challenges that the existing approaches have only partially addressed. First, many subjects exhibit “multiple switching behavior” (MSB), meaning they make inconsistent choices that are difficult to interpret, by switching between “buying” vs. “not buying” multiple times as prices change monotonically (Yu et al., 2021). Based on these decisions, their WTP may lie in a very wide interval or not be recoverable at all.<sup>4</sup> Second, many subjects exhibit “never-switching behavior” (NSB), meaning they choose the same option throughout the MPL, which may imply a very wide interval for the WTP including potentially + _∞_ or _−∞_ . Sometimes, one of these choices is inconsistent because the selected option is strictly dominated.<sup>5</sup> Last but not least, even consistent responses in MPLs only provide interval identification of WTP.

We begin by introducing a framework aimed at understanding choice error in WTP elicitation, and its potential to add noise to WTP estimates. We argue that MPL can be an effective tool for measuring WTP because of the repeated choice data from the same subject that permits learning about error. However, due to their format of repeated parallel questions, MPL may also be vulnerable to framing and order effects. These create bias because they introduce a correlation between the error and the (change in) value difference between the two options, which is used in an MPL to identify WTP. We argue that many widely used MPL designs do not accurately measure error and are unable to prevent or even detect order effects. Worse, some designs may introduce additional bias. Moreover, most estimation approaches do not model choice error, with implications for the estimated variation and standard errors in WTP.

We therefore propose two measures to improve how MPL-based WTP elicitation incorporates choice error and bias. The first measure is to randomize how subjects view choices in a way designed to address potential framing effects. We propose to vary both – the order of binary choices within MPL, so that the value difference between options – aka the “price” is either ascending or descending,<sup>6</sup> and the order of options within each binary choice, that is, whether an option appears first or second/on the left or right.<sup>7</sup> This

> 4Take the case of a “reverse switch” where the subject declines to buy at all low prices offered, but then switches and agrees at a series of higher prices. Formally, they express that their WTP is below _x_ but also above _x_ + _t_ , with _t ≫_ 0.

> 5Dominated choices are often included in the MPL as a test of rationality.

> 6As we discuss in more detail in section 3.1, we do not propose full randomization within MPL to reduce subjects’ cognitive load; see also Andersen et al. (2007) for the same argument.

> 7We think here in particular of visual presentations of the MPL, e.g. on paper or on a screen, but the order in which the two options are listed may also matter in orally administered surveys. When subjects make yes/no decisions about a good at different prices, the researcher may vary order within choice by varying whether the subject is asked to buy or sell a good, or whether the “yes” or “no” answer option is presented first.

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