Allocation under Justice

This paper addresses the problem of allocating 30 unclaimed items to researchers in a fair manner. Five definitions of fairness are derived, considering philosophical, social, and economic aspects. A quantitative evaluation system is established to measure fairness. The allocation is then evaluated using this system. Foundational models, based on zero-one integer linear programming, are developed for each definition. Social interactions between researchers are incorporated into the models, including competition, collaboration, and an auction model. The second section introduces the concept of item relationships, as the value of items can be enhanced when certain items are possessed together. Matrices are used to represent these relationships, making the model more applicable to real-world situations. Sensitivity analysis is conducted to assess the accuracy of each model. The coding implements linear programming and analysis, presenting the results in various visual forms. After refining the model, distributions are calculated using different models and compared. The model is then applied to distribute items among five researchers, and multiple fairness assessments are conducted based on different definitions. The results indicate that, out of four definitions (sixteen in total), two are fair, one is relatively fair, and one is unfair. In conclusion, this paper utilizes linear programming to evaluate fairness in allocation scenarios. The model is refined with adjustments such as mutual interactions, auctions, item interdependencies, and relationships. It provides a comprehensive assessment of fairness and offers practical insights for decision-makers when addressing allocation issues, not only for this particular problem but also for similar situations in society.