A Defense of Pluralist Egalitarianism under Severe Uncertainty: Axiomatic Characterization*

Abstract

Severe uncertainty plays a critical role in many problems of distributive justice, such as social security, public health, public projects, budget deficits, and climate change. Under severe uncertainty, available information does not allow us to assign precise probabilities to possible states of affairs. A recent example of severe uncertainty is the impact of COVID-19. How policy-makers should evaluate different distributions of well-being in such a situation of severe uncertainty is of vital importance to society. Indeed, the COVID-19 pandemic has induced a need to ration medical resources, such as vaccines, using relevant principles of distribution. Such principles have been hotly debated by egalitarians, many of whom are pluralists.1 This article addresses the problem of the distribution of well-being by using an axiomatic approach to pluralist egalitarianism.

Rowe and Voorhoeve’s view can be interpreted as an axiomatic approach to pluralist egalitarianism; it helps to clarify competing claims of a relevant kind and thereby enables policy-makers to evaluate uncertain social situations. They illustrate this by showing how RV pluralist egalitarianism works in particular examples.

There is a need to articulate the axioms involved more explicitly, however, as well as to analyze more rigorously whether and to what extent those axioms are compatible with each other. Furthermore, to assess and choose between competing claims, it would be useful to have a criterion for social evaluation that satisfies the relevant axioms and that orders all possible distributions in a consistent manner. In this article, we introduce axioms of impartiality, efficiency, ex post egalitarianism, and social rationality under severe uncertainty, and address the issue of their compatibility. We then characterize a social evaluation criterion, statewise maximin, by those axioms.3

Although we focus on cases of severe uncertainty, our results show that axiomatization is invaluable in determining what kind of value pluralism is promising as an egalitarian theory. As Iwao Hirose has argued in a different but related context, pluralist theories are often unclear about how many principles they include and/or to what extent those principles are (in)compatible with each other.4 An axiomatic analysis can address these issues—through axiomatic characterization, we can spell out a normative criterion of pluralist egalitarianism.

The argument in this article proceeds as follows. Section II presents our basic framework. Section III specifies the principles of egalitarianism, impartiality, and social rationality. Section IV argues that a standard efficiency axiom under uncertainty, ex ante Pareto, is not compelling, and substitutes another axiom, Pareto for equal or no risk. Section V addresses statewise maximin and its axiomatic representation. Section VI presents some brief concluding remarks. The Appendix lays out a formal analysis.

In this section, we introduce the framework used for our analysis. Following Rowe and Voorhoeve, we use an Ellsberg-type example to epitomize the situation in which decision-makers cannot assign precise probabilities to the possible outcomes of their choice. Suppose that two individuals, Amy and Bob, choose a ball from an urn that contains an unknown number of red and black balls. This represents severe uncertainty. Suppose further that the final distribution of levels of well-being depends on the color of the ball drawn. Thus, the color refers to a state of the world. A social evaluator is expected to compare prospects by appealing to social preferences to evaluate uncertain social situations in terms of their relative desirability.

Let $R$ be the set of real numbers. $X\in R^4$ denotes a social prospect (or distribution) in question, which is described in Table 1.

Here, we assume that $i=A,B$ denotes Amy and Bob, and $s=r,b$ denotes the state of the world described by the color of a drawn ball, respectively. $x_{\mathrm{is}}$ represents individual $i$’s well-being in $X$ in state $s$. For each individual $i$, $X_i=\left(x_{\mathrm{ir}},,,,x_{\mathrm{ib}}\right)$. Moreover, let $X_r$ (resp. $X_b$) be a final distribution of $X$ when a red (resp. black) ball is drawn: that is,

Well-being levels are represented by real numbers that are fully measurable and ordinally interpersonally comparable.5 We assume that, although individuals do not ex ante know their final well-being levels, a social evaluator precisely estimates the final distributions in each state.

Each individual $i$ has a function $U_i:R^2\to R$ to evaluate the person’s own uncertain situation. For each $X_i$ and $Y_i$, $U_i\left(X_i\right)\ge U_i\left(Y_i\right)$ means that $X_i$ is at least as good as $Y_i$ for individual $i$. $U_i$ is referred to as individual $i$’s ex ante utility function. We assume that $U_i$ is continuous and strictly monotonic: for each $X_i$ and $Y_i$, if $x_{\mathrm{is}}\ge y_{\mathrm{is}}$ for all $s$, then $U_i\left(X_i\right)\ge U_i\left(Y_i\right)$; in addition, if $x_{i{s}^{\prime }}>y_{i{s}^{\prime }}$ for some s′, then $U_i\left(X_i\right)>U_i\left(Y_i\right)$. Moreover, for simplicity, we assume that, for $X_i$ such that $x_{\mathrm{ir}}=x_{\mathrm{ib}}=x$, $U_i\left(X_i\right)=U_i(x,x)=x$. Although our setting is general, our main results hold even if ex ante utility functions are restricted to particular forms satisfying these conditions.

Our framework assumes that Amy and Bob may have different ex ante utility functions. A notable example is the case in which they have subjective expected utility functions with different probabilistic beliefs. The occurrence (or even mere possibility) of differences in probabilities like these leads us to address an important problem under severe uncertainty: namely, the problem that Philippe Mongin called “spurious unanimity.”7 As will become evident, this problem affects many cooperative projects, and thus needs to be taken seriously as a fundamental problem for a pluralist egalitarian view.

There are also problems associated with situations in which the social evaluator has access to more (relevant) information than the individuals. A pandemic is a paradigmatic example of this kind of problem. In situations like these, the evaluator can use her own probabilities based on the relevant information available to her. Although our main results still hold in cases where individuals’ situations are evaluated in terms of the social evaluator’s probabilities, for the sake of generality, we also consider the case in which the social evaluator uses the individuals’ probabilities, such as the problem of public goods provision discussed in Section IV.

This principle seems intuitively plausible. To see this, compare the following two situations: (1) both Amy and Bob can enjoy a reasonable quality of medical service; (2) Amy can enjoy a very high-quality medical service, while Bob has no access to medical services at all. Suppose that higher-quality medical service leads to higher well-being, because better health resulting from appropriate medical treatment in the high-quality medical service condition improves people’s quality of life. From an egalitarian point of view, it is reasonable to judge (1) to be at least as good as (2).

It might be objected that ex post egalitarianism is too strong because it requires excessive inequality aversion. Our response to this objection is twofold. First, this axiom can be applied without cardinal interpersonal comparisons of well-being. It is important to note that full cardinal interpersonal comparability is not assumed, but rather obtained as a result of characterizing the maximin criterion. Second, and more importantly, the conflicts between relevant principles of a pluralist egalitarian view revealed below still follow if ex post egalitarianism is replaced with the Pigou−Dalton condition, which is a much weaker principle. According to the Pigou−Dalton principle, the same value $t$ of well-being is “transferred” from the better off to the worse off. Conflicts arise between the Pigou−Dalton principle and other relevant principles, similar to those apparent between ex post egalitarianism and those principles.9 On a related note, we show a different way of expressing statewise maximin by replacing ex post egalitarianism with a weak version of the Pigou−Dalton condition, impartiality, and ordinal full comparability of well-being (see Appendix for details).

Table 2 illustrates what dominance requires.

Suppose that the social evaluator supports ex post equality. Then $Y_r$ and $Y_b$ are socially preferred to $X_r$ and $X_b$, respectively. This implies that the final distributions of $Y$ are socially chosen over those of $X$ in all states of the world. Dominance requires that, under this situation, $Y$ should be chosen over $X$ ex ante. If this axiom is violated, society may choose a policy that results in the worse consequence, such as $X$ in this example.

Impartiality is an essential requirement for theories of egalitarian justice. John Rawls emphasized it as the most important premise.10 From impartiality, together with other relevant premises, various key principles can reasonably be derived. They include Rawls’s principle that gives lexical priority to the improvement of the situation of the worst off, which would be unanimously selected by people in a society under the veil of ignorance—that is, by people who have no information about their congenital capacities and social status.

According to impartiality, these distributions are equally good, which is intuitively appealing. Consequently, we should consider impartiality as a central requirement for a pluralist theory of egalitarian justice.

Our version of pluralist egalitarianism does not include this principle. This requires some explanation. Ex ante egalitarianism is often considered to be one of the most important principles of pluralist egalitarianism. For example, Richard Arneson argues that the ideal of equality of opportunity for welfare would obtain if and only if all agents “face equivalent decision trees—the expected value of each person’s best (=most prudent) choice of options, second-best … nth-best is the same” in an effective sense, among other things.13 It follows that the less some situation deviates from the ideal, the more desirable it is from an egalitarian perspective. This idea is included in RV pluralist egalitarianism, according to which we should aim to reduce inequality in people’s prospects.

As stated above, our pluralist egalitarianism does not include ex ante egalitarianism, for three reasons. First, it conflicts with ex post egalitarianism under dominance.14 Consider the case described in Table 3.

On the one hand, the expected well-beings are more equal in $X$. On the other hand, because the final well-beings are more equal in $Y,$ $Y$ is better according to ex post egalitarianism and dominance. This illustrates a conflict between ex ante egalitarianism and ex post egalitarianism under dominance.

Second, ex ante egalitarianism is also in conflict with dominance and impartiality, which are intuitive and compelling requirements in egalitarian justice. This conflict can be shown by using an example summarized in Table 4.

By reflexivity15 and impartiality, $X_r$ and $X_b$ are as good as $Y_r$ and $Y_b$, respectively. Then, dominance implies that $X$ is as good as $Y$ ex ante. However, ex ante egalitarianism claims that $X$ is better than $Y$ ex ante, which comes into conflict with dominance and impartiality. Note that this conflict does not depend on the two people’s probabilities, because we use dominance only.

It might seem counterintuitive to evaluate $X$ and $Y$ as equally good. However, from the perspective of an impartial evaluator, these distributions could be considered equivalent in the sense that their final distributions of well-being are equally good in each state of the world. This is a reasonable evaluation because, even if the evaluator does not know which state will occur, s/he knows (and thus can evaluate) the final distributions in each state and can combine the evaluations by dominance. This implication supports our focus on distributions of final well-being.16

Third, it is not clear precisely what equality of ex ante utility means. John Broome’s critique of the notion is relevant here.17 While well-being may be valuable in and of itself, the same is not necessarily true for ex ante utility—the latter is valuable simply because achieving ex ante utility is a way of promoting well-being. Hence, it is merely instrumentally valuable, while equality of final well-being may be inherently valuable; therefore, they are not valuable in the same way. It could still be claimed that ex ante equality can be justified on the basis of the notion of a fair process of choice by randomization: that is, by focusing on fairness. In Table 4, $X$ has a fairer distribution of probabilities than $Y$, for example. However, such an argument from fairness cannot justify equality of ex ante utility, because fairness is satisfied by giving fair chances to the satisfaction of all individuals’ equal claims, not by promoting equality of ex ante utility.

To grasp this, consider the case where we can choose from two courses of action, A and B: A gives one indivisible medicine to either Amy or Bob, two ill persons, by lot, whereas B gives it to either Amy or Bob on the basis of a genealogical investigation into which of the two has the least African ancestry. Even when, as in A, B can equalize their expected utilities, it would be fair to choose A.18 We can conclude, thus, that there is no good reason to include a principle of ex ante egalitarianism that requires equality of ex ante utility.19

Why is ex ante Pareto so common? It is because it apparently prescribes that a society respect individual evaluations by their own ex ante utility functions.20 Ex ante Pareto could be taken to befit the liberal view of justice—this principle does not require a person to participate in a public insurance scheme if the person prefers not to do so. However, we argue that ex ante Pareto conflicts with the axioms introduced in Section III. We also insist that ex ante Pareto should not appeal to theorists of egalitarian justice, and introduce another Pareto principle that is more compelling under severe uncertainty.21

First, following Fleurbaey and Voorhoeve,22 we can demonstrate that, under dominance, ex ante Pareto is not compatible with ex post egalitarianism. We assume here that, for each $i$ and each $X_i$, $U_i\left(X_i\right)=0.5(x_{\mathrm{ir}}+x_{\mathrm{ib}})$. However, conflicts of a similar kind can be obtained in broader sets of beliefs. Consider the following prospects in Table 5.

Similarly, we can show that under dominance, ex ante Pareto is not compatible with impartiality (Table 6).

Suppose that all individuals are subjective expected-utility maximizers and that $p_{\mathrm{Ar}}=0.8$ and $p_{\mathrm{Br}}=0.2$. By impartiality, the final distributions in both states are indifferent between $X$ and $Y$ and, therefore, $X$ and $Y$ are indifferent ex ante. However, ex ante Pareto claims that $X$ is better than $Y$, which shows a conflict with impartiality.

Given the above conflicts, we give three reasons why ex ante Pareto is not compelling, and will later introduce a weaker efficiency axiom. The first reason concerns the problem of “spurious unanimity” pointed out by Mongin: a unanimous agreement may not be compelling if the individuals reach agreement for different reasons: that is, when individuals have heterogeneous beliefs and distributions have different rankings of final well-being levels between individuals in different states.24

Mongin gives an example. Consider a plan to build a bridge between two countries, T (a developed country) and L (a developing country). In L, some people expect some economic benefits (for example, benefits from tourism), while others are concerned that they may lose their traditional culture and lifestyle under the influence of T. Suppose that people in L are divided into two groups, A and B. Those in A believe that the benefit is large enough and that their outdated traditions will (and should) be destroyed. Those in B think that the tradition at stake is important, but will not be damaged, because the influence from T will be moderate, and that the bridge will only bring some benefits. This situation is illustrated by Table 7, where if the bridge is constructed in $X$, the influence from T is large in Red and not in Black. $Y$ is the distribution when the bridge is not constructed. Suppose that all individuals are subjective expected-utility maximizers and that $p_{\mathrm{Ar}}=0.8$ and $p_{\mathrm{Br}}=0.2$. Both groups support the construction of the bridge, although one group is subsequently proved wrong. Such an ex ante agreement is not compelling.

The second reason is that, under severe uncertainty, it is difficult for individuals to make decisions in an accountable way, because they do not have exact information about the probabilities of the options they are choosing between. Because of this, their final well-being levels would depend on uncertain states. In such a situation, individuals cannot be held fully responsible for their decisions, because they cannot control fortune.25 Moreover, in our environment, individuals may have some heuristics and biases under uncertainty, making it more difficult for them to be responsible for the decisions; they do not have enough capacities to handle uncertain choices.26 These points show that ex ante Pareto is not a compelling principle.

Those points are also important for egalitarian justice with respect to the so-called “harshness objection” against luck egalitarianism.27 To see this, suppose that Amy did not take out health insurance because of her (overly) optimistic views about future events, whereas Bob purchased insurance to provide for the worst. Then, when both Amy and Bob contracted a serious disease and lost their jobs, only Bob is compensated for his unemployment, whereas Amy is on the verge of death because she cannot pay her expensive medical bills. In this case, even though Amy did not purchase the insurance through her own free choice, it seems too harsh to hold her fully responsible for her final situation due to her own decision (based on a mistaken assessment of probabilities) and leave her in severe poverty (or even dying). This argument may (at least partially) support a mandatory system of public insurance that covers Amy in advance, which would seemingly contradict ex ante Pareto.28

The third reason is that ex ante Pareto impels social criteria to focus only on each person’s prospects, as argued by Rowe and Voorhoeve.29 Under ex ante Pareto, social evaluations must be insensitive to the possible patterns of final well-being, which would be a reason for incompatibility between ex ante Pareto and dominance and ex post egalitarianism (or impartiality).

In the context of this axiom, to say that a prospect is “equal” means that all individuals have the same levels of well-being in each state, while a prospect is “riskless” if each individual has the same level of well-being in all states.

Table 8 illustrates that Pareto for equal or no risk is a plausible principle. Suppose Amy and Bob were to choose a ball from an urn where the number of red and black balls is arbitrary.

Note that $X$ is equal and that $Y$ is riskless. Suppose that $X$ provides higher ex ante utility values than $Y$ for all individuals. In this case, this axiom requires that $X$ should be better than $Y$.

In cases like this, Pareto for equal or no risk is a compelling principle because, under severe uncertainty, individuals reach a unanimous agreement for the same reason. That is, they have the same levels of final well-being and thus agree on the improvement they achieve. As explained above, spurious unanimity can occur when individuals prefer the same prospect for different reasons.31 Ex ante Pareto allows spurious unanimity in cases like this, where, as a consequence, some individuals benefit while others lose. In contrast, Pareto for equal or no risk can fend off the problem of spurious unanimity because, under uncertain prospects (for example, $X$ in Table 8), different individuals have the same level of final well-being in each state. This is also relevant to Rowe and Voorhoeve’s argument,32 because Pareto for equal or no risk allows social criteria to favor possible patterns of final well-being, and is thus compatible with both ex post egalitarianism and dominance.

In light of our pluralist framework, it is imperative to choose a final distribution in which all agents would reach higher well-being levels.

As an illustration of how the criterion evaluates an uncertain distribution, consider a case with distribution $X$ (Table 9), in which individuals have $\alpha$-maxmin expected utility functions with $C_A=\left(0.2,,,,0.6\right)$ and $C_B=[0.5,0.8]$.

Amy’s value is taken by the criterion if and only if $72-16{\alpha }_A\le 60-12{\alpha }_B$: that is, 3${\alpha }_B\le 4{\alpha }_A-3$.

According to this theorem, statewise maximin, as a social evaluation criterion, can be fully derived from the relevant principles for egalitarian justice. This could be considered a remarkable result because it is often assumed in debates about egalitarianism that a principle that is applicable to one kind of case or circumstance may have counterintuitive implications in another and, therefore, it is common to appeal to a variety of different principles in different kinds of situations. In Derek Parfit’s pluralist construal of telic egalitarianism, for example, it is better if there is more equality and utility, but the two may come into conflict. Supposedly, to solve such conflicts, weights are assigned.35 However, because these weights are not well defined, it is insufficiently clear how to resolve conflicts between the two goals or principles. In contrast, in our pluralist egalitarianism the relevant principles are fully compatible and, therefore, such conflicts between competing principles are avoided and we can appeal to a single and simple criterion to evaluate uncertain prospects. In other words, we present a non-conflicting pluralist egalitarian view characterized by statewise maximin (which is based on ex post egalitarianism, dominance, impartiality, and Pareto for equal or no risk). Our view is further supported by (a set of) general intuitions that reflect multiple values and/or principles. By utilizing statewise maximin, we can reasonably determine which public policy should be employed without recourse to particular historically formed intuitions, such as liberal egalitarian intuitions.36

It is important to note that we assume only ordinal interpersonal comparisons of well-being. In particular, ex post egalitarianism can be applied even when cardinal interpersonal comparisons are not possible. As discussed in the Appendix, statewise maximin satisfies cardinal full comparability; in other words, cardinal full comparability derives from the combination of our axioms. This entails that statewise maximin can be used even when cardinal interpersonal comparisons are impossible. To see the importance of this entailment, note that even in situations with population-level uncertainty, such as a global pandemic (discussed in detail below), each person’s life is too complex and subtly different to allow for interpersonal comparisons in a cardinal manner.37 According to statewise maximin, we can reasonably claim that what policy-makers should do in terms of interpersonal comparability is to compare people’s well-being ordinally in the context of public policy.

Statewise maximin has some properties that are worth paying some attention to. First, when individuals have different probabilities, the criterion aggregates well-beings and probabilities separately. The combination of the lowest levels of well-beings is evaluated by individuals’ ex ante utility functions. This is due to the violation of ex ante Pareto, which enables us to avoid spurious unanimity and the impossibility result. There is no separation between individuals’ probabilities and social prospects when ex ante Pareto is satisfied, on the other hand, simply because under ex ante Pareto their prospects are evaluated in terms of their ex ante utilities.38

Second, we discuss the evaluator’s uncertainty-aversion under statewise maximin when individuals are uncertainty-averse. This is in a way analogous to Rowe and Voorhoeve’s discussion of uncertainty-aversion.39 For simplicity, we assume here that Amy and Bob have the same maxmin expected utility functions. Illustrative examples are given in Tables 10 and 11.

$X$ is an uncertain situation and Amy and Bob have the same probability set $\left(0,1\right)$ (and hence $p_b\in \left(0,1\right)$). $Y$ is a risky situation where the final distributions are the same as $X$ and the states are equiprobable. In this case, statewise maximin is indifferent between $X$ and $Y$ because the worst off stand at the same level of well-being (that is, $50$) with certainty in the two distributions. That is, there is no risk for society on the levels of worst-off well-being in the two distributions. In this case, the maxmin expected values of the worst-off are also $50$. Thus, statewise maximin does not take the differential degree of uncertainty into consideration when the final distributions are the same in all states of the world.

Next, let us consider the prospects in Table 11, one of which contains population-level uncertainty.

Thus, Y′ is better than X′ according to statewise maximin. This evaluation comes from Pareto for equal or no risk. Thanks to this efficiency axiom, statewise maximin respects individuals’ uncertainty-aversion and chooses risky Y′ over uncertain X′. The ex ante utility values of both Amy and Bob are higher in Y′. Moreover, both X′ and Y′ are equal. Therefore, Y′ is socially better than X′ by Pareto for equal or no risk.

It could be considered a problem that statewise maximin, or any other criterion that satisfies Pareto for equal or no risk, violates some famous rationality conditions such as eventwise dominance, because of its uncertainty-aversion.40 Admittedly, this is a cost of respecting individuals’ attitudes toward uncertainty. However, for statewise maximin, uncertainty-aversion is a desirable property for egalitarianism under severe uncertainty, because it is likely to allow us to avoid uncertainty of the worst-off individuals. Put differently, for two social prospects, $X$ (riskless) and $Y$ (uncertain), giving the same ex ante utility to the worst-off individual, statewise maximin prefers $X$ to $Y$ so as not to expose the worst-off individual to uncertainty. This is because statewise maximin evaluates the worst-off well-being levels by the most uncertainty-averse preference. Consequently, it can be argued that violations of some rationality conditions stronger than dominance are not just unavoidable, but are a legitimate or even necessary cost. Statewise maximin chooses an uncertain distribution over a certain one only when the former guarantees a sufficiently larger benefit to the worst-off individuals than the latter, according to the most uncertainty-averse evaluation in society.

Statewise maximin provides reasonable guidelines for public policies under severe uncertainty. The social evaluation criterion justifies mandatory vaccination for COVID-19 if it is beneficial for the worst-off people, for example. A global pandemic like COVID-19 spreads throughout populations, disregarding socioeconomic background or status. Now suppose that highly effective vaccines with excellent safety records have been developed and are available. Then, according to statewise maximin, vaccination should be made compulsory, provided that the worst-off individuals enjoy a greater benefit from getting vaccinated. While, admittedly, cases of this kind do not always hold under severe uncertainty, statewise maximin as such provides reasonable guidance for policy-makers considering mandatory vaccination in the face of a global pandemic.

It could be objected, of course, that mandatory vaccination conflicts with the widespread liberal principle that the interest of an individual should not be violated unless the interest-based action is harmful to other individuals. This liberal principle is based on the notion of the separateness of persons, according to which people are separate, autonomous individuals, all leading different, separate lives, whose interests cannot be sacrificed for the interests of others or for the greater good.41 Because this liberal principle also applies in the context of public health, the objector may continue, it seems to preclude mandatory vaccination, and, therefore, this example fails as a confirmation of the strength of our pluralist egalitarianism.

It should be noted, however, that the suggested vaccination scheme in light of statewise maximin does not conflict with individual claims based on the separateness of persons, because all agents would have the same outcomes in each state under population-level uncertainty. The separateness of persons requires policy-makers to respect the interest-based claims of each person in cases where their outcomes are different in different states of the world. However, the notion of the separateness of persons is irrelevant in case of decisions in situations with population-level uncertainty, and this has important implications, not just in the context of public health, but also for egalitarianism itself. The guideline for public policy advocated by our pluralist egalitarianism does not imply a conflict between the liberal principle and statewise maximin in cases under population-level uncertainty, which hints at the salience of the principles of justice in general. In other words, our pluralist framework maintains the inviolability of key principles—including the liberal principle—that have gained wide support in debates about justice in a global pandemic.

Arguably, this point also makes our pluralist egalitarianism more appealing than RV pluralist egalitarianism, the view that includes both ex ante egalitarianism and ex post egalitarianism, while declining ex ante Pareto. Furthermore, RV pluralist egalitarianism does not clearly show how ex ante egalitarianism and ex post egalitarianism are compatible, nor how they are related to other principles of egalitarian justice, such as impartiality and dominance. This may lead to indeterminacy with regard to the relevance of fairness and final distributions of well-being in the process of drafting and implementing public policy in the face of a global pandemic. As a guideline for policy-makers, RV pluralist egalitarianism lacks a comprehensive standard and, thus, allows a significant role for decision-makers’ intuitions; but intuitions do not necessarily agree; consequently, RV pluralist egalitarianism fails to provide a method to adjudicate between competing claims.

In contrast, our pluralist proposal includes a social evaluation criterion that stems from the relevant principles of justice: an egalitarian requirement (ex post egalitarianism), impartiality (impartiality), social rationality (dominance), and efficiency (Pareto for equal or no risk). Therefore, our pluralist egalitarian view can provide comprehensive guidance for policy-makers in their choice of (or between) public policies. Such a view is exactly what is needed as a comprehensive theory of egalitarian justice when we are confronting a global pandemic.

We have argued that the social evaluation criterion, statewise maximin, is characterized by the axioms of efficiency, ex post egalitarianism, impartiality, and rationality. Our argument shows that statewise maximin is the only criterion of pluralist egalitarianism that meets the relevant axioms (that is, the principles of egalitarian theories). This can be considered to be a solution to the crucial (but often overlooked) issue of the (in)compatibility of the relevant principles. Furthermore, through this study, we have shown that axiomatization is a useful approach in philosophical debates about egalitarianism.