations. When confronted…
Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with…
Voting is a very general method of preference aggregation. A voting rule takes as input every voter's vote (typically, a ranking of the alternatives), and produces as output either just the winning alternative or a ranking of the…
Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach…
The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and…
We investigate when non-dictatorial aggregation is possible from an algorithmic perspective, where non-dictatorial aggregation means that the votes cast by the members of a society can be aggregated in such a way that there is no single…
Let $\mathcal{C}$ be an additive category. The nilpotent category $\mathrm{Nil} (\mathcal{C})$ of $\mathcal{C}$, consists of objects pairs $(X, x)$ with $X\in\mathcal{C}, x\in\mathrm{End}_{\mathcal{C}}(X)$ such that $x^n=0$ for some…
We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of "category" for which equality…
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…
In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning…
Dokow and Holzman determined which predicates over $\{0, 1\}$ satisfy an analog of Arrow's theorem: all unanimous aggregators are dictatorial. Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over…
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world…
Preference aggregation is a fundamental problem in voting theory, in which public input rankings of a set of alternatives (called preferences) must be aggregated into a single preference that satisfies certain soundness properties. The…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Given a set of $n$ individuals with strict preferences over $m$ indivisible objects, the Random Serial Dictatorship (RSD) mechanism is a method for allocating objects to individuals in a way that is efficient, fair, and…
We propose a framework for probability aggregation based on propositional probability logic. Unlike conventional judgment aggregation, which focuses on static rationality, our model addresses dynamic rationality by ensuring that collective…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…