Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

What aggregation rules can be classified as logical concepts?

Nikolay L. Poliakov

Abstract

In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such rules. Our primary tools are methods of universal algebra and the theory of closed classes of discrete functions.

What aggregation rules can be classified as logical concepts?

Abstract

In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such rules. Our primary tools are methods of universal algebra and the theory of closed classes of discrete functions.

Paper Structure

This paper contains 5 sections, 6 theorems, 27 equations, 1 table.

Table of Contents

  1. Introduction
  2. General design
  3. The simplest case: Logicality $+$ Locality $\approx$ Neutrality
  4. Universal algebraic approach and the proof of Theorem \ref{['Th1']}
  5. Concluding remarks

Key Result

Proposition 1

Let $\mathfrak C=(A, B, C, \ast)$ be a model of individual choice and $\mathcal{F}$ the set of all possible aggregation rules for $\mathfrak C$. Then for any set $\mathscr D\subseteq \mathscr P(C)$ $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (19)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • Proposition 1
  • proof
  • Remark
  • Proposition 2
  • proof
  • definition 5
  • ...and 9 more