Related papers: Aggregation for potentially infinite populations w…
This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
We demonstrate that individual behaviors directed at the attainment of distinctiveness can in fact produce complete social conformity. We thus offer an unexpected generative mechanism for this central social phenomenon. Specifically, we…
Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of…
A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they…
Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by $Z_0$ and the size of the $n$th change by $C_n$, $n= 1, 2,…
We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time…
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
We study social welfare relations (SWRs) on an infinite population. Our main result is a new characterization of a utilitarian SWR as the \emph{largest} SWR (in terms of subset when the weak relation is viewed as a set of pairs) which…
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…
S.Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529--563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a…
Partial orders are a natural model for the social hierarchies that may constrain "queue-like" rank-order data. However, the computational cost of counting the linear extensions of a general partial order on a ground set with more than a few…
A central theme in social choice theory is that of impossibility theorems, such as Arrow's theorem and the Gibbard-Satterthwaite theorem, which state that under certain natural constraints, social choice mechanisms are impossible to…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
Universality in the behavior of complex systems often reveals itself in the form of scale-invariant distributions that are essentially independent of the details of the microscopic dynamics. A representative paradigm of complex behavior in…
This paper revisits impossibility results on the tyrannies of aggregation and non-aggregation. I propose two aggregation principles (quantitative aggregation and ratio aggregation) and investigate theoretical implications. As a result, I…
When can a majority of voters find common ground, that is, a position they all agree upon? How does the shape of the political spectrum influence the outcome? When mathematical objects have a social interpretation, the associated theorems…
Combinatorial preference aggregation has many applications in AI. Given the exponential nature of these preferences, compact representations are needed and ($m$)CP-nets are among the most studied ones. Sequential and global voting are two…