Optimal preference satisfaction for conflict-free joint decisions

TL;DR

This paper develops a theoretical framework for conflict-free joint decision-making that maximizes preference satisfaction under probabilistic preferences, providing conditions for perfect satisfaction and methods for minimizing loss when perfect satisfaction isn't possible.

Contribution

It introduces a novel probabilistic preference-based model for conflict-free joint decisions, extending prior deterministic approaches with new theoretical insights.

Findings

Derived conditions for zero-loss conflict-free decisions.

Proposed methods to minimize loss when perfect satisfaction isn't achievable.

Validated approaches through numerical benchmarks.

Abstract

We all have preferences when multiple choices are available. If we insist on satisfying our preferences only, we may suffer a loss due to conflicts with other people's identical selections. Such a case applies when the choice cannot be divided into multiple pieces due to the intrinsic nature of the resources. Former studies, such as the top trading cycle, examined how to conduct fair joint decision-making while avoiding decision conflicts from the perspective of game theory when multiple players have their own deterministic preference profiles. However, in reality, probabilistic preferences can naturally appear in relation to the stochastic decision-making of humans. Here, we theoretically derive conflict-free joint decision-making that can satisfy the probabilistic preferences of all individual players. More specifically, we mathematically prove the conditions wherein the deviation of the resultant chance of obtaining each choice from the individual preference profile, which we call the loss, becomes zero, meaning that all players' satisfaction is perfectly appreciated while avoiding decision conflicts. Furthermore, even in situations where zero-loss conflict-free joint decision-making is unachievable, we show how to derive joint decision-making that accomplishes the theoretical minimum loss while ensuring conflict-free choices. Numerical demonstrations are also shown with several benchmarks.