Nozick on Reflexivity, Algorithmic Justice, and Utopia
"Anarchy, State, and Utopia" after 50 Years
Preliminary Note: I’ve just finished writing the first draft of a working paper titled “Complexity and the Case for Liberal Neutrality and Skepticism. Aron, Hayek, and Gaus on the Limits of Political Knowledge” which I will present at the 7th Economic Philosophy International Conference at the end of this month. I realized only after the work on this paper was too advanced that Nozick could have been an interesting addition to the general argument. What follows below is thus somehow related to the aforementioned working paper but is strictly speaking completely independent material.[1]
We are celebrating this year the 50th anniversary of the publication of Robert Nozick’s Anarchy, State, and Utopia (ASU).[2] Interestingly, while three years ago the same milestone for Rawls’s A Theory of Justice led to a large number of conferences and other manifestations, this doesn’t seem to be so much the case for Nozick’s book. This may be because although at the time of its publication, ASU proved to be a quite popular and influential answer to Rawls’s liberal theory of justice, this work has not aged well. Part of the argument developed by the book has been largely discredited (I’m thinking here, especially, of Nozick’s contentious interpretation and use of Locke’s philosophy). Among libertarians, Nozick’s defense of a minimal state has never been as popular as one could expect (hard-core libertarians have been more impressed by Rothbard). The fact that Nozick himself has taken some distance from some of the ideas exposed in the book later in his career and that he never wrote about political philosophy again may also have given the impression that there is not much to keep from it.[3]
Be as it may, there is still valuable content in Nozick’s political philosophy, whatever one may think of the underlying politics. One of the most interesting aspects is the implicit use of the notion of reflexivity that Nozick makes to defend some core ideas of the book, more specifically his critique of so-called “patterned principles of justice” and his account of political utopia in terms of a “framework of utopias.”
Let me clarify first what I mean by “reflexivity.” I shall say that an agent A (i.e., a choice-making entity whose behavior can be accounted for in terms of intentional attitudes such as desires, wants, or beliefs) has reflexive capacities if their choices can be described as intentional responses to actual or expected changes in their environment. In general, any agent has reflexive capacities but these capacities come in degrees. For instance, the agent who forms and acts based on rational expectations is highly reflexive. The ant who modifies the path she takes to reach a resource when a new obstacle appears is minimally reflexive. The form of reflexivity that is interesting appears when an agent is able to form a model of the system in which they evolve in such a way that the behavior of a system made of reflexive agents depends on how those agents model the system and their models are responsive to change in the behavioral pattern of the system. The classroom example of such a system whose components display reflexivity is the case of the bank run. If enough agents form the expectation that their bank will fail because their model of the economy indicates that other agents will have the same expectation and run to the bank, then they will update their behavior accordingly and run to the bank. In general, the reflexivity of a system’s components is an important characteristic that accounts for that system’s complexity and the unpredictability of its behavior.
The word “reflexivity” never appears in ASU but the idea is nonetheless well present. Consider Nozick’s discussion of distributive justice in the seventh chapter. In this chapter, Nozick exposes his “entitlement theory” according to which a just distribution only depends on whether the historical process that led to it respects some principles.[4] Nozick argues that his theory is the only one that doesn’t rely on “patterned” principles of justice, i.e., principles that specify “that a distribution is to vary along with some natural dimension, weighted sum of natural dimensions, or lexicographic ordering of natural dimensions.”[5] In particular, falls into this category “end-state” principles such as Rawls’s that indicate that justice is realized only if the actual distribution conforms to some criterion independently given. What is the problem with patterned principles? According to Nozick, they are incompatible with freedom of choice. To understand why, it is useful to take a look at Gerald Gaus’s critique of “algorithmic justice” which is nothing but a slightly more formal version of Nozick’s point.[6] Also, the merit of Gaus’s critique is that it explicitly relies on the notion of reflexivity.
Let's say that you’ve got a theory T that says that, in the present context, the distributive outcome Ox is the more just. Moreover, T provides you with an “algorithm” to transition from the actual state Os to Ox – the algorithm can correspond for instance to a redistributive policy taking the form of a progressive income tax. If we want to put this more mathematically, we can say that your algorithm helps you to identify a function f(.) such that Ox = f(Os). Here, Ox corresponds to the pattern that the algorithm aims to implement. Now, as Gaus remarks, “any algorithm that produces outcome Ox is immediately confronted with the problem that agents react to Ox, upsetting Ox.” He continues:
“Take any algorithmic procedure A, which is a set of instructions (rules) for achieving Ox [i.e., to find the function f(.) so that the outcome is Ox]. Suppose the desired outcome is achieved, but individuals adjust their actions (collectively, say the pattern of adjustment is a) to produce a new outcome that is inconsistent with Ox. Now, if A could predict the a patterns of actions, it could include these as ‘feedbacks,’ altering the algorithms; seeking to bring society back to Ox.”[7]
Now, Gaus argues that the outcome of such an algorithm would be “incalculable,” without being clear about what that exactly means. The obvious difficulty is that if we want A to incorporate the adjustment pattern a, we need to conceive a more complex algorithm A’. In turn, the use of A’ to implement Ox is likely to trigger an adjustment pattern b, which would necessitate conceiving an even more complex algorithm A’’, and so on. Gaus’s version of Nozick’s argument that “liberty upsets patterns” is that the only way out is to block any further adjustment pattern. That means (i) curtailing people’s freedom and (ii) undermining the reflexivity that is constitutive of the open society’s complexity and at the roots of the benefits it brings.
This is an interesting reformulation of Nozick’s argument in terms of reflexivity but we should be clear about what is meant by “incalculable.” Reflexivity is not incompatible with the existence of an equilibrium. In principle, it is possible that for some target outcome Ox, there exists an algorithm and more specifically a function f such that f(Os) = Ox = f(Ox). The obvious problem is to discover such an algorithm. The more complex the society, the less likely it is. This is the weak version of the “liberty upsets patterns” argument. The stronger version consists of the claim that there is no fixed point f(Ox) = Ox, i.e., algorithmic justice is an impossibility.
The notion of reflexivity also tacitly appears in Nozick’s intricate discussion of utopia in the tenth and last chapter of ASU. In this chapter, Nozick asks us to do the following thought experiment:
“Imagine a possible world in which to live; this world need not contain everyone else now alive, and it may contain beings who have never actually lived. Every rational creature in this world you have imagined will have the same rights of imagining a possible world for himself to live in (in which all other rational inhabitants have the same imagining rights, and so on) as you have. The other inhabitants of the world you have imagined may choose to stay in the world which has been created for them (they have been created for) or they may choose to leave it and inhabit a world of their own imagining. If they choose to leave your world and live in another, your world is without them. You may choose to abandon your imagined world, now without its emigrants. This process goes on; worlds are created, people leave them, create new worlds, and so on.”[8]
Note first that this thought experiment involves the capacity of reflexivity in its highest form. We are asked to imagine a possible world inhabited by agents that are themselves able to do the thought experiment. This becomes quickly complex, and indeed far too complex to reach a definite conclusion. As Nozick notes, we can think of this in terms of stable associations where what we are looking for is an association S of agents such that no subset S’ of S wants to secede to create their own coalition. This can be related to the concept of the core of a game where an allocation A is in the core if and only if there is no subset of agents that can guarantee for themselves an alternative allocation A’ such that they are better off with A’ than A.[9] Even with imposing constraints, this model is obviously unsolvable. But this is not the point of the thought experiment. The idea is rather to apply the underlying model to our actual world. In this context, the range of possible worlds is restricted and corresponds to a finite set of communities “which people can enter if they are admitted, leave if they wish to, shape according to their wishes; a society in which utopian experimentation can be tried, different styles of life can be lived, and alternative visions of the good can be pursued.”[10]
Nozick calls this real-world application of his model “a framework for utopias” and is itself a model of the liberal/libertarian utopia. In this utopia, people are free to associate at their will and to follow the rules and principles of their choice. Its rationale is partly based on “the fact that people are complex” and, therefore, reflexive. As for distributive patterns, there is no algorithm to calculate the ideal society because there is a never-ending adjustment pattern such that once we have arrived at a society some identify as the ideal one, others may want to change it. This disqualifies the use of what Nozick calls “design devices” to navigate within the infinite sea of social possibilities. The more plausible alternative is to use “filter devices,” i.e., principles that ground a process to eliminate possible worlds that obviously fail to meet minimal requirements. This necessitates leaving individuals the freedom to experiment, to innovate, and to judge by themselves if the results conform to their expectations. Design devices should be used only within communities and possible worlds, not to construct the framework of communities as a whole.[11]
In so far as reflexivity is a feature that makes up for the complexity of social systems and this complexity largely accounts for the limits of our knowledge, Nozick’s account thus largely converges with Hayek’s epistemological argument for liberalism as most clearly stated in The Constitution of Liberty:[12]
“The case for individual freedom rests chiefly on the recognition of the inevitable ignorance of all of us concerning a great many factors on which the achievement of our ends and welfare depend... Liberty is essential in order to leave room for the unforeseeable and unpredictable; we want it because we have learned to expect from it the opportunity of realizing many of our aims. It is because every individual knows so little and, in particular, because we rarely know which of us knows best that we trust independent and competitive efforts of many to induce the emergence of what we shall want when we see it.”
[1] Of course, I gladly welcome any comments on the working paper!
[2] Robert Nozick, Anarchy, State, and Utopia (New York: Basic Books, 1974 [2013]).
[3] Though the comparison is imperfect, there is some similarity between the respective legacies of ASU and Popper’s The Open Society and its Enemies. Like Nozick, Popper mostly kept himself away from political philosophy for the rest of his career, and as for ASU, The Open Society has been largely disparaged by professional philosophers for its shaky history of philosophy.
[4] It is in this context that Nozick famously develops his example of Wilt Chamberlain which I’ve discussed in a previous essay here.
[5] Nozick, Anarchy, State, and Utopia, p. 156.
[6] Gerald Gaus, The Open Society and Its Complexities (Oxford University Press, 2021), p. 141-4.
[7] Ibid., p. 142.
[8] Nozick, Anarchy, State, and Utopia, p. 299.
[9] Interestingly, the argument against algorithmic justice can also be framed this way, the point being that there is no allocation in the core.
[10] Ibid., p. 307.
[11] This is clearly reminiscent of the Hayekian opposition between spontaneous and made orders.
[12] F. A. Hayek, The Constitution of Liberty: The Definitive Edition (Routledge, 1960 [2020]).
Nozick's current obscurity is well deserved. He added his own errors to Locke's, but Locke's are more important and interesting
https://crookedtimber.org/2016/10/16/locke-nozick-locke/