Estimating the Membership Function of the Fuzzy Willingness-to-Pay/Accept for Health via Bayesian Modelling

Abstract

Determining how to trade off individual criteria is often not obvious, especially when attributes of very different nature are juxtaposed, e.g. health and money. The difficulty stems both from the lack of adequate market experience and strong ethical component when valuing some goods, resulting in inherently imprecise preferences. Fuzzy sets can be used to model willingness-to-pay/accept (WTP/WTA), so as to quantify this imprecision and support the decision making process. The preferences need then to be estimated based on available data. In the paper, I show how to estimate the membership function of fuzzy WTP/WTA, when decision makers’ preferences are collected via survey with Likert-based questions. I apply the proposed methodology to a data set on WTP/WTA for health. The mathematical model contains two elements: the parametric representation of the membership function and the mathematical model how it is translated into Likert options. The model parameters are estimated in a Bayesian approach using Markov-chain Monte Carlo. The results suggest a slight WTP-WTA disparity and WTA being more fuzzy as WTP. The model is fragile to single respondents with lexicographic preferences, i.e. not willing to accept any trade-offs between health and money.