Network Preference Dynamics using Lattice Theory

TL;DR

This paper introduces a lattice-theoretic framework and a message-passing algorithm for modeling how agents update preferences in a network, demonstrating equilibrium existence and convergence conditions.

Contribution

It develops a novel algebraic approach to preference dynamics using lattice theory and proposes a distributed algorithm for preference updates in networks.

Findings

Existence of equilibrium points in the preference update system

Convergence conditions for preference trajectories

Numerical simulations supporting the theoretical results

Abstract

Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information about other agents. Exploiting the ordered algebraic structure of preferences, we introduce a message-passing algorithm for heterogeneous agents distributed over a network to update their preferences based on aggregations of the preferences of their neighbors in a graph. We demonstrate the existence of equilibrium points of the resulting global dynamical system of local preference updates and provide a sufficient condition for trajectories to converge to equilibria: stable preferences. Finally, we present numerical simulations demonstrating our preliminary results.