Marc Kilgour

Title: Fair Division: Old and New

Abstract: Often goods must be shared among several individuals who all have their own preferences. What makes an allocation of goods fair? One famous criterion is envy-freeness: An allocation is envyfree if each participant feels that his or her portion is at least tied for best – and therefore does not envy anyone else. With such a criterion in mind, how can we use information about preferences to find a fair allocation? Indeed, does a fair allocation always exist? If so, can the parties find it themselves, or is a central authority necessary? A prototype procedure for fair division between two persons is “I Cut, You Choose,” (ICYC) for splitting a divisible (continuous) good between two people. ICYC is assessed, and various improvements and extensions introduced. ICYC also lies at the heart of some new procedures for the allocation of indivisible items, particularly in situations with very limited information about preferences. One special case has been identified in which there is an elegant, easy-to-compute solution. Fair division algorithms and principles are related in a fundamental way to procedural approaches to allocation and interest negotiation. For example, group decision and negotiation can be broken down into two linked processes – the parties share limited information about their preferences, and then use it to craft a solution, a “fair” allocation. Thus, fair division principles and procedures can be applied to problems in economics, computer science, operations research, management, and politics.

Biography:D. Marc Kilgour is Professor of Mathematics at Wilfrid Laurier University, Waterloo, Ontario, Canada and Adjunct Professor of Systems Design Engineering at University of Waterloo. He holds BASc, MSc, and PhD degrees in Engineering Physics, Applied Mathematics, and Mathematics from the University of Toronto. Most of his publications can be broadly described as based on a mathematical analysis of decision problems. He has contributed innovative applications of game theory and related techniques to international relations, arms control, environmental management, negotiation, arbitration, voting, fair division, and coalition formation, and has pioneered the application of
decision support systems to strategic conflict. Active in 12 professional societies, Marc Kilgour has held many editorial responsibilities including co-editing the Springer Handbook of Group Decision and Negotiation. He was
President of the Peace Science Society in 2012-13, and President of the INFORMS Section on Group Decision and Negotiation in 2014-17.

D. Marc Kilgour
Wilfrid Laurier University