¹ Sometimes described as political liberalism or justificatory liberalism.

² Vallier, Kevin and D’Agostino, Fred, “Public Justification,” http://plato.stanford.edu/entries/justification-public/Google Scholar.

³ The literature on modeling stability within a well-ordered society is new and focuses almost exclusively on how to understand Rawls’s account. For some older pieces, see Krasnoff, Larry, “Consensus, Stability, and Normativity in Rawls’s Political Liberalism,” Journal of Philosophy 95 (1998): 269–92Google Scholar, and Hill, Thomas E., “The Problem of Stability in Political Liberalism,” Pacific Philosophical Quarterly 75 (1994): 333–52CrossRefGoogle Scholar. Recent literature includes Macedo, Stephen and Hadfield, Gillian K., “Rational Reasonableness: Toward a Positive Theory of Public Reason,” Law and Ethics of Human Rights 6, no. 1 (2012): 7–46Google Scholar; Paul Weithman, Why Political Liberalism? On John Rawls’s Political Turn (New York: Oxford University Press, 2010); Gerald Gaus, “The Turn to a Political Liberalism,” in John Mandle and David Reidy, eds., A Companion to Rawls (Chichester: Wiley, 2013), 235–50; Thrasher, John and Vallier, Kevin, “The Fragility of Consensus: Public Reason, Diversity, and Stability,” The European Journal of Philosophy 23, no. 4 (2015): 933–54CrossRefGoogle Scholar; George Klosko, “Rawls, Weithman, and the Stability of Liberal Democracy,” Res Publica 21 (2015): 235–49; Paul Weithman, “Reply to Professor Klosko,” Res Publica 21 (2015): 251–64; George Klosko, “Stability: Political and Conception: A Response to Professor Weithman,” Res Publica 21 (2015): 265–72; Paul Weithman, “Inclusivism, Stability, and Assurance,” in Tom Bailey and Valentina Gentile, eds., Rawls and Religion (New York: Columbia University Press, 2015), 75–96; Weithman, Paul, “Relational Equality, Inherent Stability, and the Reach of Contractualism,” Social Philosophy and Policy 31, no. 2 (2015): 92–113CrossRefGoogle Scholar; and John Garthoff, “Rawlsian Stability,” Res Publica (2015): 1–15. Two unpublished pieces are also helpful. See Sharon Lloyd, “Private Reasons, Public Judgments, and the Requirements of Reciprocity,” University of Southern California, 2015, along with Andrew Lister, “Public Reason and Reciprocity," Queens University, 2015.

⁴ Rawls, John, Political Liberalism (New York: Columbia University Press, 2005), pp. xl-xliGoogle Scholar.

⁵ This includes Thrasher and Vallier, “The Fragility of Consensus: Public Reason, Diversity, and Stability.” Also see Weithman’s summary of Rawls’s approach in Weithman, “Inclusivism, Stability, and Assurance.”

⁶ I promise that “WOS” and “ABM” are the only acronyms I use in the essay. For discussion of the power of these models within social science, see Miller, John H. and Page, Scott E., Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton, NJ: Princeton University Press, 2007)Google Scholar.

⁷ Wilensky, Uri and Rand, William, An Introduction to Agent-Based Modeling: Modeling Natural, Social, and Engineered Complex Systems with Netlogo (Cambridge, MA: MIT Press, 2015), 22.Google Scholar

⁸ Railsback, Steven and Grimm, Volker, Agent-Based and Individual-Based Modeling: A Practical Introduction (Princeton, NJ: Princeton University Press, 2012), 10Google Scholar.

⁹ I thank Steven Stich for encouraging me to make my reasons for building an ABM more explicit.

¹⁰ For an explanation of the compliance assumption, see Rawls, John, A Theory of Justice (New York: Oxford University Press, 1971), 8CrossRefGoogle Scholar.

¹¹ Rawls, Political Liberalism, 48–54.

¹² Nowak, Martin, “Five Rules for the Evolution of Cooperation,” Science 314 (2006): 1560–63, at 1561CrossRefGoogle Scholar.

¹³ Since immunity describes the ability of a system to recover from external shocks, and there are many kinds of external shocks, there will be many types of immunity. I expand on this point below.

¹⁴ Rawls, Political Liberalism, 35.

¹⁵ Rawls, John, A Theory of Justice (Cambridge: Belknap Press, 1999), 6CrossRefGoogle Scholar.

¹⁶ Ibid., 119. Penal institutions are meant to supplement the forces maintaining stability for the right reasons (Rawls, Theory of Justice, 502–503). I thank Steven Stich for encouraging me to make this point explicit.

¹⁷ Rawls, Political Liberalism, p. xlvi.

¹⁸ This condition allows that different reasonable persons accept different reasonable political conceptions from one another. That is, they can converge on different conceptions at the same time and in the same society (ibid., 35).

¹⁹ Weithman, “Reply to Professor Klosko,” 254.

²⁰ Rawls, Theory of Justice, 103.

²¹ Ibid., 497.

²² Also see ibid., 6.

²³ Ibid., 272.

²⁴ Rawls, Political Liberalism, 66–72.

²⁵ Weithman, “Inclusivism, Stability, and Assurance,” 88–90.

²⁶ Thrasher and Vallier, “The Fragility of Consensus: Public Reason, Diversity, and Stability.”

²⁷ Here I understand an agent’s position and improvements upon that position as including his or her moral commitments and personal projects.

²⁸ I agree with Rawls that a WOS is best modeled as requiring some coercion but whose stability is driven almost entirely by the voluntary choices of citizens.

²⁹ Rose, David, The Moral Foundation of Economic Behavior (New York: Oxford University Press, 2014).Google Scholar

³⁰ Ibid., 21.

³¹ For a review of the empirical literature on the benefits of social trust, see Banerjee, Sanjay, Bowie, Norman, and Pavone, Carla, “An Ethical Analysis of the Trust Relationship,” in Bachmann, Reinhard and Zaheer, Akbar, eds., Handbook of Trust Research (Northampton: Elgar, 2008), 318–31Google Scholar.

³² Rose, The Moral Foundation of Economic Behavior, 30.

³³ Rawls, Political Liberalism, 48–54. I do not include the requirement that agents recognize the burdens of judgment, as it would unnecessarily complicate the model. See ibid., 55–58.

³⁴ Gaus, Gerald, On Philosophy, Politics, and Economics (Belmont, CA: Wadsworth, 2007), 19–27Google Scholar.

³⁵ Agents with longer memories unnecessarily complicate the model.

³⁶ In another work, I appeal to the notion of social trust defined in Castelfranchi, Christiano and Falcone, Rino, Trust Theory: A Socio-Cognitive and Computational Model (West Sussex: Wiley, 2010)CrossRefGoogle Scholar. For a survey of different views, see Rose, The Moral Foundation of Economic Behavior, 19–38.

³⁷ Nowak, “Five Rules for the Evolution of Cooperation,” 1561.

³⁸ It also explains why public reason needs an assurance mechanism to make sense of stability for the right reasons. See Weithman, Why Political Liberalism? 327–35.

³⁹ Though, clearly Rawls thought the generation of publicity was critical for maintaining stability; but he was not at all clear about how facts about cooperation are made public knowledge. It appears that he believed that public reasoning functions as an assurance mechanism. As noted, John Thrasher and I have argued that public reasoning is not an effective form of assurance. In light of that paper, my model bases assurance on observed cooperation with others.

⁴⁰ For a review of the model, and my data sets, see http://www.kevinvallier.com/stability.

⁴¹ I’m grateful to Alan Hamlin for helping me to see this point.

⁴² We will see below that immunity is a kind of first-order stability, though we could also measure the variability of immunity to create a fourth concept of stability.

⁴³ For discussion, see Gaus, Gerald, The Tyranny of the Ideal: Justice in a Diverse Society (Princeton, NJ: Princeton University Press, 2016)Google Scholar, and Muldoon, Ryan, Diversity and the Social Contract (New York: Routledge, 2017)Google Scholar.

⁴⁴ For discussions of Rawls’s approach to ideal theory, see John Simmons, A., “Ideal and Nonideal Theory,” Philosophy and Public Affairs 38, no. 1 (2010): 5–36CrossRefGoogle Scholar and Amartya Sen, The Idea of Justice (Cambridge, MA: Harvard University Press, 2009), 52–74.

⁴⁵ The name is not meant to imply that the reasonable agents act irrationally in any sense.

⁴⁶ I worry that network reciprocity effects only work for small groups. To adjust for this possibility, I have instructed each reasonable agent not to keep tabs on its own record with each other agent, but rather instead to calculate a general location that is the average x and y coordinates of all agents who have cooperated in the previous turn or are presently cooperating.

⁴⁷ I omit social sensitivity levels of 0 and 0.1 since they give little or no weight to observation.

⁴⁸ I ignored a social sensitivity of 1, as this eliminates the influence of intrinsic propensity.

⁴⁹ Merely rational players have a small effect on balance, so I set it aside here.

⁵⁰ Agents enter with the average score of those who share its strategy.

⁵¹ Gaus, in On Philosophy, Politics, and Economics, pp. 135–42, has a concise and clear discussion of the idea of an evolutionary stable strategy for the uninitiated.

⁵² The data I have compiled demonstrates that a simple WOS with an entry-exit dynamic is both durable and balanced.

⁵³ Rawls, Theory of Justice, 214. Also see Gaus, The Tyranny of the Ideal.

⁵⁴ For a detailed discussion of nonideal theory as a form of exploration of ways to realize certain social and political ideals, see Gaus, Gerald and Hankins, Keith, “Searching for the Ideal: The Fundamental Diversity Dilemma,” in Vallier, Kevin and Weber, Michael, eds., Political Utopias: Contemporary Debates (New York: Oxford University Press, 2016)Google Scholar.

⁵⁵ Rawls, Political Liberalism, p. xliii.

⁵⁶ An underanalyzed assumption in the essay is that agents interacting over time can accumulate resources, building on previous cooperative effort. Thus, immunity might be a function of a growing economy. I hope to explore this effect in a future paper.