Abstract
Recently, philosophers have investigated the emergence and evolution of the social contract. Yet extant work is limited as it focuses on the use of simple behavioral norms in rather rigid strategic settings. Drawing on axiomatic bargaining theory, we explore the dynamics of more sophisticated norms capable of guiding behavior in a wide range of scenarios. Overall, our investigation suggests the utilitarian bargaining solution has a privileged status as it has certain stability properties other social arrangements lack.
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Notes
This is in part due to the fact that the dynamic and static approach have different targets. Authors in the static approach to the social contract tend to have justification in mind. This is not always the case for those writing in the dynamic tradition, although Kenneth Binmore and Gerald Gaus may be two notable exceptions.
This is of course just one of a slew of issues relating to the social contract. For instance, Skyrms (2013) conceives of the social contract as involving three stages. The first pertains to determining who to interact with (i.e., the problem of partner choice), the second pertains to whether the agents involved successfully cooperate (the problem of collective action or the ‘stag hunt’), and the third addresses how to divide the fruits of cooperation (the problem of division). For simplicity, we focus only on this last problem. For more on these latter two steps, see Wagner (2012) and Bruner and O’Connor (2017).
We use the term ‘norm’ here rather loosely and do not presuppose a particular account of norms (although see Bicchieri 2006 for a rich theory of norms and conventions).
Barrett (2014) has conducted work exploring how different signaling conventions can be appropriated to function in unfamiliar environments. I do not know of any formal work in political philosophy or ethics taking this approach, although Bednar and Page (2007) and Zollman (2009) are in the vicinity.
Although we do not address this in much detail, it is also possible to see the present paper as a contribution to the ‘static’ approach to the social contract. In particular, we are providing an account of how one of the many rationalizable social contracts will come to fruition via cultural-evolutionary dynamics. This in some ways is similar to recent work on the social contract by Gaus (2010), who argues there are a variety of publicly justifiable social contracts and cultural evolution plays a crucial role in selecting a uniquely justified set of social-moral rules to govern the behavior of a community. See also Moehler (2018).
We in the course of this paper consider the simplest case involving just two bargainers.
See, however, Thrasher (2014) for an argument as to why the seemingly innocuous ‘symmetry’ axiom may be problematic.
We also assume, as Alexander and Skyrms (1999) do, that the resource in dispute is homogeneous and divisible.
For a nuanced discussion on the limitations of ESS methodology see, Huttegger and Zollman (2013).
This is due to the fact that the norm which ends up being widely adopted will in large part simply hinge on the initial composition of the population. If egalitarians are for whatever reason initially prevalent then they are likely to go to fixation since more of their interactions result in the avoidance of the disagreement point.
While van Damme first introduced the notion of metabargaining in this 1986 paper, it should be noted that van Dame’s primary interest was not the dynamics of divisional norms.
A reader may at this point wonder whether there are connections between the so-called Nash program and metabargaining. There is a sense in which these two approaches are very similar. The Nash program is occupied with outlining procedures that underly the Nash bargaining solution. Metabargaining can be thought of as exploring which metabargaining procedures result in the Nash bargaining solution. However, there is no strong tie between the Nash program and this paper, as our interest is primarily in the dynamics of divisional norms given some underlying metabargaining procedure.
We can also modify the feasible set to reflect the fact that neither solution recommends that Bob receive less than 3 units and Rob less than four units. This is possible but complicates the dynamic analysis conducted in Sect. 4.1. For this reason we stick with this simpler metabargaining procedure but note that this alternate metabargaining procedure is well worth investigating and may yield different qualitative results than those uncovered in this paper.
We further assume, as is commonly done in the bargaining literature, that the feasible set is compact and convex.
This also excludes the case in which a portion of the frontier is a horizontal or vertical line since the slope would be either zero or undefined and thus ruled out by our restriction that the slope always be strictly negative.
In other words, we presuppose that there is no correlation between the bargaining solution an agent decides to utilize and the agent’s bargaining position. We grant that this is not always a reasonable assumption to make. For instance, it may be the case that those who advocate for utilitarian arrangements tend to have quite a bargaining advantage.
For the K–S solution to converge on the recommendation of its obstinate counterpart, the bargaining problem must be such that the recommendations made by both bargaining solutions are on the pareto frontier and the ideal point is not a member of the feasible set. If these conditions fail to hold, then the K–S solution will not converge and the disagreement point will be reached.
Recall that the minimax relative concessions solution is identical (in the two-person case) to the K–S solution of Sect. 2.
Gauthier contends a just individual will adhere to the following condition, namely, that ‘each person will select a fair optimizing response to the choice he expects the others to make, provided such a response is available to him; otherwise, his choice must be a utility maximizing response. A just person is disposed to interact with others on the basis of [this condition]’ (157). In other words, a just agent will do their part to bring about desirable and fair outcomes if they have assurance others are doing their part to promote justice. When the agent in question does not have reason to believe others are similarly compelled, they will instead act on the basis of self-interest.
For instance, Gauthier’s just agent is allowed to break contracts and simply behave in a fashion that maximizes her self-interest if she has no reason to believe her counterpart will abide by the terms of an agreement. Thus Gauthier’s just agents will not be preyed upon by the egoist in situations resembling Hume’s farmer’s dilemma (which is essentially a sequential prisoner’s dilemma).
Gauthier also says at certain points that his minimax just agent will cooperate with those who approximate the minimax relative concessions bargaining solution. This seems to indicate that the minimax just agent may often agree to utilitarian arrangements not out of self-interest, but instead because the utilitarian bargaining solution often reasonably approximates the minimax relative concessions solution.
Conditional minimax bargainers will do as well as utilitarians when placed to interact with utilitarian bargainers. Yet when paired with minimax bargainers, utilitarians outperform the invaders. Thus utilitarians can resist invasion from Gauthier’s just agents.
This observation is similar to one made by Binmore (1990). Binmore contends that conditional utilitarians (those who settle on the utilitarian bargaining solution with in-group members but accommodate out-group members by opting for their counterpart’s favorite bargaining solution) will be able to invade a population of unconditional bargainers (bargainers who all unconditionally utilize the same bargaining solution). Our observation complements this, as we contend that unconditional utilitarians will be able to invade a community inhabited by conditional bargainers.
In other words, when utilitarians meet fellow utilitarians they settle on the utilitarian division, but when they are tasked to interact with minimax bargainers, they act on the basis of their beliefs regarding the likely behavior of their counterpart (and vice versa).
In particular, Young studies a process whereby individuals interact and update their beliefs regarding the likely behavior of others based on a shared history of past play. He finds that this process results in agents converging on a generalization of the Nash bargaining solution. This result is somewhat robust and still obtains even when agents are more sophisticated best responders (Saez-Marti and Weibull 1999)
Note that this means conditional utilitarians are not the only strategy that can destabilize the population. Any conditional bargaining strategy could potentially infiltrate the population so long as the average payoff associated with the Nash bargaining solution is greater than the average payoff associated with the minimax relative concessions solution.
It is worth noting that this problem has not gone completely unnoticed. See, for instance, Binmore (2005). However, Binmore’s analysis differs from ours substantially since he both invokes cultural evolutionary theory and the veil of ignorance to argue for certain principles of justice. Our contribution is purely naturalistic as it doesn’t appeal to the device of the veil.
We can see why this may be so. When some mechanism or procedure exists that allow those with differing norms to avoid the disagreement point, the utilitarian solution should always be an NSS since utilitarians still always do at least as well (if not better) against fellow utilitarians than invaders do against utilitarians. Yet it is clear that other bargaining solutions may not be an NSS as they could be invaded by the utilitarian. This, of course, crucially depends on the details of the mechanism or procedure in question.
I thank Brian Skyrms, John Thrasher, Simon Huttegger, Keith Dowding, Ryan Muldoon, Jeff Barrett, Rudolf Schuessler, Hannah Rubin, Aydin Mohsen, and the participants of the MSPT Seminar as well as MSPT Works In Progress Group at ANU, the Evolutionary Approaches to Moral Behavior Workshop at Monash University, the Social Dynamics Research Seminar at UC Irvine, the 9th Decisions, Games and Logic Conference at the University of Michigan, Ann Arbor and the PPE Society Meeting in New Orleans. Special thanks goes to RJ Leland who helped me carefully think through many of these issues.
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Bruner, J.P. Bargaining and the dynamics of divisional norms. Synthese 197, 407–425 (2020). https://doi.org/10.1007/s11229-018-1729-4
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DOI: https://doi.org/10.1007/s11229-018-1729-4