Fairness and Manipulation: An Empirical Study of Arrow’s Impossibility Theorem
C. McComb, K. Goucher-Lambert, and J. Cagan
2015, International Conference on Engineering Design
The design process often requires work by teams, rather than individuals. During these times it is likely that situations will arise in which members of a team have different opinions, yet a group decision must still be made. Unfortunately, Arrow’s Impossibility Theorem indicates that there is no method for aggregating group preferences that will always satisfy a small number of “fair” conditions. This work seeks to identify methods of combining individual preferences that can come close to satisfying Arrow’s conditions. Experiential conjoint analysis was used to obtain empirical utility functions for drinking mug designs. A number of functions for constructing group preference were then analysed using both empirical conjoint preferences and randomly generated preferences. This analysis involved checking each of Arrow’s conditions, as well as computing the likelihood that a method will be susceptible to manipulation by a dishonest individual. Based on the results, methods that should be used to aggregate group preference in practice are recommended.