by Katherine Carr
As a concept, willingness to pay (WTP) is simple and effective. Unsure what value something holds? Ask people what they are willing to pay! Unfortunately the approach is not without issue; simply presenting a list of values for respondents to choose from or a giving a ‘starting-point’ figure can bias valuations. We can attempt to prevent this type of bias and many others during data collection and analysis by controlling for influencing factors. However, even controlling for such bias other challenges, such as preference reversals, remain. In the standard WTP approach, participants are asked to explicitly rank intervention options from most to least preferred to generate an explicit rank order. Respondents are then asked their WTP for each intervention, generating an implicit rank by ordering the interventions according to their respective WTP value. Preference reversals can then occur when the order of interventions according to the implicit rank does not match that expressed in the explicit rank.
In 2002, Shackley & Donaldson proposed an ‘incremental’ (originally coined as ‘marginal’) approach to willingness to pay in an attempt to overcome some of the challenges associated with the standard WTP approach. The incremental approach obtains the explicit rank of interventions in the same way as the standard approach, however the WTP valuation process is conducted in stages rather than seeking values outright. This is done by first ascertaining a value for the respondent’s least preferred option from the explicit rank. Respondents are then asked how much more they are willing to pay for their next preferred option and so on in an incremental fashion until WTP values are obtained for all interventions on offer. This system depends on carrying the value of each intervention forward, creating an exogenous framework in which preference reversal becomes theoretically impossible; the value of each intervention should therefore be equal to, or greater than, the previous value in the order of the explicit rank.
As part of the RAINDROP study (Resource Allocation In NHS Dentistry: Recognition Of societal Preferences) we generated new data and conducted an analysis on willingness to pay. Using two versions of a questionnaire (one for the incremental approach and one for the standard approach) we collected data regarding societal values for five different dental interventions. What we found in our early analysis was surprising. The two approaches generated distinctly different values but neither approach offered much difference in values between interventions. We also discovered the possibility of preference reversals in the incremental approach.
Both of these results contradict the existing body of evidence. So, what’s going on? The easy answer is that we aren’t sure. We can speculate, however.
In our study, we were assessing five different dental interventions: fluoride varnish for children, supervised tooth brushing in schools, molar root canal, dentures in care homes and extended orthodontics. These treatments and services are not obvious substitutes for each other– some were preventative measures, others were treatments restoring functionality or treating pain whilst one was cosmetic. Between each dental service option the methods of treatment settings differed, as did the target population and the number of beneficiaries. It is not difficult to appreciate that the complicated trade-off between these interventions may impede discrimination between the options. We hypothesise that respondents randomised to the incremental WTP approach may have offered a moderate sum for their least preferred option, reflecting perhaps a want to be seen to support the cause or to ensure it is provided for the use of others which would be a form of strategic bias in itself, then offer small, consistent increases in value for each next preferred option. This could explain the lack of difference between WTP values, reflecting no true strength of preference.
The incremental approach may dominate the standard approach in terms of generating distinctly different WTP values in situations where interventions are close substitutes for each other, as seen in Lamiraud et al., as the approach allows for better relative comparison between treatment options, enabling individuals to think about the true value their next preferred option provides.
What about preference reversal?
Theoretically, preference reversals are impossible using the incremental approach. The framework carries the previous value forward, meaning at each stage the intervention holds the same value as the immediately lower-ranked intervention, or higher. It should therefore come as no surprise that for this approach we saw no evidence of preference reversal. The incremental approach dominates in this respect yet it was not without issues; the approach did not prevent protest votes occurring. A protest vote is a £0 value which is given for a reason thought not to reflect a belief that the intervention is worth nothing and instead holds issue with the elicitation process. Traditionally, protest values are eliminated from analysis. This is problematic for the incremental approach as WTP values depend on the previous value being brought forward –protest votes prevent a value being carried forward and the observations for that participant are eliminated from analysis. This happened in a significant number of cases in the incremental approach sample.
The individuals who gave protest votes tended to follow one of two patterns. Firstly, protest responses were given for least preferred options then non-zero values given for the remaining interventions. This behaviour indicates that the respondents are indifferent between their least preferred options, but have a positive WTP value for those ranked highest. Secondly, a protest vote was given to a mid-ranked option, with some participants indicating that the intervention should not be provided on the NHS or they are unwilling to make a tax contribution for the intervention. This could be seen as a preference reversal in the incremental approach. The nature of the incremental approach creates problems for accurately recording protest votes adhering to the latter pattern since the positive value of the lower-ranked option is carried forward, thus overriding the protest vote value, resulting in the protested intervention appearing to have a positive WTP value when in reality its value should be £0.
It appears from our analysis that the incremental approach promises too much for this particular, complex valuation task. But we should not completely dismiss it. Our results indicate that the incremental approach may be suitable for a different trade off where the intervention options are less multi-faceted. It also indicates that the current way in which £0 values are eliminated in the current analyses is too simplistic and may diminish sample size unnecessarily.
The data will be presented at HESG 2017 and a subsequent full paper will follow.
 Slovic, P., & Lichtenstein, S. Comparison of Bayesian and regression approaches to the study of information processing in judgement. Organisational Behaviour and Human Performance, 1971, 6: 649-744
 Shackley, P. and Donaldson, C. Should we use willingness to pay to elicit community preferences for health care? Journal of Health Economics 2002; 21(6): 971-992
 Lamiraud, L. Oxoby, R. and Donaldson, C. Incremental Willingness to Pay: a Theoretical and Empirical Exposition. Theory and Decision 2016; 80(1): 101-123