Impossible by design? Fairness, strategy, and Arrow's impossibility theorem. (23rd February 2017) - McComb, Christopher; Goucher-Lambert, Kosa; Cagan, Jonathan
Abstract : The design process often requires work by teams, rather than individuals. During team based design it is likely that situations will arise in which individual members of the 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, enabling decisions that are fairer in practice. First, experiential conjoint analysis was used to obtain individual empirical utility functions for drinking mug designs. Each empirical utility function represented individual members who were part of a design team. Then, a number of functions for constructing group preference were analysed using both randomly generated preferences and empirical preferences derived from the experiential conjoint survey. The analysis involved checking each of Arrow's conditions, as well as assessing the potential impact of strategic voting. Based on the results, methods that should be used to aggregate group preference within a design team in practice were identified and recommended.