Related papers: The structure of two-valued strategy-proof social …
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…
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…
We establish that all strategy-proof social choice rules in strict preference domains follow necessarily a two-step procedure. In the first step, agents are asked to reveal some specific information about their preferences. Afterwards, a…
Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in…
We study three axioms in the model of constrained social choice under uncertainty where (i) agents have subjective expected utility preferences over acts and (ii) different states of nature have (possibly) different sets of available…
Let V be a finite society whose members express weak orderings (hence also indifference, possibly) about two alternatives. We show a simple representation formula that is valid for all, and only, anonymous, non-manipulable, binary social…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
Standard decision theory seeks conditions under which a preference relation can be compressed into a single real-valued function. However, when preferences are incomplete or intransitive, a single function fails to capture the agent's…
We study the design of voting mechanisms in a binary social choice environment where agents' cardinal valuations are independent but not necessarily identically distributed. The mechanism must be anonymous -- the outcome is invariant to…
Actual individual preferences are neither complete (=total) nor antisymmetric in general, so that at least every quasi-order must be an admissible input to a satisfactory choice rule. It is argued that the traditional notion of…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
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…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
In the theory of social choice the research is focused around the projection of individual preference orders to the social preference order. Also, the justification of the preference order formalism begins with the concept of utility i.e.…
Let X be a finite set of alternatives. A choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A rational choice function is one for which there is a linear ordering on the alternatives such that c(S)…
The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…
Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent…
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…