Measuring and optimizing design variety using herfindahl index

In this paper, we propose a new design variety metric based on the Herfindahl index. We also propose a practical procedure for comparing variety metrics via the construction of ground truth datasets from pairwise comparisons by experts. Using two new datasets, we show that this new variety measure aligns with human ratings more than some existing and commonly used tree-based metrics. This metric also has three main advantages over existing metrics: a) It is a super-modular function, which enables us to optimize design variety using a polynomial time greedy algorithm. b) The parametric nature of this metric allows us to fit the metric to better represent variety for new domains. c) It has higher sensitivity in distinguishing between variety of sets of randomly selected designs than existing methods. Overall, our results shed light on some qualities that good design variety metrics should possess and the non-trivial challenges associated with collecting the data needed to measure those qualities.