Related papers: Classification Aggregation without Unanimity
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…
This paper analyzes a society composed of individuals who have diverse sets of beliefs (or models) and diverse tastes (or utility functions). It characterizes the model selection process of a social planner who wishes to aggregate…
Budget aggregation is a process in which citizens vote by declaring their individual ideal budget allocation, and a pre-determined rule aggregates all votes into a single outcome. Recent theoretical work has proposed various aggregation…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
This study considers the method to derive a ranking of alternatives by aggregating the rankings submitted by several individuals who may not evaluate all of them. The collection of subsets of alternatives that individuals (can) evaluate is…
Arrow's Impossibility Theorem is a seminal result of Social Choice Theory that demonstrates the impossibility of ranked-choice decision-making processes to jointly satisfy a number of intuitive and seemingly desirable constraints. The…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
Data classification, the process of analyzing data and organizing it into categories, is a fundamental computing problem of natural and artificial information processing systems. Ideally, the performance of classifier models would be…
Given a pair of adjoint functors between two arbitrary categories it induces mutually inverse equivalences between the full subcategories of the initial ones, consisting of objects for which the arrows of adjunction are isomorphisms. We…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
Arrow's `impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the…
Arrow's Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and…
Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof…
Learning the true ordering between objects by aggregating a set of expert opinion rank order lists is an important and ubiquitous problem in many applications ranging from social choice theory to natural language processing and search…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them(e.g., transitivity when describing preferences).…