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Design variety metrics measure how much a design space is explored. We propose that a generalized class of entropy measures based on Sharma-Mittal entropy offers advantages over existing methods to measure design variety. We show that an exemplar metric from Sharma-Mittal entropy, which we call the Herfindahl–Hirschman Index for Design (HHID) has the following desirable advantages over existing metrics: (a) More Accuracy: It better aligns with human ratings compared to existing and commonly used tree-based metrics for two new datasets; (b) Higher Sensitivity: It has higher sensitivity compared to existing methods when distinguishing between the variety of sets; (c) Allows Efficient Optimization: It is a submodular function, which enables us to optimize design variety using a polynomial-time greedy algorithm; and (d) Generalizes to Multiple Measures: The parametric nature of this metric allows us to fit the metric to better represent variety for new domains. The paper also contributes a procedure for comparing metrics used to measure variety via constructing ground truth datasets from pairwise comparisons. 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. 

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. 

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.