The Boltzmann fair division for distributive justice.

Area of Science:

• Economics
• Game Theory
• Social Justice

Background:

• Fair division is a critical issue in social and economic justice.
• Traditional methods like cut-and-choose are impractical for real-world scenarios due to complexity and unrealistic assumptions.
• Existing methods often fail to account for diverse human factors.

Purpose of the Study:

• To propose a novel and practical fair division method.
• To develop a mathematical model for Boltzmann division applicable to various resource allocation problems.
• To integrate realistic human factors such as contributions, needs, and preferences into the division process.

Main Methods:

• Developed a mathematical model for Boltzmann division for homogeneous and heterogeneous resource division.
• Integrated player-specific factors (contributions, needs, preferences) into the model.
• Optimized the division method by maximizing the total utility of all players.

Main Results:

• The Boltzmann division model successfully incorporates diverse human factors.
• The method is shown to be favorable to socially disadvantaged or underprivileged groups.
• Demonstrated simplicity, versatility, and ease of fine-tuning for practical applications.

Conclusions:

• Boltzmann division offers a significant advancement over conventional fair division methods.
• The method provides a simple, versatile, and equitable approach to resource allocation.
• It has broad applicability to social, economic, and political division challenges.