How to divide things fairly

Brams, Steven and Kilgour, D. Marc and Klamler, Christian (2014): How to divide things fairly.

Abstract

We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or Borda maximin—maximize the minimum rank, or the Borda score—of the items received by a player. Although SA is potentially vulnerable to manipulation, it would be difficult to manipulate in the absence of one player’s having complete information about the other players’ preferences. We discuss the applicability of SA, such as in assigning people to committees or allocating marital property in a divorce.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fair division; indivisible items; envy-freeness
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D6 - Welfare Economics; D - Microeconomics > D6 - Welfare Economics > D61 - Allocative Efficiency ; Cost-Benefit Analysis; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions

References

Brams, Steven J., and Daniel L. King (2005). “Efficient Fair Division: Help the Worst Off or Avoid Envy?” Rationality and Society 17, no. 4 (November): 387-421.

Brams, Steven J., and D. Marc Kilgour (2001). “Fallback Bargaining.” Group Decision and Negotiation 10, no. 4 (July): 287-316.

Brams, Steven J., D. Marc Kilgour, and Christian Klamler (2014). “Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm.” Notices of the AMS 61, no. 2 (February): 130-141.

Brams, Steven J., D. Marc Kilgour, and Christian Klamler (forthcoming). “An Algorithm for the Proportional Division of Indivisible Items.” Preprint.