Validating Generic Metrics of Fairness in Game-Based Resource Allocation Scenarios with Crowdsourced Annotations

Being able to effectively measure the notion of fairness is of vital importance as it can provide insight into the formation and evolution of complex patterns and phenomena, such as social preferences, collaboration, group structures and social conflicts. This paper presents a comparative study for quantitatively modelling the notion of fairness in one-to-many resource allocation scenarios -- i.e. one provider agent has to allocate resources to multiple receiver agents. For this purpose, we investigate the efficacy of six metrics and cross-validate them on crowdsourced human ranks of fairness annotated through a computer game implementation of the one-to-many resource allocation scenario. Four of the fairness metrics examined are well-established metrics of data dispersion, namely standard deviation, normalised entropy, the Gini coefficient and the fairness index. The fifth metric, proposed by the authors, is an ad-hoc context-based measure which is based on key aspects of distribution strategies. The sixth metric, finally, is machine learned via ranking support vector machines SVMs on the crowdsourced human perceptions of fairness. Results suggest that all ad-hoc designed metrics correlate well with the human notion of fairness, and the context-based metrics we propose appear to have a predictability advantage over the other ad-hoc metrics. On the other hand, the normalised entropy and fairness index metrics appear to be the most expressive and generic for measuring fairness for the scenario adopted in this study and beyond. The SVM model can automatically model fairness more accurately than any ad-hoc metric examined with an accuracy of 81.86% but it is limited by its expressivity and generalisability.