A core topic in population-level bioethics concerns how to distribute scarce health-related resources at population-level. In these debates, some have focused on and defended universal substantive normative criteria, e.g., cost-effectiveness ideals, special concerns for the most severely ill, and/or inequality aversion (see, e.g., Johansson, 2014; Cookson, 2015; Cookson et al., 2022; Tännsjö, 2018; Hausman, 2023). Others have focused on the decision process distributors use and typically highlight the importance of deliberation and public reasoning (see, e.g., Rawls, 1993; Gutmann & Thompson 1997; Daniels & Sabin 2002; Daniels, 2008; Friedman, 2008; Fleck, 2009). A combination of substantive and procedural criteria seems desirable, but it is not obvious how they should be combined. This paper shows how accepting that substantive criteria admit of value incommensurability such that two options can be incommensurable with respect to them can be useful in hybrid approaches. In some sense, since value incommensurability (in the technical sense this paper adopts) can be a consequence of vagueness and/or incompleteness such ideas are already implicitly present in the literature (see, e.g., Daniels, 2008). However, explicitly recognizing that options can be incommensurable with respect to substantive criteria promises to bring clarity to both challenges and opportunities that ensue. It makes it easier to see, understand and solve the decision-theoretical challenges that arise for these hybrid theories and provides a way of understanding the role of the decision process in relation to substantive criteria.

The paper is structured as follows. In the next session, I introduce how I will understand value incommensurability and outline its implications in some further length. The section that follows shows how accepting incommensurability can be a way for proponents of procedural approaches to hold on to the idea that decision processes, deliberation and active participation in decision making matter while simultaneously accepting that substantive criteria of what is good determine how scarce resources should be distributed. In the last substantial section, I discuss three objections to the idea that incommensurability is important when developing hybrid theories: (i) the idea that equally as good as—the value relation—is simpler; (ii) the question of why any potential incommensurability should give us reason to go hybrid rather than just introduce an additional substantive criterion to settle a conventional ranking of all items; and (iii) the question of why reasons established with certain decision processes do a better job than substantive, independent reasons at ranking incommensurable options. There is a brief concluding section.

1 Value incommensurability and the scope of choice freedom

In a sense, all action-guiding substantive norms restrict the freedom of choice of agents that commit to them. They do not restrict what agents are able to do in a general sense, of course, but what they are able to do without violating the norms. Insofar as someone binds or commits themselves to a norm, this norm will restrict what they can choose without going against their commitments. The norm “distribute health resources in a cost-effective way” restricts what distributors who commit to it can do without violating the norm. Some norms—like “maximize expected Quality-Adjusted Life Years (QALY) per $”—are very restrictive in this way since they often tell decision making agents exactly what to do. Other norms—like “do not discriminate based on sex”— are less restrictive since they only tell decision making agents to avoid certain options. Accepting value incommensurability is a way of reducing the restrictiveness of a normative approach that puts forward substantive norms and expanding what I will call the scope of choice freedom. The more incommensurability one accepts, the more initially justified options decision makers will face. But before developing this argument, some clarifications regarding what I mean with value incommensurability are needed.

The recent literature on value incommensurability is riddled with terminological confusion that is partly due to disagreements regarding how to explain the phenomenon (cf. Andersson & Herlitz 2022a). Some use “incommensurability” in a very precise way to describe the phenomenon that a certain value cannot be placed on the same cardinal scale as another (e.g., Chang, 1997, 2015), some use it to describe incomparability (e.g., Anderson, 1993; Raz, 1986), and some use it to describe these phenomena but also vagueness and non-conventional comparative relations such as parity (e.g., Rabinowicz 2022a, b). In this paper, I will use value incommensurability (or incommensurability for short) in a broad sense to cover a wide range of comparability problems:

Value incommensurability: two items, x and y, are incommensurable with each other if it is not determinately true that x is better than y, not determinately true that y is better than x, and not determinately true that x and y are equally good.

On this definition, incommensurability obtains if some items are incomparable, if it is indeterminate which relation obtains between them or if some non-conventional comparative relation like parity obtains between the items (the term “determinately” is included in the definition in order to cover indeterminacy). Value-theoreticians debate which of these phenomena best explain incommensurability (see, e.g., Broome, 2022; Chang, 2022), but for this paper those discussions have limited importance (cf. Andersson & Herlitz 2022b). The focus here lies on the failure of a normative approach to fully determine a conventional ranking of items that have value such that an at least as good as-relation determinately holds between all pairs of items.

The question of how to explain the failure to determinately rank items in conventional ways can be set aside in this paper, but it might be good with some illustrations. If the substantive criteria “maximize health” is incomplete because some health states are incomparable (cf. Hausman, 2015), there is incommensurability between items that are compared with respect to health maximization on my definition. If a multi-criteria decision analysis approach put forward five substantive criteria for assessing options but no substantive notion of how to combine the criteria, there is incommensurability with respect to the substantive criteria on my definition (cf. Gongora-Salazar et al., 2023). If the principle of equality of opportunity is vague or indeterminate, some items can be incommensurability with respect to the principle on my definition (cf. Daniels, 2008). If some distributive options can be on a par with respect to the applicable distributive principles, there is incommensurability on my definition (Herlitz, 2023a).

A common argument that aims to establish the possibility of incommensurability is the so-called “small improvement argument” (cf., Chang, 2002; Andersson & Herlitz 2022a; Herlitz, 2017a, 2017b, 2017c, 2023a). The argument asks us to imagine two dissimilar valuable items, x and y, neither of which is determinately worse than the other, and contemplate if a small improvement of one of the items necessarily makes it, e.g., x + , determinately better than the other. x + is, by stipulation, determinately better than x. If x + is not also determinately better than y, one can infer that x and y cannot be determinately equally good, since determinate better than is transitive across determinate equal goodness. Since it was stipulated that neither of x and y was determinately worse than the other, the only remaining option is that they are incommensurable.

It is easy to come up with small improvement arguments in the context of healthcare policy and planning since prioritizations in this area need to weigh and compare very different goods against each other (cf. Herlitz, 2017a, 2017b, 2023a). How bad are mental health problems compared to back pain? How many people with paralysis are as bad as a life lost? How does an information campaign that aims at preventing drug use among teenagers compare to a campaign that aims at making young children exercise more? These are underlying questions that any general approach to priority-setting in healthcare contexts must address, and this raises questions about comparability: Do health states relate to each other so that there is a degree of mental health problems that is determinately exactly as bad as a certain degree of back pain, such that any improvement of one of the health states changes the comparative relation? Do health-related quality of life and loss of life relate to each other so that some exact number of people having a certain reduced health-related quality of life is determinately exactly as bad as the loss of a life and a small sweetening of either side will change the comparative relation? Do different public health policies that aim at improving different aspects of public health relate to each other so that there is an expected value of an anti-drug policy that is determinately equal to the expected value of a policy that aims at making children exercise more, so that the tiniest change in cost for the policies changes the comparative relation? A negative answer to any of these questions indicates the presence of incommensurability in the healthcare sector. Needless to say, there are countless other examples that can be put forward.

A common, initial, reaction to incommensurability is that it causes decision problems. If the only two alternatives (or the two “top” alternatives) are incommensurable, there is no determinately optimal option, no option that is determinately at least as good as all alternatives. A conventional view of rational choice holds rationality to require choosing an optimal option. If there is no determinately optimal option, it seems no choice can be rational (cf. Hsieh, 2005). This worry should not be exaggerated. Even in situations in which no option is determinately optimal, it is plausibly possible to make rational choices. It is of course true that one must change the conditions for what makes a choice rational from the determinate optimality condition to something else, but there are several ways to do that, the most straightforward being replacing the determinate optimality condition with a determinate maximality condition (see, e.g., Sen, 1997). On this line of thought, an option is a rational choice if it is not determinately worse than any alternative. When the only two options are incommensurable, it is true for both of them that they are not determinately worse than any alternative, and the determinate maximality condition then says that choosing either is rational. Interesting questions arise regarding whether being determinately maximal is sufficient for being a rational choice, but the idea that rational choice is impossible if options can be incommensurable is mistaken (cf. Rabinowicz 2008; Herlitz, 2016, 2020a, 2022).

A more troublesome decision-theoretical problem that follows from accepting incommensurability is so-called dynamic choice inconsistency (cf. Herlitz, 2022). If alternatives can be incommensurable, and if one takes choices of determinately maximal options to be rational choices, it is perfectly possible that a decision maker who makes rational choices at each choice node forms a set of choices that is itself not rational. Here is a simple illustration of that. Assume that x and y are incommensurable, that x + and y are incommensurable, and that x + is determinately better than x. Faced with a choice between x + and y, it is perfectly rational to choose y. If that is followed by an option to change the choice to x, it is perfectly rational to do that (y stands against x, and x and y are incommensurable). The problem is—of course—that by making two perfectly rational choices, the decision maker has ended up choosing an option that is determinately worse than some alternative that was available (choosing x + in the first choice node).

Dynamic choice inconsistency seems irrational on purely formal grounds, but it should also be noted that a decision strategy that is dynamically inconsistent can lead to significant value loss. If bureaucrats in a healthcare system were ordered to make distributive decisions with a method that is dynamically inconsistent (e.g., ordered to follow a vague distributive principle and choose determinately maximal options), they might end up forming a set of choices that generates significantly less value than what they could have generated, or a set of choices that attains a fixed set of values to a price that is significantly higher than it needed to be. To see this, consider how x + , x and y could represent healthcare materials such as scrubs and painkillers. A decision maker responsible for purchasing healthcare material in a hospital might face the choice first between scrubs and painkillers (x + and y), and then between slightly more expensive (but in no way better or nicer) scrubs and painkillers (x and y). It would here be rational, and in line with the orders given, to choose first painkillers and then change that choice to the more expensive scrubs. It is easy to see how a significant loss in value could arise at a system level if choice situations like this were common.

At a system level, a related problem also arises. Groups of decision makers who make simultaneous choices can together choose alternatives that are determinately worse than alternative options. Consider a healthcare system that puts in place a policy according to which decision makers working for the system should pursue two distinct values: maximize health and minimize severe health conditions. The policy does not specify exactly how these values should be combined so that it can be used to establish a determinately best option in all cases. Instead, the policy admits of incommensurability. Decision makers are told to choose any determinately maximal option in all choice situations. It is perfectly possible that two decision makers simultaneously face two almost identical choices between two incommensurable options where one option is determinately best with respect to health maximization and the other is determinately best with respect to severe health conditions minimization. The choice situations only differ in that the option that is determinately best with respect to health maximization is slightly better in one of them. It would in this context be perfectly permissible for the decision makers to make choices that generate less value at a system level than some other available choices would have generated: they can permissibly choose the slightly worse option that is determinately best with respect to health maximization and the option that is determinately best with respect to severe health conditions minimization, but it was possible for them to choose the slightly better option that is determinately best with respect to health maximization and the option that is determinately best with respect to severe health conditions minimization. They permissibly form a set of choices that generate less value than an alternative, available set of choices. At a system level, this general approach—that allows for options to be incommensurable and instructs decision makers to choose determinately maximal options—could lead to big losses of value.

There are problems that arise when one accepts the possibility of options being incommensurable, but there are also potential upsides. When substantive normative criteria do not admit of incommensurability and always fully determine how all options relate to each other in conventional ways there will always be an option that is determinately optimal, i.e., determinately at least as good as all alternatives. Sometimes, there will be more than one such option (because two or more options are determinately equally good), but in the context of healthcare policy and planning it will plausibly most often be the case that there is only one. In healthcare policy and planning, substantive criteria typically express the desirability of meeting health needs or maximizing health (or its value), sometimes in combination with inequality aversion of different kinds (see, e.g., Ord, 2013; Herlitz & Horan, 2016; Sharp & Millum 2015; Hausman, 2023). It will plausibly be extremely rare that two or more distributive options will satisfy health needs to the exact same extent or generate exactly the same amount of health (or value of health) and adding inequality aversion to the mix will not change that. In most situations, there will be one and only one option that is determinately optimal in light of the substantive approaches that are most often discussed, and a decision maker who is committed to acting in accordance with substantive criteria will be compelled (sometimes required) to choose that option.

If one accepts the possibility of incommensurability, things change. If one accepts a set of substantive criteria and also the possibility that these—due to incommensurability—will sometimes fail to fully determine a conventional ranking, there will more frequently be several options that are determinately maximal. This might not be true in all contexts, but it seems very plausible in the context of healthcare policy and planning. Consider, for instance, someone who embraces the idea that distributors should maximize health (or its value), minimize inequality in health, and minimize the number of people who live with very severe health conditions. One distributive option (A) might be best in terms of health maximization, another (B) best in terms of reducing inequalities in health, and a third (C) best in terms of making sure as few people as possible live with very severe health conditions. This is illustrated in Table 1:

Table 1 When options are good in different ways
Full size table

If one rejects the possibility of incommensurability, in most situations like these, one of these options (A, B, C) is determinately optimal (overall, determinately best) and a decision maker committed to the three substantive criteria will choose that option (it is of course possible that some of the options are determinately equally good, but considering the overall judgment will be based on a function that takes the three substantive criteria as arguments, that will be very rare). If one instead accepts that incommensurability is widespread, in many situations like these some options will be incommensurable and a decision maker who is committed to the substantive criteria will not be bound to make any specific choice, but instead face a menu of options that are justified by the substantive criteria.

One might, in other words, say that the scope of normative choice freedom increases with the acceptance of incommensurability (cf. Chang, 2022). Furthermore, the scope of choice freedom continues to increase the more widespread and persistent the incommensurability is, i.e., the more one can change an item that is incommensurable with another without changing the comparative relation (cf. Herlitz, 2020b). A decision maker who wants to follow substantive normative criteria has more options to choose between the more incommensurability there is.

This increase in the scope of choice freedom has interesting theoretical implications. One challenge for approaches to how to distribute scarce healthcare resources that put forward and defend specific substantive distributive principles is that if they are implemented, they leave little room for other types of values such as considerations for the beliefs and preferences of those affected. In a sense, they are value-imposing. Since accepting incommensurability is a way of increasing the scope of choice freedom, accepting incommensurability is a way of meeting this challenge. Paired with an acceptance of incommensurability, substantive approaches are less value-imposing. They still impose some value on those that accept them, but as the scope of choice freedom increases, the value imposition decreases. A normative approach that puts forward the idea that societies should rely on a determinately complete prioritarian ideal that combines health maximization and inequality aversion and always fully determines how distributive options relate to each other will impose this precise prioritarian ideal on whomever accepts the approach as correct. A normative approach that puts forward an incomplete prioritarian ideal that combines the ideals of health maximization and inequality aversion and fails to always fully determine how distributive options relate to each other will impose the values of health maximization and inequality aversion on whomever accepts the approach as correct but leave it unspecified exactly how these values should be weighed against each other. In this sense, accepting incommensurability can help reduce the worry that substantive approaches are value-imposing.

It should, of course, be noted that this increase in the scope of choice freedom also introduces some challenges. These will be different depending on what context one talks about. In the context of healthcare policy and planning, a challenge that stands out relates to discrimination. Whatever substantive decision criteria one has, the less frequently they manage to fully guide action, the more frequently the decision makers own biases, prejudices and attitudes will influence which decisions are made. When decision makers are distributors of healthcare resources of different kind, this actualizes an increased risk of discrimination (Herlitz, 2023b).

2 Incommensurability and procedural approaches

Whereas the previous section emphasized a feature of incommensurability which proponents of universal substantive normative criteria can see as attractive, this section shows a way in which accepting incommensurability might be attractive to proponents of procedural approaches.

One reason to reject independent substantive criteria is that they seemingly come at a cost of agency. If the same substantive criteria apply to all agents, agents that accept them seemingly have no influence over what they ought to do. This point is familiar from debates regarding utilitarianism, and in particular a version of the so-called “demandingness objection” (see, e.g., de Lazari-Radek & Singer, 2014). If we ought to always do that which maximizes the total sum of expected well-being in the world, there is always an objective benchmark that determines what we ought to do, and those who use the benchmark never get to influence what they ought to do. If substantive criteria were universally valid such that all societies ought to always distribute scarce healthcare resources in accordance with some substantive criteria, distributors who in specific choice situations want to do the right thing are bound by the substantive criteria and must choose the option that is most supported by the criteria, e.g., the most cost-effective option. Within a theoretical framework that puts forward universal substantive norms for distributors in societies, members of society are not ascribed any opportunity to influence how their scarce goods should be distributed by the theory.

Following that line of thought might lead one to reject theoretical frameworks that put forward universal substantive criteria such as cost-effectiveness and inequality aversion and instead embrace procedural approaches that put the emphasis on outlining how distributive choices should be made. In the context of healthcare policy and planning, a particularly influential such procedural approach is Norman Daniels’s “Accountability for Reasonableness”, according to which what matters when distributors deliberate and make decisions about how to distribute scarce healthcare resources is that (i) they only rely on reasons that are relevant, (ii) they make the decisions in a public/transparent way, (iii) the decisions can be appealed, and (iv) the decisions are enforced (see, e.g., Daniels, 2008). According to Daniels, implementing decision processes that satisfy these conditions will lead to fair decisions in pluralist societies where different people value different things. Clearly, relying on this kind of decision process will not bind distributors to any universal substantive distributive criteria (besides potential substantive criteria that might be baked into the elusive relevance condition which on some understandings is partly substantive), and members of society are provided a chance to influence the distribution of scarce goods. Of course, often only a few individuals can be present in the actual deliberation process, but in the ideal scenario all points of views are represented in the deliberation process and decisions that are made can be appealed.

However, Daniels’ proposal—and indeed all proposals that reject significant and explicit importance to clear and well-defined substantive criteria—risk leading to decisions that are seemingly obviously bad and objectionable. Only substantive criteria can ensure that discriminatory decisions such as always prioritizing men over women get recognized as bad and objectionable. Only substantive criteria can ensure that purely wasteful choices are avoided, e.g., choosing a more expensive contractor who in no way can be expected to do a better job over a cheaper option when a hospital needs renovations. And only substantive criteria can ensure that healthcare policy and planning reflects an empathetic attitude and special concerns for those who suffer the most. It is of course perfectly possible that those individuals that take part in the deliberation will put forward arguments and reasons that establish that discrimination and waste are bad, and that empathy is good, but the conditions posed on the decision process in no way ensures this.

The possibility of incommensurability provides a different path. Rather than dismissing substantive criteria with reference to how they undermine self-determination, proponents of procedural approaches can invoke incommensurability and point to how substantive criteria must admit of incommensurability such that they only manage to partly determine how to distribute healthcare resources. According to this line of thought, substantive criteria can be important, but they cannot be the be-all and end-all. Since substantive criteria will establish that some options are incommensurable, they are perfectly compatible with procedural approaches.

This way of thinking reveals a theoretical space for thinking about procedural approaches in a different way, as a complement to substantive criteria that fail to fully determine how to distributive scarce resources. On the one hand, this limits the possible influence of decision processes. Instead of fully determining which of all existing options to choose, they determine which of a set of determinately maximal, incommensurable options to choose. This is in line with how some in deliberative democracy theory have suggested that an important role of public deliberation can be to specify underspecified principles or ideals (cf. Herlitz & Sadek, 2021; Herlitz, 2018, 2023a). On the other hand, one can ascribe decision processes an additional role. As mentioned in the previous section, accepting incommensurability means that one runs into decision-theoretical problems such as dynamic choice inconsistency. To mitigate this problem, one can ascribe decision processes the role of ensuring that one does not violate rationality requirements (more on this in the next section).

In other words, incommensurability is an essential part of a special kind of hybrid approaches. If one accepts that substantive criteria admit of incommensurability in the sense that they fail to determinately rank all options in conventional ways in all choice situations, space opens up for procedural approaches to complement substantive criteria in a special way. The procedural approaches provide an answer to what can justify a choice between options that are incommensurable: the outcome of a certain process.

Hybrid approaches that accept incommensurability can of course look very different from each other. Different substantive criteria can be invoked to discard impermissible alternatives, one can accept incommensurability to different extents, different procedural approaches can be used to complement substantive criteria, and there are different ways of combining substantive criteria and procedural approaches. The purpose of this paper is not to defend any specific hybrid approach, but rather to point out theoretical advantages with hybrid approaches that accepts incommensurability.

Arguably, some hybrid approaches of this kind are already present in debates on how to evaluate distributive options in healthcare planning and policy. An example of a type of hybrid approach that seem committed to incommensurability without being explicit about it is a certain type of multi-criteria decision analysis approach. These approaches suggest that alternatives should be evaluated according to a set of evaluative criteria (substantive criteria), but that the relative importance of the of the different evaluative criteria should be determined with reference to what stakeholders express in deliberative process (cf. Gongora-Salazar et al., 2023). Insofar as the reason for invoking a deliberative process is something like the importance of self-determination or public justification, this is a hybrid approach. Since the approach says nothing substantially about how the substantive, evaluative criteria should be combined, many alternatives will be incommensurable with respect to these criteria, and the procedural element is introduced as a way of complementing substantive criteria that admit of incommensurability.

3 Answers to objections

In the previous two sections, I attempted to show that accepting incommensurability provides fruitful grounds for developing a certain kind of hybrid theory of how to allocate scarce healthcare resources. Such hybrid theories promise to build on both substantive and procedural approaches, and to face weaker versions of certain objections to these approaches. In this section, I address three issues relating to the usefulness of incommensurability in this context.

3.1 Why incommensurability and not equally as good as?

One objection to the idea that accepting incommensurability helps us develop good hybrid theories is that it is unnecessarily complicated. It might be suggested that the introduction of incommensurability is a very cumbersome path toward a hybrid theory. Incommensurability is a strange phenomenon that can be hard to understand, why not build hybrid theories in a simpler way? For instance, why not say that some substantive normative criteria operate as side-constraints and in that sense determine what is impermissible, while the options that are not deemed impermissible are considered determinately equally good (cf. Rid, 2009)?

The short answer to why this is an unsatisfactory solution is that the value relation determinately equally as good as is not persistent, whereas incommensurability is, at least to some extent, persistent. Value relations differ from each other with respect to how persistent they are, i.e., the extent to which they remain unchanged when one changes the items between which they hold, something which has received increasing attention in the value-theoretical literature (see, e.g., Handfield & Rabinowicz, 2018, Rabinowicz 2022a; Herlitz, 2020b). The relation determinately better than is, e.g., persistent through all improvements of the determinately better item, all worsenings of the worse item, and depending on its type, some or all improvements of the worse item and worsenings of the determinately better item. If an apple is determinately better than a pear, the apple will remain determinately better than the pear no matter how much better one makes the apple, no matter how much worse one makes the pear, and through some (unspecified) amount of improvements of the pear. The relation determinately equally as good as is, notably, completely impersistent. This becomes obvious if one considers that if determinately equally as good as was not completely impersistent there would exist an improvement ( +) of an item, x, that is determinately equally as good as another item, y, such that the following would be true:

  1. (1)

    x is determinately equally as good as y (basic assumption)

  2. (2)

    x + is determinately better than x (+ is an improvement; it renders items determinately better)

  3. (3)

    x + is determinately equally as good as y (follows from accepting that determinatelg equally as good as is persistent, the hypothesis)

  4. (4)

    x + is determinately equally as good as x (follows from (1), (2) and the transitivity of determinately equally as good as)

  5. (5)

    x + is both determinately better than and determinately equally as good as x (follows from (2) and (4))

(5) is obviously false. Nothing can be both determinately better than and determinately equally as good as something else, just like a presidential candidate cannot both win and tie with another presidential candidate in a single election and no man can be both taller and equally as tall as another man. One of the previous steps must thereby be false. Of (1), (2), (3) and (4), (3) is clearly the weakest premise. Items can be determinately equally good (1). Improving an item makes it determinately better; that is what it means to improve an item (2). It is an analytic truth that determinately equally as good as is a transitive relation (4). Meanwhile, we seem to have no reason at all to expect determinately equally as good as to be persistent; that was just a hypothesis that was introduced to investigate whether it was true.

Incommensurability is, by its nature, persistent to an unspecified non-zero degree. Incommensurability persists through some improvements (cf. the small improvement argument in the first substantive section of this paper). It is the persistency of incommensurability that makes it possible that items can relate to each other in the following way:

x is incommensurable with y

x+ is determinately better than x

x+ is incommensurable with y

The reason this constellation is unproblematic in the case of incommensurability is that incommensurability is not transitive, something which is completely uncontroversial (see, e.g., Raz, 1986; Carlson, 2010; Andersson & Herlitz 2022a).

Allowing for the relation that obtains between two items when no unique determinately best item exists to be persistent to some extent has some very significant upsides in the context of healthcare allocation and substantive criteria that might apply in that context. First, the possibility of the constellation above is directly appealing in the context of healthcare allocation. Consider again the types of choice situations decision makers in healthcare face. These are situations in which hard choices must be made between, for instance, saving identified lives and preventing (perhaps much larger number of) future deaths, between benefitting a patient group with mental illnesses and benefitting a patient group with backpain, and between cost-effectively providing maternal care in major cities and less cost-effectively ensuring that also women living in rural areas have easy access to maternal care. In some of these choice situations (as well as in many others), neither option will be determinately better than the other. Allowing the relation that holds between two such options to be persistent means that small changes to the options do not necessarily change how they relate to each other. Since situation in healthcare policy and planning often involve very different values, this is—I contend—just the way it should be. Small changes in financial costs are bad arbiters when we need to choose how to weigh identified present lives lost against expected lives lost, how to weigh the interests of a patient group with mental illnesses against the interests of a patient group with backpain, and how to compare cost-effectiveness and concerns for underserved, rural communities. The persistency of the value relation is what secures against bad arbiters of this kind.

Secondly, persistency is needed to secure a sizeable scope of choice freedom. Insofar as one is attracted by hybrid theories because of their ability to combine substantive normative criteria with ascribing importance to beliefs and preferences of the people affected by the decisions as well as deliberation of decision makers, it is important that the approach leaves some room this. If the substantive criteria fully determined what decision makers ought to do to a too great extent, there would be little room for other aspects to influence the choice, and the hybrid nature of the approach would be minimal. The persistency of incommensurability ensures that there is space for non-substantive criteria to play a significant role. Consider again Table 1:

If the substantive criteria did not admit of incommensurability, there would exist a precise set of values for A that made A determinately not worse than B and B determinately not worse than A, given a fixed distribution of other values. Any deviation from that set of value—no matter its size—would change how A and B relate to each other and strip the decision maker of influence. Assuming that some different ways of measuring health maximization, minimize inequality and minimize very severe conditions have been established, this can be illustrated in Tables 2 and 3:

Table 2 When options are good in different ways (with values)
Full size table
Table 3 When options are good in different ways with small improvement
Full size table

In Table 2, values in the different value dimensions have been plotted into the table. The higher the value, the better an item is in the dimension. The assumption is that this is a distribution of values that makes it true that A is determinately not worse than B and B is determinately not worse than A (for simplicity, assume that C is determinately worse than both). If the approach did not admit of incommensurability, A and B are determinately equally good, which is impersistent. This means that any improvement or worsening of either A or B would change the comparative relation, illustrated in Table 3:

A slight increase in the amount of health generated by A would mean that it (A +) is determinately better than B, which means that the substantive criteria fully determine a best option. Decision makers that bind themselves to the substantive criteria but use other considerations when these criteria fail to fully determine what option to choose will no longer resort to these other considerations to make their choice between A + and B; A + is determinately best. The same would be true regardless of how one improved (or worsened) A or B. This illustrates how extremely limited the role of considerations other than substantive criteria are in hybrid theories that do not invoke incommensurability. For all situations in which considerations other than substantive criteria are relevant to rank two or more options that are determinately maximal, it will be true that discovering the smallest of mistake in one’s calculations will turn the choice situation from one in which deliberation was important to one in which one simply ought to follow substantive criteria. That is not what one wants from a hybrid theory.

Since determinately equally as good as is impersistent and persistency is a desirable feature in the context of hybrid theories of how to distribute scarce resources in the healthcare sector, building hybrid theories around the fact that substantive criteria sometimes establish that some alternatives are determinately equally good is unappealing. By invoking incommensurability, one gets a comparative relation which is persistent. This can enable a sizeable scope of choice freedom, and one is able to provide ample space for considerations other than the substantive criteria.

3.2 Why not use some other reason as “tiebreaker”

Some of those willing to accept incommensurability might remain unimpressed by the idea that decision processes should settle the issue of what to choose, as opposed to simply using some other substantive criterion to settle the matter. For instance, it might be proposed that if three health policies are incommensurable, one should choose the policy that benefits the population that was benefitted the least by previous policies. That might seem like a fair “tiebreaker”.

The idea that some substantive criterion should be used as tiebreaker when initial substantive criteria fail to fully determine what to do runs into problems; the approach can violate basic contraction consistency, a condition that is typically considered a basic requirement of rationality. To see this, consider a situation where one has three health policies under consideration (X, Y, Z), and they relate to each other in the following way:

With respect to the substantive criteria: Policy X is determinately better than Policy Y, Policy X and Policy Z are incommensurable, and Policy Y and Policy Z are incommensurable. (To shorten, I will write that: X > Y; X ≈ Z; Y ≈ Z.)

With respect to the tie-breaker criterion: Policy Y is determinately better than Policy Z, which is determinately better than Policy X. (In short form: Y > Z > X.)

Basic contraction consistency says that it would be irrational if an option’s status as permissible changes when the choice set shrinks:

Basic contraction consistency: If an alternative, p, is permissible in a choice set C, then it is also permissible in a choice set C’ that is a subset of C and contains p (Chernoff, 1954; Fleurbaey et al., 2009; Herlitz, 2019, 2022).

As long as the options remain the same and there is no reason to evaluate the options differently with respect to the substantive criteria when the choice set changes, violating basic contraction consistency seems irrational.Footnote 1 It is like ordering a double espresso in a coffeeshop and upon learning that the coffeeshop has run out of ice-cream change the order to a single espresso.

In the specific context of hybrid approaches to healthcare policy and planning, violations of basic contraction consistency entail an arbitrariness to the approach that undermines its ability to provide good justifications of decisions to those that are affected by them. An explanation for why a patient group does not receive treatment that entails that they would have received treatment if the decision maker had had another option that they in any case would not choose seems problematic. For instance, a group of cancer patients might get told that they will not receive the treatment they want because the decision maker prioritized funding a different treatment for a different group of cancer patients, but the explanation for the decision is such that they realize that if the decision maker had had a third option which would have benefited a third group, the outcome would have been different and the first group would have received the treatment they need. That is the kind of explanation that sometimes would be provided by an approach that violates basic contraction consistency.

In the example above, it is obvious that basic contraction consistency is violated (cf. Herlitz, 2019, 2022). From the full set of options, Policy Z would be chosen. Y is determinately worse than X and thereby discarded as an unfeasible option; it is covered. The only remaining options, X and Z, are incommensurable and the tiebreaker needs to settle the issue. According to the tiebreaker, Z is determinately better than X. However, from a contracted set consisting only of Y and Z, Y would be chosen. Y and Z are incommensurable, and according to the tie-breaker Y is determinately better than Z. In other words, this is a choice strategy according to which it is required to change one’s mind merely due to the fact that some unchosen option disappears from the set of available options.

The argument against using (unconstrained) substantive criteria as tiebreakers when dealing with options that are incommensurable is, in other words, that this can lead to violations of rationality requirements. They can do this because tiebreakers are not constrained (Herlitz, 2019). They are not constrained by formal constraints (e.g., an independent reason is invalid if it violates rationality requirements), and they are not constrained by requirements inferred from the substantive criteria they are supposed to complement (e.g., they are not reasons that specify vague substantive criteria).

If some options are incommensurable with respect to health maximization and inequality aversion it might seem reasonable and fair-minded to choose between them by ranking them in terms of what benefits the patient group that has been waiting for assistance the longest. But since that criterion is neither constrained by formal constraints or content-wise related to the first two criteria, it is perfectly possible that it will lead to violations of rationality requirements. When health maximization and inequality aversion rank three options in the following way: X > Y; X ≈ Z; Y ≈ Z, a criterion that focuses on how long patient groups have waited for benefits might well rank the options as follows: Y > Z > X. That is why (unconstrained) substantive criteria make for bad complements when initial criteria lead to incommensurability.

3.3 Why treat reasons grounded in decision processes differently?

The introduction of substantive considerations as tiebreakers can lead to violations of rationality requirements. This could lead some to believe that all types of tiebreakers actualize this problem. However, different types of tiebreakers have different properties, and some types of tiebreakers promise to do significantly better with respect to rationality requirements. Tiebreakers that are established with certain decision processes can, for instance, do significantly better in this respect.

To see how different tiebreakers can function in different ways in relation to substantive criteria, consider how different types of reasons can have different properties depending on where they come from, how they are grounded. There are different views of what can ground practical reasons. Notably, it has been suggested that they might be grounded in both emotions and facts. A different distinction can be drawn between reasons that are given and reasons that are created (Chang, 2013). According to this line of thinking, some reasons are reasons just in virtue of how the world is; they are just there, given, which might be due to emotions or facts in the world. These reasons can be contrasted with reasons that are not just there, but rather get created through acts of volition; they arise in the world when individuals with agency put themselves behind certain decisions and make choices.

Reasons that are grounded in the fact that they follow from decisions that are the outcome of processes with certain features are structurally different than independent reasons in a way that tracks the distinction between created and given reasons. This has implications for what sorts of features they have and how they can be introduced as tiebreakers. When dealing with reasons that are given, we can put conditions on which substantive reasons to select. When dealing with reasons that are created, we can put conditions on how to create them. Created reasons are thereby different from given reasons in the sense that we can put constraints on what form created reasons can take while given reasons seem to simply come to us in whatever form they come.

Because one can introduce formal constraints on what created reasons are valid, these reasons can avoid violations of rationality requirements. One can task decision processes that ground the basis for choosing between incommensurable alternatives with coming up with such bases that do not lead to violations of rationality requirements. For instance, if the substantive criterion used is an incomplete prioritarianism, one can suggest that the decision process that aims at establishing a basis for choosing between options that are incommensurable with respect to the prioritarianism should lead to a specification of the prioritarianism in question. That would not lead to any violations of rationality requirements.

Now, it could be objected that there is no difference between this and simply invoking as a tiebreaker a certain specification of prioritarianism, a substantive criterion. But there is a difference, a big difference. Whereas invoking a specification of prioritarianism as a substantive criterion removes the incommensurability all together and gets one back to imposing a certain prioritarian value, suggesting that a decision process should come up with a specification of prioritarianism will preserve the incommensurability, and thereby it allows for different societies to exert their own agency and come up with their own specifications of how much priority they want to give to the worse off.

If one wants to preserve the space for deliberation that incommensurability enables it is a bad idea to complement substantive criteria that admit of incommensurability with reasons that are given. Furthermore, if we want a “tiebreaker” that not only guides choice but also ensures that we do not violate rationality requirements, we need to rely on tiebreakers that can be tailored to this task, or that actually do this. We can ensure that we get tiebreakers of this kind by tasking those who participate in the decision processes that establish tiebreakers with coming up with such tiebreakers.

4 Conclusion

Value incommensurability is a phenomenon that can arise when items are good in very different ways. Neither of two items is determinately worse than the other, but they are not determinately equally good either. This causes problems for decision theory, but it also reveals theoretical opportunities to develop alternative approaches to what sound decision making amounts to. This paper explored whether incommensurability is a helpful tool in the pursuit of hybrid approaches to how to distribute scarce healthcare resources. It suggested that one appealing feature that appears when one accepts the possibility of value incommensurability is that it increases the scope of choice freedom. Such increase in the scope of choice freedom makes it easier to avoid the criticism that substantive approaches are too value-imposing. Furthermore, accepting incommensurability is a way for proponents of procedural approaches to accept some substantive criteria without having to give up on ideals of agency and the importance of deliberation and public reasoning. Incommensurability is a useful tool in hybrid theories. Those working with hybrid theories of how to distribute healthcare resources should recognize this.

Those who already endorse hybrid theories that entail that options can be incommensurable with respect to substantive criteria can benefit by explicitly recognizing this. Such recognition can make it easier to identify decision-theoretical challenges that arise due to incommensurability, and it sheds light on the procedural elements of the theories. The procedural elements of a hybrid theory can be designed so that one avoids dynamic choice inconsistency and violations of rationality requirements, but a first step is to recognize that the problems might arise, which is helped by recognizing the possibility of incommensurability.