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The Unconventional, but Conventionalist, Legacy of Lewis’s “Convention”


The philosopher David Lewis is credited by many social scientists, including mainstream economists, with having founded the modern (game-theoretical) approach to conventions, viewed as solutions to recurrent coordination problems. Yet it is generally ignored that he revised his approach, soon after the publication of his well-known book. I suggest that this revision has deep implications (probably not perceived by Lewis himself) on the analytical links between coordination, uncertainty and rationality. Thinking anew about these issues leads me to map out an alternative social scientific research programme. The traditional ontological equipment of methodological individualism should be reinforced in order to admit the existence of an “intersubjective” world beside the two familiar worlds: the “objective” world of observable things, and the “subjective” world of expectations and individual beliefs. In particular, language becomes necessary to understand coordination via conventions, rather than the other way round. That has led a group of institutionalist economists and pragmatist sociologists to develop an enlarged model of rationality, no longer isolated from questions of coordination and values. This model is the basis for the “Economics of Conventions”.

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  1. 1.

    Of course, perfect coordination could be called certainty, but it would be non-sense to call “coordination” the case of certainty in games against nature.

  2. 2.

    There is a general agreement on the 4 distinctive features of conventions, as rules: (1) implicit (or no canonical expression); (2) arbitrary (multiple alternatives); (3) unknown origin; (4) not legally enforced.

  3. 3.

    Such change to the initial analysis has been published in Lewis (1975) and reprinted in Lewis (1983).

  4. 4.

    Another strange feature: Lewis published only 3 texts of very different size on conventions, within a few years. The last one, closely following the publication of the revised definition, is quite brief and contains some ultimate precisions. Then Lewis never again commented upon conventions, as if this subject had gone out of interest for him. The last text is generally ignored.

  5. 5.

    This term is designed to cover non-subjective meanings, in full generality, which does not preclude, as we will see, finer distinctions, such as “intersubjective meanings” and “common meanings” (Taylor 1971; Descombes 1996). As shown by those references, it is an unexplored land for economists, not for sociologists or philosophers.

  6. 6.

    For a general view on intersubjectivity, see the collection of essays gathered by Fullbrook (2002); see also Lawson (2006), Latsis (2006), and Latsis et al. (2007).

  7. 7.

    They are enumerated in § 2.2.3.

  8. 8.

    Agreement understood in a paradoxically realistic way, excluding the epistemological laziness of “as if” argument.

  9. 9.

    (1969, p. 42; see also the more complete definitions: pp. 58 and 76–78).

  10. 10.

    In the 1975 definition, Lewis uses the word “action” (probably because the notion of action stands in sharper contrast with the notion of belief, or, may be, to weed out the last marks of “behaviourism”), rather than the word “behaviour”. But it should be added that the following sentences of the 1969 definition had recourse to the word “action”, where “behaviour” could have been expected.

  11. 11.

    By this we mean that the behaviour could be checked and confirmed by an external observer or a third party. Mainstream economists, in contract theory, would say: “verifiable” (and not only “observable”): see Bolton and Dewatripont (2005, 40, 172–178). In the remainder of the paper, I will stick to the more usual word “observable” but according to that stronger meaning. Taylor (1971) likewise stresses “brute-data identification”. For a view stressing that even observable behaviours are actually not so easy to characterize, see Latsis (2004, chap. V; 2005, 715, no. 2).

  12. 12.

    “Everyone” could be replaced by “almost everyone”, or by some quantitative definition (1969, 78–79). Asterisks (*) are used to mark those aspects of the first definition that will be substantially integrated and/or changed in the second definition.

  13. 13.

    That means that the various facts listed in conditions (1) to (5) are known to everyone, it is known to everyone that they are known to everyone, and so on.

  14. 14.

    The first axiomatic treatment was given by Aumann (1976); See Brandenburger and Dekel (1989) and Binmore (1980), for surveys of subsequent developments in the framework of game theory.

  15. 15.

    Owed to the referee.

  16. 16.

    This clause is mentioned by Lewis, to reply to an obvious objection.

  17. 17.

    The similarities between the vocabularies of Lewis (imitation, behaviour, action) and of Skinner (stimulus, reinforcement), look superficial, but the complementarity may be elsewhere: between the definition of equilibrium solution, and the characterization of the process leading to it.

  18. 18.

    Beliefs forged independently of language, as we will see later, when using Grandy’s insightful comments (1977).

  19. 19.

    According to Lewis himself (1983, p.170).

  20. 20.

    Bennett (1973) himself chose another way.

  21. 21.

    The reader interested in the treatment of beliefs, in logic and philosophy, could refer to the collection of essays by Bogdan (1986).

  22. 22.

    See the 1st * in the definition given supra in § 1.1.

  23. 23.

    See the 2nd * in the definition given supra in § 1.1.

  24. 24.

    There are minor (stylistic, I would say) differences as well: “behaviour” replaced by “action”, “expects” replaced by “believes”, clause /5/ simplified, and CK written as a 6th condition. What does not change is that “a few exceptions to the ‘everyone’s can be tolerated” (1983, p. 165).

  25. 25.

    It is the case of Ullmann-Margalit (1977) in the theory of norms, Schotter (1981) in the theory of institutions, Pavel (1986, chapter 4) in the theory of literature, Becker (1986, chapter 2) in the sociology of art, Leibenstein (1987) in the economic theory of business firms, Skyrms (1996, chapter 5) in the theory of social contract, Miller (2001) in the theory of joint action (he actually refers to Lewis (1968/1972) but did not exploit the reference, because of his exclusive stress on actions), Taylor (1987) and Sugden (2004) in the theory of cooperation, etc.

  26. 26.

    For two distinct reasons, both borrowed from Popper (1979): (i) in chapter 3 § 1, instances of “objective contents of thought” are as diverse as scientific, poetic and artistic works. Popper was flexible enough to “distinguish more than three worlds”. So, if the reader wishes to stick to a strict definition of World 3, he is invited to read the 2nd part of this paper with the label World 3′, the world of intersubjectivity, including World 3, since there is no doubt that “objective contents of thought” are, if anything, a subset of intersubjective entities; (ii) in chapter 2 § 15, whereas subjective knowledge is made of dispositions and expectations, objective knowledge is made of expectations expressed in a language, thus allowing a critical discussion. As the reader will see, in the 2nd part, we will argue that conventions need language to be taught, understood and practiced.

  27. 27.

    The substitution of “conventional” to “mainstream” is of course a temptation too strong to be resisted, but the non-informed reader should be told this epithet is commonplace, although less usual. Keynes’s phrase (1936) was rather “orthodox”. Galbraith (1958) coined the term “conventional wisdom”.

  28. 28.

    On this point, see Batifoulier et al. (2002) and Cubitt and Sugden (2003).

  29. 29.

    Supra note 26.

  30. 30.

    For this reason, it is doubtful to use the criterion of subjective expected utility in strategic games (Mariotti 1995), in spite of a universal practice.

  31. 31.

    See Dupuy et al. (1989) and Eymard-Duvernay (2006). I borrow the emphasis on the triplet rationality/coordination/values, from Thévenot et al. (2005).

  32. 32.

    Let us give an example (from Lewis 1983, p. 187) of “trust in £”: “X (a hearer) believes Y (a speaker) uttered a true sentence”. So trust is both a belief (as said in the 1st part), i.e. a propositional attitude, but with two variables (once the sentence is determinate), i.e. a two-place function: a relation between X and Y, or, in other words, an interaction between X and Y (by contrast with the action of Y, who uttered the sentence), as said here. Notice that trust, here, is an asymmetrical relation, an interaction without reciprocity (Castelfranchi 2008).

  33. 33.

    It may be that the problem was already there in the first definition, if we note, with Jones (1983, pp. 10–11) that it does not seem very realist to tell about truth, at the speaker’s level, without telling about beliefs, at the level of the audience…

  34. 34.

    The assumption of “Common Knowledge” obscures this point from the reader’s view. For another criticism of Lewisian individualism, and a defense of a “holist” alternative, see the paper by Gilbert, in this issue.

  35. 35.

    Lewis himself is not reluctant to use this kind of formulation (1969, pp. 25 and 208).

  36. 36.

    The reader is referred, for details, to Favereau (2005), and for an exploration of intersubjectivity in terms of “rules + objects”, to Favereau (2001).

  37. 37.

    See for instance 1969, pp. 181–182; also, 1983, pp. 184–185.

  38. 38.

    Lewis would agree (1983, p. 181).

  39. 39.

    Contrary to the orthodox view of institutions, defined by its set of “constitutive rules” (and the violation of which seems to produce exclusion), Pollock’s project is to offer a view of institutions, making it possible to cheat. There are two kinds of constitutive rules: “definitive” rules, which cannot be broken, “prescriptive” rules, which can (1982, p.212–3).

  40. 40.

    The language is, for him, a “conventional institution”.

  41. 41.

    And, may be also, other conventions similar to conventions of language, not considered by Lewis.

  42. 42.

    Lewis occasionally gave some hints as for the possibility of using lighter versions of CK (1969, pp. 63–64): this amendment was rhetorically admissible, for the 1st definition, not for the 2nd one, all the more so as Lewis made a big step towards a comprehensive methodology, by recoursing to the “reasons” (rather than the “preferences”) of the agents. But see also Lewis (1976).

  43. 43.

    Supra note 23.

  44. 44.

    I felt intrigued by the recurrence of the term “practice” in writings of philosophers or logicians, indebted to Lewis (for instance: Macdonald and Pettit (1981, chapter 3), Pollock (1982, chapter X), Haugeland (1990), Latsis (2005) and Marmor (2007)); Bennett (1973, p. 152) had rather forge a new concept, dubbed “doing”, which mixes “action” and “belief-acquisition”—exactly my metaphoric B, and a nice introduction to the notion of practice.

  45. 45.

    That would be exactly the limit-case of intersubjectivity restricted to the condition of CK, which is examined by Taylor, under the heading “consensus”, i.e. convergence of subjective meanings.

  46. 46.

    Reprinted in Rabinow and Sulivan (1987, pp. 56–57). This paragraph is also used by Descombes (1996, p. 294). Marmor (2007) develops a parallel argument with a sequence convention-practice-know how. And of course, we are very close to Wittgenstein’s famous dicta: “meaning is use” + “obeying a rule is a practice” (1953, § 43, 202) where “practice” means the practice of a community (see Peacocke 1981, for a comment).

  47. 47.

    Once more we are close to Wittgenstein (see the previous note).

  48. 48.

    That is: social practices with the 4 distinctive features of conventions (supra, n.2). See also Pollock (1982, chapter X) on institutions.

  49. 49.

    See Favereau and Lazega (2002) and Favereau (2005) on interpretive rationality (subsuming computational rationality).

  50. 50.

    See Latsis (2005) on a very innovative non-Lewisian theory of conventions, using the notion of ‘exemplar’ due to Kuhn.

  51. 51.

    Not so neutral, according to this paper.

  52. 52.

    The reader, not familiar with modal logics, could refer to Bogdan (1986).

  53. 53.

    If this analysis is correct, in Hume’s famous example of two rowers, rowing in tandem, without any instruction, from the fact they do not use their linguistic abilities, you must not infer that they do not need them, in their capacity to coordinate one another silently…

  54. 54.

    This expression is borrowed from Arendt (1958), and reinterpreted by Boltanski and Thévenot (2006) in terms of a “City”.

  55. 55.

    Keynes’s use of convention, on the financial market, is much closer to a B-convention than to a A-convention: see Favereau (1986).

  56. 56.

    The reader will easily check that the “B-conventions”, no less than the “A-conventions”, show the 4 distinctive features of conventional phenomena, gathered supra (footnote 2).

  57. 57.

    See Kreps (1990).

  58. 58.

    Wittgenstein (1953, § 122).


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I express my deep gratitude to John Latsis and also to Gilles Raveaud, for their efforts to improve the form and the content of this paper, which benefited also from comments by participants to a workshop, at Columbia University, especially Yuval Millo, David Stark, Daniel Beunza, Harrison White and Laurent Thévenot. Jacques Merchiers and Philippe Batifoulier were very helpful readers too. Finally, I am grateful to Luca Tummolini and an anonymous referee for constructive criticism. The usual caveat applies.

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Correspondence to Olivier Favereau.

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Favereau, O. The Unconventional, but Conventionalist, Legacy of Lewis’s “Convention”. Topoi 27, 115–126 (2008). https://doi.org/10.1007/s11245-008-9038-z

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  • Coordination
  • Action
  • Belief
  • Social practice
  • Common knowledge
  • Common world