My First Draft: A Modified Lewisian / Hartian Account of Social Conventions as a Union of Primary, Duty Imposing Social Conventions of Obligation and Secondary Power Conferring Social Conventions of Authority

A Modified Lewisian / Hartian Account of Social Conventions as a Union of Primary Duty Imposing Social Conventions and Secondary Power Conferring Social Conventions

Sarah Braasch

Introduction

David Lewis, in Convention, and HLA Hart, in The Concept of Law, craft accounts of social conventions that include what they deem to be something closely akin to the essential feature of a quasi-obligatory character.  The both wish to explain why most people most of the time act and behave and speak as if there were a real obligation to comply with the social conventions of one’s social group and the social / legal rules (conventions) of one’s social group’s legal system.  However, neither Lewis nor Hart are under any illusions about the fact that they have only an individual instrumental rationality / normativity with which to work. Both Lewis and Hart back themselves into a normative corner from which there is no escape.  They both decide that if there is but a single rational thing to do in a situation that gives rise to a social convention (or rule, in Hart’s case), which is what everyone else in one’s social group is doing, then you have something closely akin to an obligation to do that one rational thing, which is to conform to the social convention of one’s social group, as everyone else in one’s social group is conforming.  This places both Lewis and Hart in a terrific quandary.  Their accounts of social conventions only capture a single class of social conventions, Lewisian social conventions, of the highest degree of conventionality and the strongest normative character.  No unilateral deviation may be tolerated at any point in time.  But, if no unilateral deviation may be tolerated at any point in time, then Lewisian social conventions must pop into and out of existence instantaneously. They cannot evolve or devolve over time, and they cannot allow for difference, dissent, pluralism, or theoretical disagreement about what the law is or should be.  But, we have pre-theoretical intuitions that we do disagree about what the law is and should be; our social conventions do arise, wax and wane over time, and, eventually, collapse, and, at one and the same time, we still recognize that most people most of the time act and behave and speak as if there were a real obligation to comply with both the social conventions of one’s social group, as well as the social rules (conventions) of one’s social group’s legal system, despite this fluidity and pluralism.  This paper is an explanation of how to modify Lewis’ and Hart’s accounts of social conventions to accommodate both a quasi-obligatory character and evolution and devolution over time, as well as pluralism for both individual dissenters and sub social groups within a larger social group.  This analysis includes a formal definition of a modified Lewisian / Hartian account of social conventions as a union of primary, duty imposing social conventions of obligation and secondary, power conferring social conventions of authority.  

The Problem(s) with a Lewisian / Hartian Account of Social Conventions

Both David Lewis, in his seminal work Convention, and HLA Hart, in his seminal work The Concept of Law, wish to capture what they deem to be an essential feature of both the social conventions of one’s social group and the social rules (actually social conventions) that comprise a legal system, which is their obligatory character.  Both Lewis and Hart recognize that they have only the beliefs, expectations, and preferences of individual rational agents with which to work.  In other words, both Lewis and Hart construct a rational choice based, game theoretic account of social conventions, relying only upon an individual instrumental (means ends) rationality to generate the normative, and perhaps, obligatory character of social conventions.  Both Lewis and Hart recognize that this may only be something closely akin to an actual obligation to comply with either the social conventions of one’s social group or the social rules of one’s legal system, because they both regard normative facts as metaphysically suspect.  But, both Lewis and Hart seem to think that the something closely akin to an actual obligation to comply, which they have captured in their accounts of social conventions, suffices to explain why most people most of the time act and behave and speak as if there were a real obligation to comply with the social conventions of one’s social group or legal system.

Both Lewis and Hart back themselves into a normative morass.  They both decide that if there is a single rational thing to do in a situation that gives rise to a social convention, which is what everyone else in your social group is doing, then you have something closely akin to an obligation to do that one rational thing, and so does everyone else in your social group, and this suffices to explain why most people most of the time act and behave and speak as if there were a real obligation to comply with the social conventions of one’s social group, including one’s social group’s legal system. But a situation in which there is a single rational thing to do, which is what everyone else in your social group is doing, is a situation in which all members of a social group are particularly motivated to align their beliefs and expectations with one another, because everyone fares far worse, if any social group member unilaterally deviates. 

This is why Lewis’ and Hart’s accounts of social conventions only capture a single class of social conventions, Lewisian social conventions, as Margaret Gilbert coined them, which are social conventions with the highest degree of conventionality and strongest normative / obligatory character.  Hart defines having an obligation to conform to the social conventions (rules) of one’s social group as the other members of your social group being in a position to demand your compliance and to sanction you for non-compliance, where the existence of the social convention (rule) is the sole justification for both the demand and the sanction, and Margaret Gilbert concurs, in “Social Convention Revisited.”  A text book example of a Lewisian social convention is driving on either the right or left hand side of the road.  No one much cares which side of the road we all drive on, but we care a great deal that everyone drives on the same side of the road.  We can appreciate how most people most of the time would act and behave and speak as if there were a real obligation to comply with one’s social group’s social convention to drive on either the right or left hand side of the road, because everyone fares far worse (death, physical damage, societal costs), if anyone deviates from the convention.  We are particularly motivated to align our beliefs and expectations with one another. In fact, we are so motivated that our legislature could promulgate a law indicating upon which side of the road to drive, and we would all comply, and this would still be conventional behavior, because we wouldn’t comply for the sake of the law itself, or because of any moral obligation to comply, but because we all want to drive on the same side of the road as everyone else in our social group, and the law allowed us to align our beliefs and expectations with one another.  

So, let’s concede that both Lewis and Hart captured something closely akin to a real obligation to comply with the social conventions of one’s social group or the social conventions (rules) that comprise one’s legal system.  They pay an exorbitant price for having done so.  A price far too dear as I see it.  Lewisian social conventions have to pop into and out of existence instantaneously.  They can neither evolve or devolve over time, either slowly or precipitously.  Social groups must jump, instantaneously and simultaneously, en masse, as a group, between alternate Lewisian social conventions.  A legal system comprised of Lewisian social conventions cannot allow for pluralism or dissent or theoretical disagreement about what the law is.  The last concern is the subject of a famous and withering critique of Hart’s legal positivist theory of law by the natural law theorist, Ronald Dworkin, in Law’s Empire.  Lewisian social conventions are so severely constrained, in that they allow for no unilateral deviation at any moment in time, that they may not exist in the real world.  Lewisian social conventions may only be a useful idealization.  And, in the real world, we have strong pre-theoretical intuitions that our social conventions and legal systems evolve and devolve over time, possessing greater and lesser degrees of conventionality and normative/obligatory character, and people disagree about what our social conventions and laws are and should be.  Activists advocate for changes in the law.  But, at one and the same time, we have strong pre-theoretical intuitions that most people most of the time continue to act and behave and speak as if there were something closely akin to a real obligation to comply with our social conventions and legal systems.  Is there a way to capture both the quasi-normative / obligatory character of social conventions and legal rules while also allowing for evolution over time, dissent, pluralism, and disagreement?

How to Solve the Problem(s) with a Lewisian / Hartian Account of Social Conventions

There is a way to modify Lewis’ and Hart’s accounts of social conventions, to accommodate both the quasi-obligatory character of social conventions and legal rules, while also accounting for the way in which social conventions/institutions arise, evolve and devolve over time, and, eventually collapse, as well as for the way in which people and sub social groups pressure the evolution and devolution of their social conventions and legal systems, and dissent therefrom.  Our modified Lewisian / Hartian account of social conventions remains a rational choice based, game theoretic account of social conventions that captures all of the essential features of social conventions, including arbitrariness, common knowledge, quasi obligatory character, and social group constitution.  There are three essential steps to modifying Lewis’ and Hart’s accounts of social conventions.

The three steps necessary to modify Lewis’ and Hart’s accounts of social conventions to accommodate both a quasi-obligatory character and varying degrees of conventionality over time are:  1 – recognize Margaret Gilbert’s brilliant insight in “Social Convention Revisited” that social conventions are social group constituting; 2 – recognize the role that practical authority plays in social conventions; and 3 – recognize that social conventions (and social groups) are step public social goods.  

While I take issue with most of what I deem to be Margaret Gilbert’s paradigmatic wholly normative account of social conventions, which are, in truth, merely social rules, I admire her profound insight that social conventions are social group constituting. The fact that a population has a social convention constitutes that population as a social group for that reason alone, if for no other.  This is a vital aspect of my modified Lewisian / Hartian account of social conventions for reasons that will become clear later.

Gilbert is highly critical of what she deems to be Lewis’ (and by extrapolation Hart’s) individualistic, rather than holistic, account of social conventions.  In contrast to Lewis, Gilbert requires neither preference for conformity to a regularity in behavior in a population, expectation of conformity to a regularity in behavior in a population, nor actual conformity to a regularity in behavior in a population.  Gilbert also chides Lewis for his demand for arbitrariness as an essential feature of social conventions.  For Gilbert, the paramount essential feature of social conventions is their obligatory character, followed closely be social group constitution. Gilbert hews closely to Hart’s definition of obligation in The Concept of Law.  For one to have an obligation to comply with a social convention (rule) is for one’s social group members to be in a position to demand one’s compliance and sanction for non-compliance, justified solely by the existence of the social convention (rule).  Gilbert chastens Lewis for limiting himself to an individual instrumental (means ends) rationality / normativity.  I think that Gilbert rightly recognizes that one’s social group members cannot be in a position to demand compliance and sanction for non-compliance, based merely upon an individual instrumental rationality.  As long as I am taking my means to my ends, and pursuing that which will secure my desired goals, I am being perfectly individually instrumentally rational, and cannot be criticized nor sanctioned by my social group members on rational / normative grounds.  My social group members are in no position to say that I have acted as I should not have done.  But, as I’ve mentioned, both Lewis and Hart are content to have captured something closely akin to an actual obligation to comply with one’s social group’s social conventions, something that explains why most people most of the time act and behave and speak as if there were a real obligation to comply.  

If find Gilbert’s paradigmatically wholly normative account of social conventions (really social rules) to be confused.  She attempts to have her normative cake and eat it too, as do the other moral contractarians, like David Gauthier.  Gilbert eschews any metaphysically suspect, supra individual notion of a social / conventional rationality or normativity that either exists outright or arises out of the aggregation of the individual preferences, expectations, and beliefs of social group members.  And, yet, much as David Gauthier attempts to construct morality out of an individual instrumental rationality, Gilbert likewise attempts to construct a social / conventionality rationality / normativity out of the individual commitments of social group members, manifested in the public space of one’s social group.  The reason why Gilbert insists that social conventions are social group constituting becomes clear.  Gilbert’s notion of joint commitment, constructed from the aggregation of the manifestations of the individual commitments of the social group members in the public space of the social group, creates joint and several ownership over the social group to whom one’s compliance is now owed.  This joint commitment generates the social / conventional branch of practical rationality / normativity.  Individual social group members are no longer at leave to rescind their individual commitments on instrumentally rational (individual) grounds, according to Gilbert.  But, at one and the same time, Gilbert appears to both eschew and desperately need to rely upon preference for, expectation of, and actual conformity to a regularity in behavior in the public space of a population.  Regardless of my criticisms of Gilbert’s paradigmatically wholly normative account of social conventions (rules), her insight that social conventions are social group constituting is a vital component of my modified Lewisian / Hartian account of social conventions.  

The second step to modifying Lewis’ and Hart’s accounts of social conventions to accommodate both a quasi-obligatory character and evolution over time is to recognize the role that practical authority plays in social conventions.  First, I must make clear that I do not mean a terribly robust view of authority, as in a legal authority or a political authority.  I need only a nominal view of authority, and I adopt the eminent legal philosopher, Joseph Raz’s, view of authority, in The Authority of Law, as the capacity or ability to alter another’s protected reasons.  A protected reason is a first order reason to do something and a second order reason to no longer consider any reason for doing otherwise. 

Practical authority is necessary, because of the risk dominance of Lewisian social conventions. As discussed above, the worst possible outcome is for anyone to unilaterally deviate from the status quo, either the existing Lewisian social convention or the state of nature.  This is why Lewisian social conventions cannot evolve or devolve over time, because no unilateral deviation may be tolerated at any point in time.  This is why social groups must jump between alternate Lewisian social conventions, and there must always exist at least two alternate Lewisian social conventions, to maintain the essential feature of conventional behavior that is arbitrariness, instantaneously and simultaneously.  This is why the status quo Lewisian social convention is risk dominant, because no one in the social group is going to risk moving to an alternate Lewisian social convention, unless she is certain that everyone in her social group is going to move likewise, en masse, as a group, instantaneously and simultaneously.  This is such a high bar to a social group being able to move between alternate Lewisian social conventions that a practical authority is required.  A practical authority makes it possible for a social group to move between alternate Lewisian social conventions, by making it known how all social group members will behave.  This intuitively makes a great deal of sense when you think about how, in the real world, it is easy and common for social groups to get stuck, so to speak, upon less optimal social conventions.  No one is particularly happy with the status quo, but it can be terribly difficult to move the group to a more optimal social convention.

This is the nature of practical authority.  Practical authority is an incredibly useful tool, but it is not one that is made as much use of as you might expect.  Why would this be the case?  Why wouldn’t a social group just assign someone as the practical authority to help solve coordination problems and move the social group to more optimal social conventions, Lewisian or otherwise?  Unfortunately, practical authorities do not grow on trees. Practical authorities are risk tolerant, far sighted individuals who recognize the potential long term benefit of paying a cost in the present to assume authority and communicate the salience of a particular social convention, in order to reap the long term benefits of being the practical authority of a social group, including being able to move the social group to alternate social conventions.  These individuals don’t always exist in a population. Coordination problems often go unsolved. Recent empirical work indicates as much.[1]  Practical authority is always assumed by a risk tolerant, far sighted individual in a population, one who is willing to pay a present cost to reap possible long term rewards.  Only after such an individual steps up to the plate is practical authority then conferred by the social group.  Assumption of authority is itself a risk, if the subsequent conferral is not bestowed. 

The quasi-obligatory character of the social convention, conforming thereto, that is the solution to a primary coordination problem extends to the secondary social convention / coordination problem, the solution to which is the identification of a practical authority who had asserted herself.  If there is a single rational thing to do, which is to coordinate one’s behavior with the rest of one’s social group, giving rise to something closely akin to a real obligation to conform to the resulting primary Lewisian social convention, then there is likewise a single rational thing to do, which is to confer power upon / identify a practical authority to make salient a particular Lewisian social convention, to which to conform.  The quasi obligatory character of the secondary power conferring social convention of authority piggy backs upon the quasi obligatory character of the primary duty imposing social convention of obligation. 

One might worry about an infinite regress of power conferring social conventions of authority, identifying ever more authorities to identify ever more authorities.  But, this need not be a concern.  Recent empirical work confirms our pre-theoretical intuitions that authority is always first assumed, then conferred.  This assumption of authority stops the regress. And, as mentioned, if there are no risk tolerant, far sighted individuals in a population to assume authority, then coordination problems may go unsolved.  It would be a great benefit to a social group to simply assign a practical authority to make salient a particular solution to a coordination problem, but this does not seem to be a tool that we have readily at our disposal. It makes sense.  It is irrational, in the short term, to put oneself forward as a practical authority.  It’s risky to put oneself forward as a practical authority.  There is a short term cost for a long term benefit that may never come to fruition.  So, it would be even costlier for someone in a social group to bear the cost of trying to force the position of practical authority upon another member of the social group.  Who would bear such an immediate cost with no hope of a long term benefit?  

A final, important point about practical authority is that compliance with authority for the sake of authority itself, or out of fear or compulsion or a sense of moral duty, would not be conventional behavior.  Just as Lewis spends significant time in Conventionmaking clear that compliance with an agreement, for the sake of the agreement itself, is not conventional behavior.  An agreement can serve as the basis for a Lewisian social convention, if the agreement serves to coordinate the beliefs and expectations and conforming behaviors of all of the social group members.  This is why Lewis concedes that it may take some time for a regularity in behavior in a population established via agreement to become a social convention.  This is also why I make clear that I do not in any sense refer to legal authority or a political authority or any kind of public or official authority when I use the term practical authority.  I need only a very nominal sense of authority as described above.  It’s important to make this point for the reason that compliance with authority for the sake of the authority itself is not conventional behavior.  

The third and final step to modifying Lewis’ and Hart’s accounts of social conventions to accommodate both a quasi-obligatory character and evolution over time is to recognize that all social conventions (and social groups, because social conventions are social group constituting) are step public social goods.  This was something that Brian Skyrms told me to consider. He told me to think of social conventions as step public social goods, and he told me to read a paper of his, “Evolutionary dynamics of collective action in N-person stag hunt dilemmas,” as well as a paper by Hugh Ward, “Three Men in a Boat, Two must Row: An Analysis of a Three-Person Chicken Pregame.”[2]  Well, in truth, what Skyrms had said was that a step public social good is like a social convention, not that a social convention is like a step public social good. But, once I realized the role that practical authority plays in social conventions, coupled with the fact that social conventions are social group constituting, it became clear to me that social conventions ARE step public social goods.  

Skyrms had said that step public social goods are like social conventions, because you have an incentive to contribute to the generation and maintenance of the step public social good, as long as everyone else does likewise.  And, no one wishes for anyone to unilaterally deviate, because, for a step public social good, any unilateral deviation whatsoever would result in the collapse of the good.  A step public social good is a good that is generated immediately upon reaching a minimum threshold level of participation in a social group.  An example that Skyrms employs effectively is a group hunt. A group hunt will fail unless 3 of the 4 lions in a pride participate in the group hunt.  Once 3 lions participate, the 4thlion has no incentive to participate, because she will still receive her portion of the kill. At the same time, the 3 lions who have agreed to participate have no incentive to cease participation, because the hunt will fail, and they will all fare far worse.  The 4thlion is now a freeriding defector, but a useful one. The successful group hunt is a step public social good sitting upon an equilibrium point.  The successful group hunt is a Lewisian social convention, the more optimal Lewisian social convention, the less optimal alternate Lewisian social convention being that each lion hunts alone for small game.  

Initially, before I fully appreciated the role that practical authority plays in social conventions and the fact that practical authority is always assumed, then conferred.  I thought of a social group residing upon the less optimal Lewisian social convention as Hugh Ward does, as a Multi Person Chicken Pre Game.  I thought of each member of the social group as exhibiting some degree of risk tolerance or risk aversion, and I thought of the social group members as jockeying to be either a contributor to the generation of the step public social good or the communicator that pays a cost in the short term to pressure enough of the other social group members to generate the step public social good, while reaping a long term benefit as a freeriding defector, once the good has been generated. But, once I realized the nature of practical authority and its crucial role in solving coordination problems, I realized how to modify Lewis’ and Hart’s accounts of social conventions to accommodate both a quasi-obligatory character and evolution and devolution over time, as well as pluralism, difference, and dissent, including dissenting sub social groups.

The far sighted, risk tolerant, communicating practical authority is the freeriding defector.  The step public social good generated is the social group itself, even if there are other goods generated via the social convention in question.  And, the social group members who contribute to the generation and maintenance of the step public social good are parties to the Lewisian social convention.  The quasi-obligatory character is generated by the fact that the social group rests upon an equilibrium point, at the moment of generation.  No one party to the Lewisian social convention has any incentive to do anything other than continue to conform to the convention, because, otherwise, the good / the social group would collapse, and everyone would fare far worse.  The practical authority / freeriding defector, who is a member of the social group, but not party to the convention, has no incentive to contribute to the generation or maintenance of the step public social good, because she fares far better by continuing to defect.  The long term benefit reaped, even if there are others, includes being the practical authority in the social group and being able to move the social group to alternate Lewisian social conventions. Thus, it is vital that the practical authority not be subject to the social convention, because, if she were, then she would not be at liberty to move the social group to alternate Lewisian social conventions.  Evolution and devolution are possible, because the quasi-obligatory character of the Lewisian social convention has been severed from the requirement of unanimity in conformity.  Because of the existence of the practical authority / freeriding defector(s), unanimity is no longer necessary.  Because the social group rests upon the equilibrium point, there is a single rational thing to do for anyone party to the social convention, which is to continue to conform thereto.  And, per Lewis and Hart, this suffices to explain why most people most of the time act and behave and speak as if there were a real obligation to comply with both the social conventions of one’s social group, as well as one’s legal system. 

So, it would seem that I’m saying that all social conventions are Lewisian social conventions, social conventions of the highest degree of conventionality and greatest normative character, because I’m stipulating that the quasi-obligatory character is still generated by the fact that there is but a single rational thing to do, which is what everyone else party to the social convention is doing, which is to continue to conform thereto.  This is the case for a sub social group.  The degrees of conventionality and normative/obligatory character vary with respect to the larger, whole social group.  The sub social groups wax and wane over time in size, but at each moment in time, each sub social group is a step public social good of its own.  The sub social groups jockey for position within the larger, whole social group.  At any moment in time, there is a fact of the matter regarding which social convention is THE social convention / institution for the entire social group.  I employ the cooperative game theoretic concepts of the Shapley value and the core to define the social conventions / institutions for the entire social group.  So, difference, dissent, and pluralism, as well as evolution and devolution over time become possible.  And we can still explain why most people most of the time act and behave and speak as if there were a real obligation to comply.  

A Modified Lewisian / Hartian Account of Social Conventions

HLA Hart in The Concept of Law famously defines a legal system as the union of primary duty imposing social rules (conventions) of obligation and secondary power conferring social rules (conventions) of authority as the paramount (as I see it) essential feature of a legal system.  As you may have noticed by this point, this is how I am defining social conventions. And, in point of fact, I do argue that once a population has language, and, thus, linguistic conventions, then they have a quasi-customary legal system.  So, what then defines an actual full-fledged legal system?  A legal institution for the entire social group is a social institution for the entire social group, for which the social group has conferred power upon the practical authority, such that the practical authority is a public legal official.  I will flesh this out in greater detail in future work.  But, if you think about it, this is what distinguishes customary law from law, the nature of the power conferred upon the practical authority by the social group.  

Lewis gives a rational choice based, game theoretic account of social conventions in his groundbreaking work, Convention, and I apply that, essentially, to a Hartian vision of social conventions as the union of primary social conventions (or solutions to coordination problems) of obligation and secondary power conferring social conventions of authority.  I slightly modify Lewis’ account, of course, particularly so to account for the role that the practical authority plays as the freeriding defector.  

Lewisian social conventions are comprised of what Lewis refers to as coordination problems with two or more proper coordination equilibria in a game of pure coordination (or near pure coordination) with common knowledge thereof.  Lewis translates his game theoretic model into the following definition:

A regularity R in the behavior of members of a population P when they are agents in a recurrent situation S is a convention if and only if it is true that, and it is common knowledge in P that, in almost any instance of S among members of P,

  • almost everyone conforms to R;
  • almost everyone expects almost everyone else to conform to R;
  • almost everyone has approximately the same preferences regarding all possible combinations of actions;
  • almost everyone prefers that any one more conform to R, on condition that almost everyone conform to R;
  • almost everyone would prefer that any one more conform to R’, on condition that almost everyone conform to R’,

where R’ is some possible regularity in the behavior of members of P in S, such that almost no one in almost any instance of S among members of P could conform both to R’ and to R.

Equilibria are choices made by players in a strategic game in a group setting for which no one could do better by choosing otherwise, holding fixed what everyone else does. If you choose to perform Behavior A, then I can do no better than to also choose to perform Behavior A.  And, if I choose to perform Behavior A, then you can do no better than to also choose to perform Behavior A.  This means that, given our preferences, we maximize our expected utilities by each choosing Behavior A, if the other does.  Proper equilibria are those equilibrium points for which, not only can each player not do better by choosing otherwise, but each could not also do as well by choosing otherwise.  And, proper coordination equilibria are those proper equilibria for which not only do I not do better or as well by choosing otherwise myself, but I also do not do better or as well if someone else chooses otherwise (and similarly for you).  A pure coordination game is one in which everyone has approximately the same preferences for all possible combinations of actions.  We both prefer to coordinate rather than not coordinate, and if you prefer to coordinate on Behavior B rather than Behavior A, then so do I.  

There are two types of social conventions:  primary duty imposing social conventions of obligation and secondary power conferring social conventions of authority.  They always exist as a union of primary and secondary social conventions.  The primary social conventions are the coordination problems, the solutions to which are the proper coordination equilibrium points, or Lewisian social conventions; however, all social coordination requires practical authority, because of the risk dominance of either the status quo Lewisian social convention or the state of nature.  For this reason, a primary coordination problem may not be solved without the existence and union thereto of a secondary coordination problem, the identification of a practical authority to make salient the solution to the primary coordination problem.  As discussed above, the practical authority is always assumed, thus stopping the regress, but a practical authority does not always arise in a population, which is why coordination problems often remain unsolved, and which is also why social groups often find themselves stuck, so to speak, at less optimal Lewisian social conventions, even though everyone in the social group might prefer to move to a more optimal Lewisian social convention.  

Primary duty imposing social conventions of obligation are step public social goods that rest upon an equilibrium point at the moment of generation, due to the existence of the practical authority / freeriding defector.  For this reason, Lewis’ formal definition of social conventions has been altered to take into account this fact.  

This translates into the following formal definition of primary, duty imposing social conventions of obligation:

A regularity R in the behavior of members of a population P when they are agents in a recurrent situation S is a convention if and only if it is true that, and it is common knowledge in P that, in almost any instance of S among members of P,

  • a minimum threshold level of or more members of P conforms to R;
  • a minimum threshold level of or more members of P expects a minimum threshold level of or more members of P to conform to R;
  • almost everyone has approximately the same preferences regarding R and R’;
  • a minimum threshold level of or more members of P prefers to conform to R, on condition that a minimum threshold level of or more members of P conforms to R;
  • a minimum threshold level of or more members of P would prefer to conform to R’, on condition that a minimum threshold level of or more members of P conforms to R’,

where R’ is some possible regularity in the behavior of members of P in S, such that almost no one in almost any instance of S among members of P could conform both to R’ and to R.

Secondary power conferring social conventions of authority arise out of necessity, out of the necessity of solving primary duty imposing social conventions (solutions to primary duty imposing coordination problems) of obligation.  A practical authority is assumed, when such a risk tolerant, far sighted individual arises in a population, then conferred.  When such an individual does not arise in a population and practical authority is not assumed, then primary coordination problems remain unsolved.  The assumption and subsequent conferral of practical authority in the form of a secondary power conferring social convention stops the infinite regress of power conferring social conventions.  The power conferring solution to a secondary coordination problem is the identification of a practical authority who makes salient the solution to a primary duty imposing coordination problem (social convention) of obligation.  This translates into the following formal definition of secondary power conferring social conventions of authority:

The identification of a practical authority to make salient the solution to a primary duty imposing coordination problem of obligation, R, by members of a population P when they are agents in a primary duty imposing coordination problem of obligation is a convention if and only if it is true that, and it is common knowledge in P that, when such practical authority, R, is assumed, then:  

  • almost everyone conforms to R;
  • almost everyone expects almost everyone else to conform to R;
  • almost everyone has approximately the same preferences regarding all possible combinations of actions;
  • almost everyone prefers that any one more conform to R, on condition that almost everyone conform to R;
  • almost everyone would prefer that any one more conform to R’, on condition that almost everyone conform to R’,

where R’ is some possible identification of a practical authority by members of P in S, such that almost no one in almost any instance of S among members of P could conform both to R’ and to R.

The simultaneous existence of these two social conventions, one primary and duty imposing, the other secondary and power conferring, in union, is the modified Lewisian / Hartian formal definition of a social convention.  

Conclusion / Future Work / Applications

Despite having provided a formal definition of a modified Lewisian / Hartian account of social conventions as a union of primary duty imposing social conventions of obligation and secondary power conferring social conventions of authority, there is yet much work to be done, including an agent based computational model and simulations of how social conventions arise in populations, evolve and devolve over time, including by being pressured by quasi-rational agents and sub social groups, and, eventually, collapse.  Also, there is much yet to be fleshed out, including many details regarding the nature of authority.  What happens when more than one person or body of persons attempts to assume practical authority in a population?  Is it possible to confer power upon a practical authority in a less totalitarian manner? I need to give a complete and detailed account of what it is to be a social convention / institution for the entire social group, as well as what it means to be a legal institution for the entire social group.  I need to flesh out how social conventions / institutions, as well as social groups, arise at all, from the state of nature.  There are an untold number of issues to be entertained in both the semantics and pragmatics of language.  Eventually, I intend this work to serve as the basis for a non ideal philosophy of law and language.  I look forward to expanding upon this work.  

Bibliography

Gauthier, David (1986). Morals By Agreement. Oxford: Oxford University Press.

Gauthier, David (1997) Resolute Choice and Rational Deliberation: A Critique and a Defense. Noûs 31(1):1-25.

Gilbert, Margaret, 1989. On Social Facts, New York: Routledge.

Gilbert, Margaret, 2008. “Social Convention Revisited,” Topoi, 27: 5–16.

Hart, H.L.A., 2012, The Concept of Law, 3rd edition (first edition 1961), Oxford: Clarendon Press.

Lewis, David (1969) Convention: A Philosophical Study. Harvard University Press, Cambridge, MA (Reissued 2002, Blackwell Publishers Ltd, Oxford).

Pacheco, J., Santos, F., Souza, M., & Skyrms, B. (2009) Evolutionary dynamics of collective action in N-person stag hunt dilemmas. Proc. R. Soc. B.276, 315-321. (doi:10.1098/rspb.2008.1126)

Ranehill, Eva, Schneider, Frédéric, & Weber, Roberto, “The unrealized value of centralization for coordination” (unpublished manuscript dated January 1, 2017 received from authors).

Raz, Joseph, 1979. The Authority of Law, Oxford: Clarendon Press.


[1]Ranehill, Eva, Schneider, Frédéric, & Weber, Roberto, “The unrealized value of centralization for coordination” (unpublished manuscript dated January 1, 2017 received from authors).

[2]Pacheco, J., Santos, F., Souza, M., & Skyrms, B. (2009) Evolutionary dynamics of collective action in N-person stag hunt dilemmas. Proc. R. Soc. B.276, 315-321. (doi:10.1098/rspb.2008.1126); Ward, Hugh, 1990. “Three Men in a Boat, Two must Row: An Analysis of a Three-Person Chicken Pregame,” The Journal of Conflict Resolution, 34(3): 371-400.

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