Juggling

Discussing a theory in which morality appears as a natural phenomenon is like juggling with a large number of slippery balls while being pelted with rotten fruit. In my own work, I have given up trying to convert the traditional moral philosophers in the audience who label themselves as rationalists, objectivists, and realists while simultaneously denying that science has anything to contribute to their subject (Binmore Reference Binmore2005, p. 37; Mackie Reference Mackie1977). Even more hopeless are the naive empiricists at the other end of the scale who generalize very freely from limited and sometimes doubtful experimental data (Binmore Reference Binmore2006; Binmore & Shaked Reference Binmore and Shaked2010).

Baumard et al. are adept at evading such throwers of rotten fruit, but they would find it easier to juggle if they took account of some work from the economics and psychology literature, which I describe here using the traditional personification of Justice as a blindfolded matron bearing a sword and a pair of scales.

Blindfold

Aristotle observed that “what is just … is what is proportional.” Baumard et al. highlight some experimental evidence that supports Aristotle's insight, but much more is to be found in what psychologists call “modern equity theory” (Adams Reference Adams1963; Reference Adams and Berkowitz1965; Adams & Freedman Reference Adams, Freedman and Berkowitz1976; Austin & Hatfield Reference Austin, Hatfield and Mikula1980; Austin & Walster Reference Austin and Walster1974; Baron Reference Baron, Mellers and Baron1993; Cohen & Greenberg Reference Cohen, Greenberg, Cohen and Greenberg1982; Furby Reference Furby and Cohen1986; Homans Reference Homans1961; Mellers Reference Mellers1982; Mellers & Baron Reference Mellers and Baron1993; Messick & Cook Reference Messick and Cook1983; Pritchard Reference Pritchard1969; Wagstaff Reference Wagstaff1994; Reference Wagstaff2001; Wagstaff & Perfect Reference Wagstaff and Perfect1992; Wagstaff et al. Reference Wagstaff, Huggins and Perfect1996; Walster & Walster Reference Walster and Walster1975; Walster et al. Reference Walster, Berscheid and Walster1973; Reference Walster, Walster and Berscheid1978).

The economics literature complements this work by offering axiom systems that characterize the “proportional bargaining solution” of cooperative game theory. My own book Natural Justice studies the circumstances under which the proportional bargaining solution follows from applying an evolutionary adaptation of John Rawls' famous original position (Binmore Reference Binmore2005, p. 165).

Sword

Philosophers commonly neglect the question of how fairness norms are enforced, but the issue is central to an evolutionary account of their origin. Baumard et al. are doubtless right in arguing that cooperatively inclined folk somehow came together in groups, and maintained their cooperative integrity by expelling asocial individuals. However, a story in which nice folk meet in the forest and set up house together is impossibly naive. The literature is full of more plausible stories appealing to assortative mating and kin selection. My own favorite involves a group selection argument that is immune to the standard criticism (Binmore Reference Binmore2005, p. 12).

As for expelling asocial individuals, it is frustrating to a game theorist that such matters are so often discussed without any mention of the folk theorem of repeated game theory (Binmore Reference Binmore2005, p. 79), which was proved some twenty years before Robert Trivers wrote on reciprocal altruism. Quoting Axelrod (Reference Axelrod1984) will not suffice, because the claims Axelrod makes for the strategy tit-for-tat are almost absurdly inflated (Binmore Reference Binmore1998b). The strategy Baumard et al. needed is called the grim strategy.

Scales

Justice bears a pair of scales to make welfare comparisons without which fairness judgments would not make sense. Tooby et al. (2008) discuss this issue in terms of a welfare trade-off ratio (WRT), but Baumard et al. argue that choices based on WRT considerations will typically be unfair.

The work of John Harsanyi (Reference Harsanyi1977) on the interpersonal comparison of utility is needed here. Harsanyi considers what I call empathetic preferences. You express such a preference when saying that you think Adam would be better off in situation X than Eve in situation Y, without necessarily having anything to gain personally either way. With standard rationality assumptions, Harsanyi shows that expressing such an empathetic preference reduces to specifying a number s, which is a fixed rate at which you trade off Adam's units of utility against Eve's units of utility. I refer to s as a social index in my own work and argue that cultural evolution will lead everyone in a society to the same value of s (Binmore Reference Binmore1998a) It is this value of s that determines the coefficient of proportionality in the proportional bargaining solution in my theory.

A social index is not the same thing as a WRT, because the latter applies to sympathetic preferences, as exemplified by Hamilton's (Reference Hamilton1963) notion of inclusive fitness. However, one can speculate that our species may have graduated from using Hamilton's rule within the family to using social indices more generally via the expedient of resolving sharing problems by treating strangers as though they were relatives, with the degree of relationship determined by the context in which the sharing problem arises.