Reducing Sample Size Requirements by Extending Discrete Choice Experiments to Indifference Elicitation

Environmental decision support aims to aid decision makers in identifying management alternatives which reflect the societal preferences as close as possible. This requires a representation of societal preferences through describing the preference structure and elicitation of individual preferences. As scientific knowledge is always incomplete, societal preferences aggregate uncertain individual preferences, and both have to be quantified by simplified models, the consideration of uncertainty is of high importance in environmental decision support. Decision analysis, in particular multi-attribute value theory and multi-attribute utility theory, provide a good theoretical basis for such a decision support process. 

Discrete choice experiments are a convenient tool for preference elicitation and their statistical evaluation leads to unbiased estimates of preference model parameters. We demonstrate that by extending discrete choice questions to the elicitation of preference indifference, we can achieve a reduction in the uncertainty of estimated value function parameters by about a factor of three or a reduction in sample size required to achieve the same accuracy by about a factor of ten. This is obtained at the cost of a higher elicitation effort for each question as it involves the provision of preference information through indifference statements. Using synthetically generated data to allow us to analyse potential bias and to perform a sensitivity analysis regarding sample size and uncertainty ranges, we quantitatively compare discrete choice experiments with indifference elicitation regarding the achieved accuracy of parameter estimates. We test these aspects by employing Bayesian inference for parameter estimation for different shapes of the value function using an error model for values as it is often used for the evaluation of discrete choice experiments, and an additional error model for the specification of the indifference point. Through the quantification of the gain in accuracy, our study provides a basis for assessing the trade-off between higher elicitation effort per choice situation and the required sample size. The elicitation of preference indifference opens new perspectives whenever the set of stakeholders from whom preferences have to be elicited is limited, for example in the case of preference elicitation from experts in environmental management. In such cases, the higher elicitation effort may be manageable and results in a similar accuracy of results with about one-tenths of the sample size compared to discrete choice replies or higher accuracy for smaller sample size reductions.