Related papers: The structure of two-valued strategy-proof social …
A set of agents has to make a decision about the provision of a public good and its financing. Agents have heterogeneous values for the public good and each agent's value is private information. An agenda-setter has the right to make a…
Referring to a standard context of voting theory, and to the classic notion of voting situation, here we show that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear. On this purpose…
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…
Social choice theory is the study of preference aggregation across a population, used both in mechanism design for human agents and in the democratic alignment of language models. In this study, we propose the representative social choice…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…
The Gibbard-Satterthwaite theorem is a cornerstone of social choice theory, stating that an onto social choice function cannot be both strategy-proof and non-dictatorial if the number of alternatives is at least three. The Duggan-Schwartz…
Given an o-minimal structure ${\mathcal M}$ with a group operation, we show that for a properly convex subset $U$, the theory of the expanded structure ${\mathcal M}'=({\mathcal M},U)$ has definable Skolem functions precisely when…
The mathematical study of voting, social choice theory, has traditionally only been applicable to choices among a few predetermined alternatives, but not to open-ended decisions such as collectively selecting a textual statement. We…
We describe a model that explains possibly indecisive choice behavior, that is, quasi-choices (choice correspondences that may be empty on some menus). The justification is here provided by a proportion of ballots, which are quasi-choices…
We consider abstract-argumentation-theoretic coalition formability in this work. Taking a model from political alliance among political parties, we will contemplate profitability, and then formability, of a coalition. As is commonly…
We study two axioms for social choice functions that capture the impact of similar candidates: independence of clones (IoC) and composition consistency (CC). We clarify the relationship between these axioms by observing that CC is strictly…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
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…
This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In…
Mechanism design is concerned with settings where a policymaker (or social planner) faces the problem of aggregating the announced preferences of multiple agents into a collective (or social), system-wide decision. One of the most important…
We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact…
We study the problem of mechanism design for allocating a set of indivisible items among agents with private preferences on items. We are interested in such a mechanism that is strategyproof (where agents' best strategy is to report their…
A model structure on the category of (small) bigroupoids and pseudofunctors is constructed. In this model structure, every object is cofibrant. In order to keep certain calculations of manageable size, a coherence theorem for bigroupoids…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…