Importance of preference reversals in the valuation of health and healthcare

The assumption of procedural invariance underlies standard economic theory. That is, it is assumed that an individual’s preference ordering over two or more goods will be unaffected by the procedure used to elicit his or her preferences. If preferences over goods could be altered simply by changing the elicitation procedure (e.g., from a choice task to a valuation task), we would face a dilemma: which procedure most accurately elicits true preferences?

This dilemma is not merely theoretical. For instance, consider the standard gamble, of which there are two main variants: the certainty equivalence method and the probability equivalence method. The probability equivalence version is the method that is generally used to elicit health state values for use in health economic evaluation, in which the individual is presented with two options that entail three outcomes, x₁, x₂ and x₃ (where x₁ > x₂ > x₃, with ‘>’ being the preference relation ‘is preferred to’). In one of the options, the individual is presented with the certainty of receiving the intermediate outcome, x₂. In the other risky option, the individual is faced with probability, p, of receiving the best outcome, x₁, and probability, 1 - p, of receiving the worst outcome, x₃. However, p is unknown, and the individual is asked to state the p that would render him/her indifferent between the two options. The value of x₂ is then given by u(x₂) = pu(x₁) + (1 - p)u(x₃), where u(.) is the value function. If the values of the best and worst outcomes x₁ and x₃ are respectively normalized at one and zero, then u(x₂) = p.

In the certainty equivalence version of the standard gamble, the certainty, x₂, is not given, but p is preset at, for example, 0.5. Therefore, instead of stating an indifference probability between the two options, the individual is required to give the outcome, x₂, that would cause him/her to be indifferent between the two options. If p is preset at 0.5, then u(x₂) = 0.5u(x₁) + 0.5u(x₃), which, after normalizing the values of the best and worst outcomes at 1 and 0, equals 0.5. By varying the preset probability, values for all outcomes can theoretically be elicited.

In terms of eliciting values for predefined health states, the probability equivalence method is clearly far more convenient. Nonetheless, under standard economic theory, the values elicited for any particular health state from the probability and certainty equivalence versions of the standard gamble ought to be identical. However, in several studies it has been demonstrated that the probability equivalence method generates significantly higher values than the certainty equivalence method for each health state [1–3]. In other words, the values elicited can be systematically influenced by the elicitation procedure used; a violation of procedural invariance.

In this editorial, we will focus on another example of procedural invariance, generally termed ‘preference reversal’, first discovered more than 40 years ago. As will be demonstrated, preference reversal has potentially profound implications for the elicitation of health state values, and indeed for health economics and economics more broadly. However, as yet, little attention has been paid to this phenomenon in the health economics community. What little evidence there is in health will be reviewed, but first a classic preference reversal example will be detailed.

Classic preference reversal

The most well-known and frequently replicated preference reversals use money outcomes, and were uncovered by psychologists in the 1960s [4,5]. The classic preference reversal involves two bets, commonly referred to as the $-bet and the P-bet. The $-bet offers a modest probability of winning a relatively large amount, the P-bet offers a high probability of winning a modest amount, and the two bets have similar expected values. Respondents are asked to place their certainty equivalents on each of the two bets, often by eliciting their selling prices, and are also asked to choose directly between the $-bet and the P-bet. In a large number of studies, a substantial percentage of respondents (sometimes as high as 70–80%) value the $-bet higher than the P-bet, but choose the P-bet over the $-bet [6].

As an example, consider the following bets, taken from Lichtenstein and Slovic [7]:

•	($16, 11/36; -$1.50, 25/36) $-bet
•	($4, 35/36; -$1, 1/36) P-bet

Here, the $-bet offers a 11/36 chance of winning $16 and a 25/36 chance of losing $1.50, and the P-bet offers a 35/36 chance of winning $4 and a 1/36 chance of losing $1. Both bets have an expected value of approximately $3.85. The study entailed three tests of preference reversal, and demonstrated that between 51 and 83% of respondents placed a higher value on the $-bet, but chose the P-bet. It is important to emphasize that in addition to being substantial, preference reversals are generally found to be systematic. That is, preference reversals in the direction of the $-bet being valued higher than the P-bet, but the P-bet being preferred to the $-bet in a direct choice, are far more common than those in the direction of the P-bet being valued higher than the $-bet, but the $-bet being preferred to the P-bet in a direct choice. For example, Lichtenstein and Slovic observed that between 6 and 27% of respondents demonstrated preference reversals in the latter unpredicted direction. Lindman concluded that “in general, choices … tend to reveal preferences for gambles in which the more favorable outcome is likely. Conversely, selling prices tend to reveal a preference for the gamble for which the more favorable outcome has the largest value” [8]. Such systematic violations of theoretical propositions cannot adequately be attributed to random error.

Most economists were initially sceptical of the psychologists’ findings, perhaps unsurprisingly, because preference reversals offer a fundamental challenge to economic theory. Grether and Plott, for instance, thought that the nonincorporation of real financial incentives in much of the psychology research was problematic [9]. They were also concerned that psychologists had not allowed respondents to express indifference in the choice tasks, thus potentially forcing the respondents to choose one way or the other. Moreover, they asserted that many respondents may have been gaming, by expressing a preference for the $-bet in one task and the P-bet in the other task, thus hedging their bets over all tasks that were presented to them.

Consequently, in an attempt to disprove the phenomenon, Grether and Plott conducted what they thought to be a more carefully designed experiment [9]. They introduced financial incentives in the form of real money payoffs, allowed their respondents to express indifference between the bets, and reduced the possibility of gaming by informing their respondents that only one of their choices would be randomly selected at the end of the experiment and played out for real, in the hope that the respondents would answer each question independently of all other questions, reducing the incentive to hedge. Systematic preference reversals nonetheless persisted. Indeed, by including a control group that were not offered financial incentives, it was actually observed that preference reversals were more common when financial incentives were offered.

Further preference reversals have been substantiated by other scholars [10,11]. It ought to be noted, however, that other studies have shown that it may be possible to reduce the prevalence of preference reversals by, for example, increasing the size of the payoffs, which might induce more careful pondering by respondents, or by employing successive round experiments, as opposed to one-shot games, which may create an environment for learning [6]. Nonetheless, even in these circumstances, substantial preference reversals tend to persist, and few now doubt that the phenomenon is genuine.

As indicated earlier, most of the research on the classic preference reversal has used money outcomes, with minimal investigation in the area of health. The next section explains why health ought to be an important area of concern in this regard, and reviews the evidence that currently exists in this domain.

Preference reversals in health

The fact that preference reversals have received only limited attention in the domain of health is potentially problematic, as evaluators of health and healthcare often employ different elicitation procedures. For example, some experts use discrete choice experiments, where preferences are elicited by asking respondents to choose directly between available alternatives [12], whereas others use contingent valuation, which encompasses both willingness to pay (WTP) and willingness to accept methodologies, and requires respondents to place a direct monetary valuation on a health outcome or healthcare intervention [13]. Classic preference reversals have been observed across these types of decision modes, suggesting that it may be possible to alter the relative value placed on particular health outcomes and interventions by simply varying the way in which preferences are elicited.

Indeed, there is some evidence that WTP and choice through ordinal ranking in health induces preference reversals. Surveys in Norway, UK, France and Denmark have shown that only 21–39% of respondents gave WTP values to healthcare programs that were consistent with their explicit rankings of those programs [14–17]. Some have speculated that this phenomenon is caused by respondents offering WTP values that are based on their estimated cost of the interventions, causing high WTP values for costly and yet relatively undesired interventions [18,19]. In an attempt to address these preference reversals, Shackley and Donaldson modified the WTP approach from the standard practice of asking respondents to place a WTP value on each individual intervention considered separately from one another (e.g., Donaldson et al.[20]), to a marginal approach, whereby respondents were first required to indicate which intervention they preferred, and were then asked to state how much extra they would be prepared to pay to have their more preferred option rather than a less preferred option [19]. They found that the percentage of respondents who were strictly consistent with economic theory was barely larger with the marginal approach (43.1 vs 42.2% with the standard approach), which, the authors concluded, casts doubt on the use of the WTP method in healthcare.

Gyldmark and Morrison observed similar patterns of preferences to those observed by Shackley and Donaldson [19], and highlight that some of the apparent inconsistency across choice and valuation decision modes may be the result of the embedding effect and an unwillingness on the part of respondents to pay anything for healthcare interventions [14]. The embedding effect is the observation that people are often willing to pay only the same amount for a basket of goods as they are for the individual components of that basket, or that they are willing to pay only the same amount for different quantities of a particular good. Some have attributed embedding to the warm-glow effect: people may gain moral satisfaction from giving to a good cause, and thus pay for that satisfaction, rather than for the good at hand [21]. Conversely, choice and ranking exercises press for the need to make a tragic choice [15]. In other words, they almost force people to prioritize between competing alternatives.

The separate observation that people are sometimes unwilling to pay anything is probably caused in part by respondents not fully engaging in the hypothetical nature of WTP exercises, and consequently expressing a reluctance to pay for services that are in many countries principally paid for via social insurance and/or tax contributions. That is, a number of respondents tend to introduce a protest bias, although others may simply be making errors or expressing a true zero valuation for the good. The insensitivity in the pricing mechanism, whatever its causes, can result in preference reversals, and seemingly undermines the WTP approach.

Stalmeier et al. report a different type of preference reversal that feeds into the notion of maximum endurable time (MET) [22]. In particular, they observed that for some debilitating health states, people often prefer to live a shorter, rather than a longer, period once a MET has been reached. For example, a respondent might prefer to live for 10 years rather than 20 years if he is told that he will suffer 4.5 days of migraine per week. However, by using the time trade-off method to ascertain the respondent’s healthy year equivalent for each of these poor health scenarios, it is possible that he might state that the 10 years with migraine is equivalent to, say, 4 years in full health, and the 20 years with migraine is equivalent to, say, 7 years in full health. By implication, the longer time with migraine would be valued higher than the shorter length, reversing the preference given by the earlier direct choice task. Direct choice MET preferences were observed in 103 of 176 (59%) respondents, and 79 of the 103 (77%) respondents demonstrated strict preference reversals [22]. Thus, of all 176 respondents, 45% were strictly inconsistent with economic theory. Moreover, the preference reversals were robust, in the sense that most respondents did not want to change their answers after their choices had been explained to them. It was concluded that preference reversals occur frequently for poor health states, where the concept of a MET becomes a relevant consideration for respondents.

The closest replication of the classic preference reversal phenomenon undertaken in the context of health used differential distributions of life expectancies across populations rather than preferences for risky healthcare treatment scenarios [23]. Nonetheless, the construct of the questions probably induced similar reasoning processes to those that would have been caused by risky options. In this study, respondents were asked to choose between two countries with different life expectancy distributions. They were also asked for their certainty equivalents in terms of life expectancy for the two countries, as a means to place a value on their options. The life-expectancy distributions in the two countries can be summarized as follows:

•	(64 years, 70%; 84 years, 30%) $-bet
•	(65 years, 3%; 70 years, 97%) P-bet

Hence, the $-bet was a hypothetical country with a modest percentage of the population enjoying a high life expectancy, with 70% of the population expecting to live to 64 years of age, and 30% of the population expecting to live for 84 years. The P-bet, a country where a large percentage of the population are faced with a more modest life expectancy, can be read similarly. Of 36 respondents, 13 (36%) demonstrated a strict preference reversal, with all of these offering the predicted pattern of preferring the P-bet over the $-bet, but then valuing the $-bet higher.

Overall, although the study of preference reversals in the context of health is nascent, there is growing evidence that a substantial proportion of people fail to hold fixed preferences over different decision modes. Specifically, choice over options often does seem to yield different preferences than the individual valuation of each option, a phenomenon known for decades in the context of money outcomes. This is problematic for health policy when one remembers that preferences for health and healthcare are often elicited through choice and valuation exercises.

Explaining & addressing classic preference reversals

Several explanations for the observance of preference reversals have been suggested [6], but the explanation that probably carries the most weight in the research community at this moment in time is that which attributes the phenomenon to the use of different heuristics across elicitation procedures. That is, valuation and choice tasks may well be driven by different cognitive processes (or rules of thumb). As first noted by Slovic and Lichtenstein [5] and iterated by Lindman [8], valuation tasks may tend to focus attention on the payoffs (which favors the $-bet), whilst choice tasks might encourage greater focus on the probability of winning (which favors the P-bet). More specifically, it has been proposed that a likely reason for why the $-bet tends to be valued higher than the P-bet is because, as a starting point when valuing the $-bet, people often anchor on its best outcome, but then fail to adjust the overall value of this bet sufficiently downwards to take account of its other attributes [7,24]. The suggestion is that this consequently causes an overpricing of the $-bet.

By accepting the plausibility of the heuristic explanation for preference reversals, Bateman et al. hypothesized that the use of a ranking procedure to obtain respondents’ valuations for bets might reduce or eliminate this phenomenon [24]. Valuations can be obtained through a form of ranking exercise by asking respondents to rank a bet al.ngside a number of sure amounts. The value of the bet is then inferred from the values of the two sure amounts that it is placed between. The idea is that by engaging the respondents in a task where they are encouraged to consider explicitly a broad range of sure amounts when considering their value for a $-bet, they will be more likely to adjust their anchoring on the best outcome in the bet downwards to take into account its other attributes, and will therefore offer a more accurate estimate of their true value for the bet.

Bateman et al. tested their hypothesis with four sets of differentially constructed $-bets and P-bets [24]. They discovered that whilst the ranking procedure (compared with the conventional valuation procedure), when coupled with a choice task, generated preference reversals that were noticeably less substantial and systematic in two of their tests, in the other two tests the anomaly remained almost as substantial and at least as systematic. They tentatively attributed their complex pattern of observed preference reversals to the range-frequency effect [25]. That is, the effect that people will often rank an option higher when it is compared to a range of worse options than when it is compared with several better options. Specifically, respondents were asked to rank each $-bet and each P-bet against ten sure amounts and nine other risky options, but the set of risky options differed across each ranking exercise. Consequently, some $-bets were ranked with a set that contained a lot of better risky options, and some were ranked against a lot of worse risky options; similarly for the P-bets. In those tests where preference reversals were made less substantial by ranking, the $-bets were ranked with many better options and the P-bets were ranked with many worse options. This suggests that if the range-frequency effect was at work, the value of the $-bet would be reduced and the value of the P-bet would be enhanced, which is indeed likely to reduce the number of preference reversals. Conversely, in the tests where preference reversals were largely unaffected by ranking, the relative rank of the $-bets was the same or higher than the relative rank of the P-bets, implying that the range-frequency effect would not decrease the value of the $-bet relative to the value of the P-bet. These findings offer a plausible explanation for the persistent substantial and systematic preference reversals in these ranking exercises.

Building on the Bateman et al. study, Oliver, with the use of the aforementioned life-expectancy bets, tested whether such ranking exercises can reduce preference reversals in circumstances where the $-bet and the P-bet are both ranked against a number of almost identical options [23]. Thus, the possible confounding influence of introducing a large set of different risky options in each ranking exercise (and thus the potential for the range-frequency effect to bias the results in complex ways) was largely absent. It was observed that, compared with the direct valuation procedure, implied valuation through ranking did indeed reduce the rate of strict preference reversal (from 36 to 20%), and that the reversals no longer occurred in a systematic direction. Moreover, the reason why the rate of preference reversal declined was because the respondents generally gave the $-bet a lower value through ranking than direct valuation. Although very tentative, this evidence lends further support to the argument that direct valuation methods (e.g., standard WTP exercises) may produce overvaluations of healthcare programs, particularly those that promise a chance of experiencing very good outcomes.

Overall, the fundamental message of the preference reversal phenomenon is that, contrary to the assumption generally held in economic theory, preferences are not always fixed within individuals, but may often, and perhaps usually, be constructed according to the way the decision task is designed and framed [26]. This represents an important, inescapable challenge to all those who wish to place individual and societal values on health and healthcare.

Financial & competing interests disclosure

Adam Oliver is Research Council UK Senior Academic Fellow and Corinna Sorenson is a Research Officer at the London School of Economics and Political Science. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this editorial manuscript.