Related papers: Geometry of anonymous binary social choices that a…
We give a structure theorem for all coalitionally strategy-proof social choice functions whose range is a subset of cardinality two of a given larger set of alternatives. We provide this in the case where the voters/agents are allowed to…
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…
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…
This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for…
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…
The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean an asymmetric and transitive binary relation, while a weak…
In this memoir, we seek to construct a constructive theory that is as complete as possible to describe the algebraic properties of the real number field in constructive mathematics without a dependent choice axiom. To this purpose, we use a…
We construct a symmetric invertible binary pairing function $F(m,n)$ on the set of positive integers with a property of $F(m,n)=F(n,m)$. Then we provide a complete proof of its symmetry and bijectivity, from which the construction of…
We analyze the problem of locating a public facility on a line in a society where agents have either single-peaked or single-dipped preferences. We consider the domain analyzed in Alcalde-Unzu et al. (2024), where the type of preference of…
We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by a problem posed by Kelly in 1991 and remained unsolved, we investigate the problem of recognizing which permutation…
Let $a,b$ be positive integers with $a\ge b$. A graph $G$ is $(a,b)$-choosable if, for every assignment of lists $L(v)$ of size $a$ to the vertices of $G$, there exists a choice of subsets $C(v)\subseteq L(v)$ with $|C(v)|=b$ for each $v$…
We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary…
Rather than anonymizing social graphs by generalizing them to super nodes/edges or adding/removing nodes and edges to satisfy given privacy parameters, recent methods exploit the semantics of uncertain graphs to achieve privacy protection…
We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional separable preferences). The analysis recovers, links and unifies existing…
Given a data-set of consumer behaviour, the Revealed Preference Graph succinctly encodes inferred relative preferences between observed outcomes as a directed graph. Not all graphs can be constructed as revealed preference graphs when the…
In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree…
This work focuses on the (k,l)-anonymity of some networks as a measure of their privacy against active attacks. Two different types of networks are considered. The first one consists of graphs with a predetermined structure, namely…
If G is a finitely generated group, and A an algebraic group, then Hom(G,A) is a possibly reducible algebraic variety denoted by R_A(G). Here we define the profile function, P_d(R_A(G)), of the representation variety of G over A to be…
Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of…