In 1969 Robert Nozick published Newcomb's Problem and Two Principles of Choice. At the time most philosophers were familiar with the decision theory of Richard Jeffrey. In Jeffrey's theory, the subjective expected utility of an act is an average of possible payoffs, weighted by degrees-of-belief of getting the payoff conditional on performing the act. Nozick framed the problem as a collision between Jeffrey's expected utility theory and the principle of dominance. Dominance says that if act A is better than act B in each possible circumstance, it is better overall.

In Newcomb's problem, and a host of similar problems, A is better than B no matter how the world is at the time of decision, but doing B is a sign or symptom that in the past something has happened with large favorable payoff consequences.

Beliefs about signs or symptoms show up in conditional degrees of belief and thus in Jeffrey's expected utility. Which act is choiceworthy in such a situation? Philosophers split up into camps defending one answer or another.

Those of us who thought that choiceworthiness should pay attention to causal consequences of an act and ignore the act's diagnostic or symptomatic status formulated various forms of causal decision theory: Bob Stalnaker, Allan Gibbard and Bill Harper, and David Lewis incorporated subjunctive conditionals in the expectation; I used a partition of possible causal backgrounds. It soon became clear that with some auxiliary assumptions these were all the same theory. Representation theorems for causal decision theory were later proved by Brad Armendt and by Jim Joyce. It also became clear that, given the right reading, the decision theory of L. J. Savage can be viewed as causal decision theory. Jeffrey's decision theory became known as evidential decision theory, in contrast to causal decision theory. Is the choiceworthiness of an act to be evaluated by viewing it as evidence or as cause?

Those who fought over the correct act in the Newcomb problem now took sides in the battle between evidential and causal decision theory. It is noteworthy that the architect of evidential decision theory, Richard Jeffrey, did not join the ranks of those defending apparent conclusions of evidential decision theory. He thought that causal decision theory gave the right answer.

ULTIMATUM BARGAINING

IN Chapter 1, we examined a bargaining game in which the position of the participants was entirely symmetric. Here we move to the other extreme, where one participant has – or appears to have – all the bargaining power. Again, there is a good to be divided if a bargain can be struck. The advantaged party gets to issue an ultimatum: “I want so much; take it or leave it.” The disadvantaged party accepts or not. If it is “yes,” the ultimatum giver gets what she asked for, leaving the rest for her partner. If it is “no,” neither gets anything.

The reasoning for the ultimatum giver’s advantage goes as follows. If the second player is offered a small amount, he will take it, since something is better than nothing. The ultimatum giver can see this, so he asks for almost all the good. Then the second player agrees.

The advantage is that the first player has only one move in the game, which is giving the ultimatum. She is not given any opportunity to revise her demand. She is committed. If the responder were given the opportunity to pre-commit to a minimum acceptable share and make it known before anything happened, then he would be the ultimatum giver, and have the bargaining advantage.

SEQUENTIAL RATIONALITY

In Stanley Kubrick’s 1963 film, Dr. Strangelove, or How I Learned to Stop Worrying and Love the Bomb, the USSR has built a doomsday machine – a device that, when triggered by an enemy attack or when tampered with in any way, will set off a nuclear explosion potent enough to destroy all human life. The doomsday machine is designed to be set off by tampering, not to guard it from the enemy but to guard it from its builders having second thoughts. For surely if there were an attack, it would be better for the USSR to suffer the effects of the attack than to suffer the combined effects of the attack and the doomsday machine. After an attack, if they could, they would disable the doomsday machine. And if their enemies could anticipate this, the doomsday machine would lose its power to deter aggression. For this reason, the commitment to retaliate had been built into the doomsday machine. Deterrence requires that all this be known. There is a memorable scene in the film in which Peter Sellers as Dr. Strangelove shouts: “You fools! A doomsday machine isn’t any good if you don’t tell anyone you have it!”

SOME things stay the same, and some things change. We know more about some of the issues addressed in this book than we did when it was written. I have made changes, some small and some larger, to bring the discussion up to date. There are new footnotes and lots of new references, of course. Some larger modifications are made in the substantive discussions.

In Chapter 1 I say a little more to preview the importance of correlation that is to be the main theme in Chapter 3. I refer to correlation set up by local interaction in the form of bargaining with neighbors. This is work done with Jason McKenzie Alexander that was produced subsequent to the publication of the first edition. I also make a historical correction: Darwin himself really cracked the sex ratio puzzle.

I am more circumspect in Chapter 2 about the connection between rationality and backward induction, perhaps one might say evasive, since I do not want to plunge into the counterfactual reasoning involved. That is not what this book is about. I change terminology from “modular rationality” to “sequential rationality” to bring it into alignment with the standard terminology in the game theory literature. The empirical discussion of behavior in ultimatum bargaining now includes the work of anthropologists, which reveals great variability across small-scale societies. This fits well with a discussion of framing of social norms that was only hinted at in the first edition. There is a reference to new work with Kevin Zollman on a model of such framing.

ON June 18, 1862, Karl Marx wrote to Friedrich Engels, “It is remarkable how Darwin has discerned anew among beasts and plants his English society… It is Hobbes’s bellum omnium contra omnes.” Marx is not quite fair to Darwin. But in 1888, in an essay entitled “The Struggle for Existence and Its Bearing upon Man,” Thomas Henry Huxley wrote:

Huxley’s portrayal of “nature red in tooth and claw” had a great popular impact, and contributed to paving the way for the social Darwinism that he himself detested. The great anarchist Prince Petr Kropotkin was moved to publish an extended rebuttal in the same periodical, Nineteenth Century, that had carried Huxley’s essay. Kropotkin’s articles, which appeared over a period from 1890 to 1896, were collected in a book entitled Mutual Aid: A Factor of Evolution. The introduction begins:

Two aspects of animal life impressed me most during my youth in Eastern Siberia and Northern Manchuria.

THE preceding five chapters do not attempt to present a full theory of the evolution of the social contract. Rather, they are an introduction to some of the elements of such a theory. From one perspective, the elements may be seen as a list of simple models of general problem areas: bargaining games and distributive justice, ultimatum games and commitment, Prisoner’s Dilemma and mutual aid, hawk–dove and the origin of ownership, and signaling games and the evolution of meaning.

But from another point of view, the elements of the theory are the basic conceptual tools that have been introduced along the way. In the first chapter, we met the basic concepts of Nash equilibrium and Evolutionarily stable strategy, and the replicator dynamics that stands behind the concept of evolutionary equilibrium. We saw how one could explore the effect of various factors on the size of basins of attraction of equilibrium states of the population. In Chapter 2, we saw the tension possible between commitment and sequential rationality. Here classical game theory and the theory of evolution begin to diverge. When we apply the replicator dynamics to the symmetrized ultimatum game, we find it does not eliminate strategies that fail the test of sequential rationality. This remains true even when we introduce the “trembling hand” into our evolutionary models by adding mutation and recombination to the replicator dynamics. In Chapters 3 and 4, we met two rather different kinds of correlated equilibria. In evolutionary game theory, there are two different kinds of (uncorrelated) mixed equilibria: one where individuals play randomized strategies and another where the randomness comes from random pairing in a polymorphic population. Generalization of the first kind of mixed equilibrium to the correlated case gives the Aumann correlated equilibrium of Chapter 4, which plays such a central role in convention formation by symmetry breaking. Generalization of the second kind of mixed equilibrium to non-random pairing gives the entirely different correlated evolutionary game theory developed in Chapter 3, which stands behind all accounts of the evolution of altruism.

THE best-known tradition approaches the social contract in terms of rational decision. It asks what sort of contract rational decision makers would agree to in a preexisting “state of nature.” This is the tradition of Thomas Hobbes and – in our own time – of John Harsanyi and John Rawls. There is another tradition – exemplified by David Hume and Jean-Jacques Rousseau – which asks different questions. How can the existing implicit social contract have evolved? How may it continue to evolve? This book is intended as a contribution to the second tradition.

Hegel and Marx are, in a way, on the periphery of the second tradition. Lacking any real evolutionary dynamics, they resorted to the fantasy of the dialectical logic of history. It was Darwin who recognized that the natural dynamics of evolution is based on differential reproduction. Something like differential reproduction operates on the level of cultural as well as biological evolution. Successful strategies are communicated and imitated more often than unsuccessful ones. In the apt language of Richard Dawkins, we may say that both cultural and biological evolution are processes driven by differential replication. There is a simple dynamical model of differential replication now commonly called the replicator dynamics. Although this dynamics is surely oversimplified from both biological and cultural perspectives, it provides a tractable model that captures the main qualitative features of differential replication. The model can be generalized to take account of mutation and recombination. These biological concepts also have qualitative analogues in the realm of cultural evolution. Mutation corresponds to spontaneous trial of new behaviors. Recombination of complex thoughts and strategies is a source of novelty in culture. Using these tools of evolutionary dynamics, we can now study aspects of the social contract from a fresh perspective.

IN 1710 there appeared in the Philosophical Transactions of the Royal Society of London a note entitled “An argument for Divine Providence, taken from the constant Regularity observ’d in the Births of both Sexes.” The author, Dr. John Arbuthnot, was identified as “Physitian in Ordinary to Her Majesty, and Fellow of the College of Physitians and the Royal Society.” Arbuthnot was not only the Queen’s physician. He had a keen enough interest in the emerging theory of probability to have translated the first textbook on probability, Christian Huygens’s De Ratiociniis in Ludo Aleae, into English – and to have extended the treatment to a few games of chance not considered by Huygens.

Arbuthnot argued that the balance between the numbers of the men and women was a mark of Divine Providence “for by this means it is provided that the Species shall never fail, since every Male shall have its Female, and of a Proportionable Age.” The argument is not simply from approximate equality of the number of sexes at birth. Arbuthnot notes that males suffer a greater mortality than females, so that exact equality of numbers at birth would lead to a deficiency of males at reproductive age. A closer look at birth statistics shows that “to repair that loss, provident Nature, by the disposal of its wise Creator, brings forth more Males than Females; and that in almost constant proportion.” Arbuthnot supports the claim with a table of christenings in London from 1629 to 1710 that shows a regular excess of males and with a calculation to show that the probability of getting such a regular excess of males by chance alone was exceedingly small.

THE CURSE OF SYMMETRY

DANTE is recycling an ancient argument. Anaximander argued that the earth remained motionless in the center of the universe for lack of any reason for it to go one way or another. Socrates, in the Phaedo, endorses the relevant principle: A thing which is in equipoise and placed in the midst of something symmetrical will not be able to incline more or less towards any particular direction. Socrates anticipates the physicist Pierre Curie who, twenty-five centuries later, enunciated the general principle that the symmetries of causes reappear as symmetries of their effects. In the theory of rational decision, Curie’s principle takes on the character of a curse. It appears that decision makers cannot choose between symmetric optimal alternatives and must remain paralyzed in indecision. Where does the curse operate? How can it be broken?

MODERN philosophy of language is saturated with skeptical doubts. Wittgenstein questions the efficacy of ostensive definition. Searle argues that nothing in the mechanics or algorithms of computation can endow the manipulated symbols with meaning or the computer with understanding. But Searle’s argument does not use the fact that computers are implemented in silicon. Shouldn’t his skepticism transfer to animals, for instance? Nagel argues that no amount of neurophysiology can tell us what it is like to be a bat. Can biochemistry endow the neurological processes of a bat – or a whale, or a chimpanzee – with meaning? But what about other humans? Quine invites us to put ourselves in the position of a field linguist in an alien culture. A rabbit runs out of the bush and a native shouts gavagai. It is consistent with the observed facts that gavagai means rabbit to the native, but any number of other possibilities are consistent with the observed facts. Gavagai might mean running rabbit or good to eat or even temporal slice of a rabbit. (After reading Searle, should we add the possibility of no meaning at all?) Quine concludes that without some preexisting shared system of language we can never know what the native means by gavagai. Quine is willing to follow his argument to its logical conclusion. In principle, the same problem is faced by people in the same culture – by any people who communicate. And he points out that his skepticism about translation is just one facet of a more general skepticism about induction, grounded on the underdetermination of theory by evidence.

Where does the skeptical philosophy of language lead? An influential group of literary critical theorists goes much further than Quine does. They give up not only on intensional meaning but also on truth and denotation, reducing language to the bare existence of text. But if there is no meaning, there is no distinction between symbol and non-symbol, text and non-text. These theorists should quietly go out of business. (And, as of this edition, they have gone out of business – or at least out of fashion.) After looking into the abyss, it is tempting simply to dismiss this skepticism as unproductive, as requiring too much of knowledge and as neglectful of non-demonstrative inference. But these skeptical musings do raise important scientific questions for naturalized epistemology.