TWO THREATS OF INSTABILITY

Just societies face two kinds of instabilities. Rawls illustrates both in this passage:

Rawls's first threat of instability is best modeled as a Prisoner's Dilemma (Figure 1). Row's most preferred outcome is where Column acts on political conception of justice P and Row does not. The same applies for Column. Row and Column's second most preferred outcome is where both act on P, and the third most preferred outcome is where both do not act on P. The worst case outcome for Row is where Row acts on P and Column does not, and vice versa for Column. The only Nash equilibrium is (not act on P, not act on P).

Figure 1.

First Threat of Instability: The Prisoner's Dilemma.

Rawls's second threat of instability is best modeled as an assurance game (Figure 2). In this game, both Row and Column most prefer mutual adherence to P, a departure from the Prisoner's Dilemma. Row's worst case outcome is where Row adheres to P, but Column does not. The opposite is the case for Column. Therefore, if Row is not assured that Column will act on P and Column is not assured that Row will act on P, then both might not act on P. There are two Nash equilibria in this game, (act on P, act on P) and (not act on P, not act on P). In general, it is easier to solve assurance games than Prisoner's Dilemmas. With the assurance game, mutual adherence to P is already in equilibrium, and we just need to make sure that this equilibrium is realized and maintained. This is not the case with the Prisoner's Dilemma.

Figure 2.

Second Threat of Instability: The Assurance Game.

If we assume that societies are not polymorphic (not filled with multiple preference orderings), then both kinds of instability cannot exist at the same time. For simplicity we assume that we are working with nonpolymorphic societies when it comes to preferences for acting on P and not acting on P. This means that these are two kinds of instability that obtain at different points in time: Society faces the Prisoner's Dilemma first and then the assurance problem.

When a society faces a Prisoner's Dilemma citizens most prefer to act unjustly when all other citizens act justly. How do we remedy this? By changing people's preferences. Rawls accomplishes this within his framework by arguing that citizens in the well-ordered society develop a sense of justice via a three-stage developmental process, which inculcates a desire to do what is just (Rawls [Reference Rawls1963] Reference Rawls1999; Rawls Reference Rawls1971, ch. 8). When they desire to do what is just, citizens are no longer playing Prisoner's Dilemmas with one another. In Rawls's words, “For given these natural attitudes and the desire to do what is just, no one wishes to advance his interests unfairly to the disadvantage of others; this removes instability of the first kind” (Reference Rawls1971, 497). When we change people's preferences the first kind of instability is mollified.

But even if everyone has a desire to act justly, we still face the second kind of instability: the assurance problem. As Rawls notes, “Even with a sense of justice men's compliance with a cooperative venture is predicated on the belief that others will do their part; citizens may be tempted to avoid making a contribution when they believe, or with reason suspect, that others are not making theirs” (Reference Rawls1971, 336). Though citizens want to do what is just because of their sense of justice, they do not want to do what is just at any cost. Returning to Figure 2, if Column does not do what is just, then Row does not want to act justly and vice versa.

One might think that Rawls posits such deep levels of consensus and strong socialization in the well-ordered society that the assurance problem does not arise: In a society where everyone has a sense of justice and thus desires to act justly, why would citizens worry about the possibility of their fellow citizens acting unjustly and thus consider preempting such behavior by being the first to act unjustly? The key here is understanding the limits of Rawls's sense of justice: Although citizens with a sense of justice are social cooperators, they are not unconditional social cooperators. In Rawls's words, citizens “are ready to propose principles and standards as fair terms of cooperation and to abide by them willingly, given the assurance that others will likewise do so” (Rawls [Reference Rawls1993] Reference Rawls2005, 49; emphasis added). This conditional nature of the desire to act justly suffices to ensure that there is an assurance problem even in the well-ordered society of deep consensus and socialization. All it takes to generate an assurance problem is a desire to not be a sucker, something even those with a sense of justice have. For there to be no such problem Rawls must say that those with a sense of justice are unconditional cooperators—that they desire to act justly regardless of what others do. It is obvious from the text that Rawls does not mean to make this claim.

How does Rawls then solve the assurance problem? He gives different answers over the course of his career—and, indeed, these different answers plausibly explain the changes from A Theory of Justice to Political Liberalism. Rawls's final answer to the assurance problem is that citizens, when deliberating in the public sphere, adhere to the norms of public reason, which are norms governing public discourse (Hadfield and Macedo Reference Hadfield and Macedo2012; Weithman Reference Weithman2010, 327; Weithman Reference Weithman, Bailey and Gentile2015). Broadly, the norms of public reason prevent citizens from appealing to their comprehensive doctrines when engaged in public discourse. Rather, citizens may only appeal to the political conception of justice. When citizens adhere to the norms of public reason while engaged in public discourse, they signal commitment to the political conception of justice over their own comprehensive doctrine, assuring their fellow citizens that they will remain faithful to P. When citizens do not adhere to the norms of public reason they signal commitment to their comprehensive doctrine over the political conception, breaking down this assurance. Row thinks Column will remain loyal to P because Column adheres to the norms of public reason when engaged in public discourse and vice versa. Adhering to these norms signals fidelity to P.

There is a puzzle here that is not discussed in the literature. Implicitly we have assumed (along with the literature) that the assurance problem is a society-wide problem and that in our toy model Row and Column stand for any two random citizens. But according to Rawls, the norms of public reason only apply to a very small group of citizens engaged in a very small set of activities. He says that the idea of public reason applies to “the discourse of judges in their decisions, and especially judges of a supreme court; the discourse of government officials, especially chief executives and legislators; and finally, the discourse of candidates for public office and their campaign managers, especially in their public oratory, party platforms, and political statements” (Rawls [Reference Rawls1997] Reference Rawls1999, 575). But if the norms of public reason only apply to very few members of society, how will they solve a society-wide assurance problem? If Row and Column are any two citizens who are not particularly politically involved, why would members of Congress debating legislation in accordance with the norms of public reason assure Row that Column will act on P, and vice versa?

It would not. But this is not a flaw with Rawls's solution to the assurance problem. Rather, the solution to the assurance problem is simply more complicated than those in the secondary literature let on. We can instead think of there being multiple assurance problems within different groups in society. These multiple assurance problems are differentiated by the strategies available to the participants; that is, how “act on P” is fleshed out. For high-ranking government officials, “act on P” means something like legislate according to the political conception of justice, decide court cases in accordance with the political conception of justice, and so on. If Row is a senator and Column a Supreme Court justice, how can Row be sure that Column will decide cases in accordance with the political conception? If Column does not do so, then Row prefers to legislate in accordance with her own comprehensive doctrine. And how does Column know that Row will legislate in accordance with the political conception? If Row does not then Column would like to decide major constitutional cases in accordance with his own comprehensive doctrine. We believe that Rawls means for the norms of public reason to solve this assurance problem, which we call the public official assurance problem. Because high-ranking public officials conduct public discourse in accordance with the norms of public reason they signal to other high-ranking government officials their fidelity to the political conception. On our interpretation of Rawls, the norms of public reason are meant to solve the public official assurance problem and only the public official assurance problem.

But, for average citizens, what does it mean to “act on P”? Because citizens do not have the capacity to legislate and decide cases, acting on P means that citizens simply obey laws whose content is in accordance with the political conception. Citizen Row wishes to follow just laws only if she is sure citizen Column will, and vice versa. How does Rawls solve this other assurance problem? He does not do so through the norms of public reason, because they do not apply. Important here is what Rawls says about the role of penal institutions in relation to stability. Rawls notes that “although men know that they share a common sense of justice and that each wants to adhere to the existing arrangements, they may nevertheless lack full confidence in one another.” In remedying this problem, “the role of an authorized public interpretation of rules supported by collective sanctions is precisely to overcome this instability. By enforcing a public system of penalties government removes the grounds for thinking that others are not complying with the rules. . . the existence of effective penal machinery serves as men's security to one another” (Rawls Reference Rawls1971, 240). The citizen assurance problem is thus solved by penal institutions. How does citizen Row know citizen Column will follow the law? Because there are penal institutions that incentivize Column to do so. The same reasoning gives assurance to citizen Column.Footnote ¹

We think Rawls's solution to the citizen assurance problem is plausible.Footnote ² As such, we want to focus on Rawls's solution to the public official assurance problem. A question: Since we think that penal institutions can solve the citizen assurance problem, why can they not solve the public official assurance problem? Because of the capacities that high-ranking government officials have—that is, what it means for them to “act on P”—there is no way for penal institutions to ensure fidelity to the political conception of justice. For penal institutions to secure assurance among high-ranking government officials there must be laws forcing these public officials to reason in accordance with the political conception, to only pass laws in accordance with the political conception, and so on. Not only is it implausible for laws to actually do this, given the ambiguity in what the political conception of justice requires in terms of concrete legislative and judicial decisions, but even if laws could do this they would violate the basic liberty of free speech. So because penal institutions cannot solve the assurance problem among high-ranking government officials given the strategies available to these officials, the norms of public reason are required.

Failure to distinguish between the two different assurance games has prevented others in the literature from successfully solving the assurance problem. John Thrasher and Kevin Vallier, after arguing that public reason fails to solve Rawls's assurance problem (their criticisms, as well as criticisms given by others, are canvassed in the next section), offer their own unique solution to the assurance problem. On the Thrasher-Vallier model, assurance is provided in the well-ordered society so long as citizens follow “public choreographers,” as well as see and believe their fellow citizens do so as well. According to Thrasher and Vallier, these “public choreographers are primarily bodies of norms, often legal, though sometimes informal or formal moral norms” (2015, 948). Of course, obeying any norms will not do—Row's obeying traffic laws will not assure Column that she will pay her taxes when the time comes, and hence act on P in the tax context. Rather, Row can provide this assurance only by paying her taxes or by obeying other norms related to tax compliance.

Thrasher and Vallier's assurance mechanism might replace or bolster the penal institution solution to the citizen assurance game. Yet it is hard to see how this solution can solve the public official assurance game given the nature of the strategies—what it means to “act on P”—available to the players. First, as we noted earlier, the relevant practices in this game—legislators legislating in accordance with the political conception of justice and judges judging in accordance with the political conception of justice—cannot plausibly be regulated by legal norms backed by penal institutions in a manner consistent with the basic liberty of free speech. But if there are no such norms regulating the relevant practices, then what does Judge Column obey that enables Senator Row to infer Judge Column's fidelity to P?

In response, perhaps there can be norms not backed by penal institutions (whether legal or informal) that regulate the relevant practices and thus do not violate the basic liberties. As an example, for judges, acting on P means judging in accordance with the political conception of justice. To do so, perhaps judges must follow interpretive rules that are not backed by formal sanctions: Say, they must adhere to originalism as an approach to legal interpretation. Part of acting on P thus involves following particular interpretive rules, and judges can signal fidelity to the political conception by following such norms.

But even here there are problems. Again, given the strategies available to the players in the public official assurance game, it will be difficult if not impossible to determine whether the relevant players are obeying the required rules. This is not so in the citizen assurance game: Citizen Row can tell rather simply if her fellow citizens are paying their taxes from existing data on the tax gap and, from there, infer whether her fellow citizens, on the whole, remain faithful to P. But can Senator Row read Judge Column's appellate-level decision and from there determine whether Judge Column obeyed the relevant interpretive norm? Given the prevalence of interpretive disputes even among those who espouse the same interpretive principles (such as originalism), this is incredibly unlikely, especially in cases decided by high-level appellate judges, which likely are the most significant for assurance purposes. As such, it is doubtful that players in the public official assurance game will be able to infer fidelity to P merely by witnessing how other players act on P, because whether a player has acted on P can be quite controversial.

THE FAILURES OF PUBLIC REASON

Does Rawls's public reason solution to the public official assurance problem succeed? Many do not think so. We agree, which is why we offer a new, discourse-based solution to the public official assurance problem later in the article. But before doing so, we outline several criticisms levied against public reason as an assurance mechanism in the existing literature and evaluate their cogency.

COSTLY SIGNALS AS SOLUTIONS TO ASSURANCE PROBLEMS

Our solution to the public official assurance problem departs from the too cheap talk problem. According to this problem, Row's too cheap talk does not provide Column any assurance that Row will act on P. But what if talk is costly? As we now argue, costly talk solves the too cheap talk problem for the public official assurance problem, and convergence discourse is sufficiently costly to serve this function. To get a feel for the general solution, consider a simpler assurance game: the Stag Hunt.

The Stag Hunt (Figure 3) is an example of an assurance problem. Both players can either hunt stag or hunt hare. If they both hunt stag, then they work together; if a player hunts hare, then she hunts alone. Players successfully catch a stag only if they both hunt stag. If a player hunts hare, then she catches a hare regardless of what the other does. Given the amount of meat on each animal, each player's most preferred outcome is (Stag, Stag), which is a strict Nash equilibrium. Given that each player hunts hare alone, and assuming that each player's hunting of hare has no effect on the other player's ability to catch a hare, Row is indifferent between (Hare, Hare) and (Hare, Stag). (Hare, Hare) is a nonstrict Nash equilibrium. The worst outcome for each player is to hunt stag while the other hunts hare. In this case she starves.

Figure 3.

The Classic Stag Hunt.

Suppose that talking is costless and that Row tells Column that she will hunt stag. What should Column infer? Nothing. Since talk is cheap, Row loses nothing by doing so. If Row plans to hunt stag then she should convince Column to hunt stag. If Row plans to hunt hare then she loses nothing by telling Column that she will hunt stag. So, once again, Column cannot infer from this talk what Row will do. This is the too cheap talk problem. Now suppose that, while telling Column that she will hunt stag, Row pulls out a knife and cuts her hand open. Why? Because cutting her hand open isn't cheap. Row is attempting to show Column that she really is committed to hunting stag. Column cannot infer a commitment on Row's part from too cheap talk. But why, if she plans to hunt hare anyway, would Row cause herself pain? She gains nothing from convincing Column to hunt stag if she plans to hunt hare. Thus, if she plans to hunt hare, cutting her hand open would be completely irrational. She would be imposing a strict loss on herself without any chance of a compensating benefit. But if Row plans to hunt stag then the behavior is rational. Row is willing to lower her utility to show Column that she is committed to hunting stag. The pain from the knife wound is a loss, but a loss that Row believes will be more than compensated by a successful stag hunt with Column. In other words, Column can infer that the knife cutting is an honest costly signal by Row.Footnote ⁴

Of course, this might not actually motivate Row to hunt stag, because Row might not have sufficient assurance from Column. Consequently, when Row offers the knife to Column, there is good reason for Column to cut his hand open as well. This provides both players strong reason to believe that the other will hunt stag, because both players have given a costly signal that would make no sense were they planning to hunt hare, and this is common knowledge. Call this the blood oath solution to the assurance game. Notice that the blood oath solution works because the signal is costly and its cost is common knowledge. As long as these conditions are met, it does not matter why the signal is costly. In particular, it is not necessary that the costs be meted out by a coercive authority via sanctions, as Rawls's solution to the citizen assurance game requires. All that matters is that there is some cost—how this cost is delivered is irrelevant to the blood oath solution's success.

The Stag Hunt is simpler than the public official assurance problem. In the Stag Hunt Row is indifferent between the Pareto-inferior Nash equilibrium (Hare, Hare) and the out-of-equilibrium solution that she prefers (Hare, Stag). Consequently, it is necessarily irrational for her to take the blood oath in order to convince Column to play the out-of-equilibrium solution. It imposes a loss on her for which there is no compensating benefit. So there is no reason for her to take the blood oath if she plans to violate it. Thus there is no reason for Column to be suspicious of any costly signal Row sends, no matter the cost. But this is not so in the public official assurance problem. This is because Row prefers the out-of-equilibrium solution (not act on P, act on P) to the Pareto-inferior Nash equilibrium (not act on P, not act on P). So there could be a reason for Row to take a blood oath to act on P even if she plans on violating the oath. She could plan to not act on P and hope to convince Column, by taking the blood oath, to act on P. Knowing all this, Column should still be suspicious. Row could simply be engaging in too cheap talk even while engaging in costly signaling.

Solving this problem requires resorting to cardinal utilities. Figure 4 is a cardinal public official assurance game with the same ordinal structure—hence, the same pure-strategy Nash equilibria—as the public official assurance game in Figure 2. But the utility each player gains from the (act on P, act on P) equilibrium is far superior to any other option. This makes a difference.

Figure 4.

The cardinal public official assurance game.

Suppose the blood oath to act on P costs Row a utility of 0.5. This behavior could be rational no matter how Row plans to act. If she plans to act on P and successfully convinces Column to act on P, then she gains a utility of 9.5 compared to the outcome that otherwise would have obtained—where she acts on P but Column does not (because her payoff in this case is zero). But if Row plans to not act on P and successfully convinces Column to act on P, then she has gained 0.5 utility compared to the outcome that otherwise would have obtained—where both Row and Column do not act on P (because her payoff in this case is two). No matter what, Row gains utility. But now suppose that cutting her hand open costs Row utility s, where 1 < s < 8. In this case, cutting her hand open is rational only if Row plans to act on P. For suppose Row plans to not act on P. Then Row has caused herself more pain than she gains from Column's switch from not acting on P to acting on P. Given that this would be irrational, Column should conclude that Row's portion of the blood oath is sincere when the blood oath costs Row utility s.

The ordinal structure of the public official assurance game guarantees that Row will be able to send such a signal, assuming that Row believes with sufficient confidence that her signal will induce a switch on Column's part from not acting on P to acting on P. To communicate that she intends to act on P, it suffices for Row to sacrifice more than she would gain by (1) fooling Column to act on P and (2) not acting on P herself. There will always be some such signal so long as the following inequality holds, letting u_Row indicate utility to Row: u_Row (act on P, act on P) – u_Row (act on P, not act on P) > u_Row (not act on P, act on P) – u_Row (not act on P, not act on P). This inequality says that Row gains more utility from inducing Column to switch from not acting on P to acting on P, given that Row will act on P, than Row gains from inducing Column to switch from not acting on P to acting on P, given that Row will not act on P. The satisfaction of the inequality suffices for the existence of a possible effective signal because the value of an effective signal is just some positive number s such that left-hand side > s > right-hand side. Thus, if left-hand side > right-hand side then, trivially, there exists some s. That this inequality will hold is guaranteed by the ordinal structure of the game because u_Row (act on P, act on P) is greater than u_Row (not act on P, act on P), and u_Row (not act on P, not act on P) is greater than u_Row (act on P, not act on P): The first term on the left-hand side is greater than the first term on the right-hand side, and the second term on the left-hand side is less than the second term on the right-hand side. Therefore, there will always be some amount that Row can spend that would signal her sincerity, assuming she believes that her signal will be effective. The same holds for Column.

CONVERGENCE DISCOURSE IS LIKE CUTTING YOUR HAND OPEN

So far we have proceeded at a high level of abstraction. We have shown that there will be some available costly signal that Row can send to assure Column, but we have not shown how Row can send such a signal. This section addresses this issue. The guiding idea is that convergence discourse is a costly signal.

First, it is important to be clear on what convergence discourse requires and how it likely proceeds. Public officials advance ideas in the public political forum. On consensus political liberalism models, public officials must justify these ideas to others only by appealing to public reasons taken from the political conception of justice. On convergence political liberalism models, conditions are much more lax: The set of considerations public officials may permissibly appeal to is much larger and includes reasons from public officials’ comprehensive doctrines. That said, convergence models of public discourse do not say that public officials may appeal to any considerations whatsoever. Vallier, for instance, imposes an intelligibility restraint, which requires that Row only appeal to reasons in her discourse with Column that are epistemically justified to Row according to her own evaluative standards (Vallier Reference Vallier2014, 183–85).Footnote ⁵ But, as Vallier notes, because many citizens’ arguments will survive this test, the “restraint will apply to relatively few reasons” (182). So although convergence discourse places some restraints on the considerations to which public officials may appeal, these restraints are quite permissive when compared to public reason. If Row is a Christian, for instance, she may appeal to Christian-based reasons from her comprehensive doctrine. On standard accounts of public reasoning she may not do this. And under the least restrictive wide-scope interpretation of public reasoning discussed earlier, Row may appeal to her Christian-based reasons only if she can back up her position with public reasons in due time. With convergence discourse Row may appeal to Christian-based considerations full stop.

Of course, appealing only to reasons from one's comprehensive doctrine as convergence discourse permits will likely result in little success for public officials. If Row is a Christian and Column a Hindu, and Row wishes to convince Column to endorse policy p, then merely giving Column Christian-based reasons to endorse p will do very little to convince him. Moreover, such discourse is at odds with having a sense of justice. According to Rawls, citizens in the well-ordered society “express a willingness, if not the desire, to act in relation to others on terms that they also can publicly endorse” (Rawls [Reference Rawls1993] Reference Rawls2005, 19; emphasis added). But Column, a Hindu, cannot publicly endorse Row's Christian-based reasons. For public officials engaged in convergence discourse to (1) successfully convince others to support their respective positions and to (2) also engage with their fellow public officials on terms their fellow public officials can endorse, they will have to engage in what Rawls calls reasoning by conjecture. When reasoning by conjecture “we argue from what we believe, or conjecture, are other people's basic doctrines, religious or secular, and try to show them that, despite what they might think, they can still endorse a reasonable political conception” (Rawls [Reference Rawls1997] Reference Rawls1999, 594).

In convincing Column that p is a good policy, Row will thus give Column Hindu-based reasons. To succeed at this effort Row must come to learn Column's comprehensive doctrine to a significant degree. If she does not know Column's comprehensive doctrine well, then she will not be able to show Column that Column's comprehensive doctrine entails p, nor will she be able to engage with Column on terms Column can endorse. Note that this style of reasoning is not a requirement of convergence discourse, but rather is a likely feature of it given (1) what it takes to convince diverse persons with no shared reasons to come to agree with one's position and (2) what convergence discourse likely looks like when engaged in by persons with a sense of justice as defined by Rawls.

In short, successful participation in convergence discourse in the well-ordered society likely requires knowing a significant amount about a wide range of comprehensive doctrines that are not one's own, which can be costly in terms of the opportunity cost spent learning the relevant doctrines. Row, whom Column does not expect to know much about Hinduism, has given a sophisticated Hindu-based argument. Because Row is not a Hindu, it must have taken her a great deal of effort to learn the doctrine sufficiently well to give this argument. That Row would be willing to incur such a cost indicates that she is serious about achieving the (act on P, act on P) outcome. Row probably would not have incurred such a cost if she merely wanted to secure the (not act on P, act on P) outcome, just as one would not likely cut one's hand open in the Stag Hunt if one planned on hunting hare. As such, if Row makes a compelling Hindu-based argument in favor of p, then Column should be assured that Row desires this outcome. As in the blood oath, costly signals work best if they go both ways. Row still needs assurance that Column will act on P. Column can so assure Row by giving Christian-based arguments for his preferred policy.

We just said that, because Row is not a Hindu, it must have taken her a great deal of effort to learn the argument based on Hinduism to convince Column. But is this effort sufficiently costly to overcome the too cheap talk worry? After all, although we argued earlier that it is a necessary feature of the assurance game that there will be some sufficiently costly signal Row can send, we have not shown that convergence discourse is costly enough. We now argue that the likelihood that this effort is sufficiently costly to overcome the too cheap talk worry is a positive function of society's diversity of comprehensive doctrines. More bluntly, the more diverse the society, the more effective the blood oath solution. To see this, consider two cases.

• Small Diversity. There are two comprehensive doctrines: Christianity and Hinduism. Row therefore can produce sufficient reasons for all members of society to endorse the (act on P, act on P) outcome by knowing arguments from these two comprehensive doctrines.

• Large Diversity. There are many comprehensive doctrines, including Buddhism, Christianity, Hinduism, Islam, Jainism, Judaism, Kantian Liberalism, Libertarianism, Millian Liberalism, Secular Humanism, Taoism, and Zoroastrianism. Row therefore must learn arguments from most or all of these comprehensive doctrines to convince the others to endorse the (act on P, act on P) outcome.

The signal from Row's convergence discourse is significantly more costly in the large diversity case than in the small diversity case. She must expend many more resources to learn arguments sufficient to convince others that their comprehensive doctrine leads them to endorse the (act on P, act on P) outcome simply because there are many more such arguments to learn. This example shows that, the more comprehensive doctrines there are to learn, the greater the chance that Row's costly signal can overcome the too cheap talk problem. Thus, although Rawls views diversity as creating a stability problem that must be solved, we conclude that diversity is an integral part of the solution to this very same problem. It is an integral part of the solution to the too cheap talk problem. We thus join a growing literature in political philosophy and the philosophy of science that seeks to show the social benefits that diversity brings to the table (D'Agostino Reference D'Agostino2009; Reference D'Agostino2010; Muldoon Reference Muldoon2013; Muldoon and Weisberg Reference Muldoon and Weisberg2011; Page Reference Page2008).

So far we have assumed for the sake of simplicity that the public official assurance game is a one-shot interaction. However, often this is not the case. Public officials interact over long periods of time: The game is iterated. We have also argued that convergence discourse is costly because it requires public officials to learn about many comprehensive doctrines. Yet these costs are mostly incurred up front. Once Column has learned enough Christian doctrine to give one Christian-based argument, giving Christian-based arguments in the future will be quite cheap—perhaps insufficiently costly to avoid the too cheap talk problem. So, large diversity is necessary but not sufficient for convergence discourse to be sufficiently costly when playing an iterated public official assurance game. Now consider the following condition:

• Dynamic Large Diversity. There are many comprehensive doctrines in society at time t₁ . There are many comprehensive doctrines in society at time t₂ . The t₁ doctrines are significantly different from the t₂ doctrines due to the evolution and reinterpretation of existing comprehensive doctrines, as well as the introduction of new doctrines. At t₁ , Row must learn arguments from the t₁ doctrines to convince the others at t₁ to endorse the (act on P, act on P) outcome. Likewise with the t₂ doctrines at t₂ .

Public officials in conditions of dynamic large diversity will maintain the costliness of their signals through iterated interactions because they must pay attention to cutting-edge doctrinal developments to (1) successfully convince others to support their respective positions and to (2) also engage with their fellow public officials on terms that their fellow public officials can endorse. This ensures the costliness of convergence discourse over time. Moreover, public officials will be able to accomplish this by citing recently published sources. For example, Column could cite the most recent papal encyclicals for Row, which are produced fairly regularly. So the blood oath solution solves the iterated public official assurance problem in conditions of dynamic large diversity.

Is it plausible that liberal societies such as Rawls's well-ordered society will contain dynamic large diversity? Yes. As Ryan Muldoon has emphasized, dynamic large diversity is the natural result of liberal institutions because liberal institutions enable persons to experiment with different ways of living. According to Muldoon, “[t]hese ways of living may embody different perspectives on how we should live together in a society” (2015, 193). Because “the process of experiments in living is continuous,” so too is the evolution of perspectives—and hence comprehensive doctrines—present in the society (180). Just as Rawls believed that the very liberal institutions constituting the well-ordered society would lead to a diversity of comprehensive doctrines in the first place (Rawls [Reference Rawls1993] Reference Rawls2005, 36–37), Muldoon rightly shows that these same institutions lead to a shifting diversity of comprehensive doctrines. We should thus expect Rawls's well-ordered society to contain dynamic large diversity. This allows the blood oath solution to solve the iterated public official assurance game.Footnote ⁶

Still, theorists who show the benefits of diversity also argue that diversity has its limits. We agree. Return to Figure 4 and suppose that learning one comprehensive doctrine costs players utility 1. In this game it is rational for players to learn at most eight comprehensive doctrines: Were they to learn nine they would get a maximum payoff of 1, but not acting on P without costly signaling guarantees a payoff of at least 2. Now suppose there are 16 comprehensive doctrines (CDs) in the society, that Row knows CD₁ through CD₈ , and that Column knows CD₉ through CD₁₆ . Row cannot send an effective costly signal because Column, not knowing the doctrines through which it is expressed, cannot verify whether Row expended significant resources in learning the doctrines. Here, diversity is too great.

Although situations like this are possible, we do not think they are plausible in the well-ordered society. Thus far we have modeled the public official assurance game between two players, but in reality the public official assurance problem has n players, where n is (probably) in the hundreds and players must perceive some number q < n of officials signaling to be sufficiently assured: Row does not need assurance from Column so long as she perceives q players costly signaling. Now add a third player, Matrix, who knows CD₅ through CD₁₂ , to the game, and suppose q = 2. If each player publicly discusses at least six comprehensive doctrines then q is necessarily satisfied for each player. Row and Column each perceive two costly signals (themselves and Matrix), and Matrix perceives three costly signals.

Matrix is a connection player between Row and Column. As the last example illustrates, connection players can facilitate assurance even when most players know no common comprehensive doctrines. Thus, connection players increase the amount of diversity a society can afford to have. Various properties of the well-ordered society suggest that the number and effectiveness of connection players will be high. First, the basic liberties governing the well-ordered society, such as freedom of speech and movement, make likely a large number of connection players because they facilitate significant social interchange (Rawls Reference Rawls1993 [Reference Rawls2005], 228).

Second, connection players are effective in proportion to the number of comprehensive doctrines they can rationally learn: If Matrix could learn only two comprehensive doctrines then she could not send effective costly signals to both Row and Column. A player's maximum rational number of known comprehensive doctrines depends on her cardinal preferences over the outcomes. In particular, if Row strongly prefers (act on P, act on P) to the other outcomes, then she can rationally learn many comprehensive doctrines—she gains a lot from inducing Column to act on P and so can rationally send a very costly signal. To see this, compare Figure 4 with Figure 2, and let Figure 2 now model cardinal utilities. Assuming that learning a comprehensive doctrine costs utility 1, players can rationally learn at most eight doctrines if they are playing the Figure 4 game and at most two if they are playing the Figure 2 game.

It is impossible to specify a priori the players’ cardinal utilities, which will depend on features particular to individual public officials. However, given that the relative cardinal utilities of the outcomes make a big difference to the well-ordered society's ability to solve the public official assurance problem, we should expect the well-ordered society to inculcate favorable preferences in its public officials as part of the general developmental process outlined by Rawls ([Reference Rawls1963] Reference Rawls1999; Reference Rawls1971: ch. 8). For example, Matrix's commitment to achieving justice plausibly leads her to strongly prefer (act on P, act on P) to the other outcomes, thereby increasing her effectiveness as a connection player. Thus, even though too much diversity is a theoretical possibility, we doubt it would obtain in the well-ordered society.

OBJECTIONS

A CONCLUDING SECTION

Individuals in Rawls's well-ordered society must assure one another that they will act in accordance with the political conception of justice. Rawls attempts to solve the citizen assurance problem with penal institutions. He succeeds. Rawls attempts to solve the public official assurance problem with public reason. He fails. Public reason as an assurance mechanism faces the problems of too cheap talk, noise, and diversity. We have proposed a different solution to the public official assurance problem: Convergence discourse is a costly signal akin to a blood oath. We have succeeded. Our solution has none of the problems that Rawls's does and is plausible more generally. The lessons to be drawn from our model are twofold. First, convergence discourse, unlike public reasoning, solves the public official assurance problem. Second, the existence of significant diversity is necessary for convergence discourse to succeed. Diversity solves the problem that diversity creates.