Related papers: Choice functions based on sets of strict partial o…
We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between…
In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…
Several rules for social choice are examined from a unifying point of view that looks at them as procedures for revising a system of degrees of belief in accordance with certain specified logical constraints. Belief is here a social…
In the paper we study choice functions on posets satisfying the conditions of heredity and outcast. For every well-ordered sequence of elements of poset, we define the corresponding `elementary' choice function. Every such a choice function…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the…
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…
We prove axiomatic characterizations of several important multiwinner rules within the class of approval-based committee choice rules. These are voting rules that return a set of (fixed-size) committees. In particular, we provide axiomatic…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
This tutorial deal with the Axiom of Choice and some of its applications to topics related to Computer Science. We will see that the Axiom of Choice is equivalent to some well-known proof principles like Zorn's Lemma or Tuckey's Maximality…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
We provide an axiomatic characterization of lexicographic preferences over the set of all random availability functions using two assumptions. The first assumption is strong monotonicity, which in our framework is equivalent to the strong…
In this note we axiomatize the classes of rudimentary functions, primitive recursive functions, safe recursive set functions, and predicatively computable functions.
We consider classes of non-manipulable social choice functions with range of cardinality at most two within a set of at least two alternatives. We provide the functional form for each of the classes we consider. This functional form is a…
The notion of preferences plays an important role in many disciplines including service robotics which is concerned with scenarios in which robots interact with humans. These interactions can be favored by robots taking human preferences…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three…