Ethical Rules, Games, and Evolution

Ted Bergstrom, Economics Dept, UCSB

Our Charge for “Debate” We know that the distinctive features of the

human body, such as our large brains, nearly hairless bodies and dexterous hands, have evolved through natural selection … Our social behaviour may have evolved in the same way…

The second point of view, however, is that our social behaviour, and the systems of ethics on which it is based, are uniquely human, and owe nothing to the processes that govern societies of ants or bacteria. Our bodies may have evolved, but our ethics requires another kind of explanation.

My Take Evolutionary thinking has much to tell us about

ethics and the presence of altruism. Game theory allows us to frame questions more

effectively. Does ethics require a “another kind of

explanation” from that of the evolution of our bodies? Well, of course, just as the evolution of our eyes require

“different “ explanations from that of our ears. Deeper difference is “cultural evolution”. You can

inherit ethical notions from “teachers” other than your parents.

This implies different calculus of inheritance and reproduction.

Two Competing Golden Rules

``Thou shalt love thy neighbor as thyself.’’ ---Old Testament: Leviticus 19:18 ``Do unto others as you would have them do

unto you’’ ---New Testament: Luke 6:31 One rule is an exhortation to extreme

sympathy, the other to extreme symmetry. Questions:

Are these rules different? Why are they so extreme?

Common to many cultures Love thy neighbor rules—Command for

sympathy Taoist version: ``Regard your neighbor's gain as

your gain, and your neighbor's loss as your loss.‘ Do unto others rules---Command for symmetry

Confucius: “Never impose on others what you would not choose for yourself.”

Aristotle: “We should behave toward friends as we would wish friends to behave toward us.”

Kant: Act only according to the maxim whereby you can at the same time will that it should become a universal law.''

Hamilton’s Rule:

(A report, not an entreaty.) Hamilton maintains that evolutionary

principles predict that:``The social behavior of a species evolves in

such a way that in each distinct behavior-evoking situation the individual will seem to value his neighbors' fitness against his own according to the coefficients of relationship appropriate to that situation.''

Who is my neighbor? The Pharisee’s Question

What is the domain of sympathy and/or symmetry?

Old Testament, Taoists, and Aristotle seem to restrict this domain to “neighbors” or “friends”.

Confucius, Kant, and Parable of the Good Samaritan seem to include all persons.

Hamilton makes very specific predictions. Individuals have sympathy only for relatives and

that only proportional to relatedness

Golden Rules and Hamilton’s Rule

When should you take an action that costs you C and benefits another person by B?

Golden Rules: Do it if: the person is a “neighbor” and B>C.

Hamilton’s rule: Do it if and only if; rB>C (where r is coefficient of relatedness to

recipient)

Coefficient of Relatedness

The coefficient of relatedness of two individuals is the probability that if one has a rare mutation, so will the other.

For sexual diploids, like ourselves, coefficient of relatedness r is r=1/2 for full siblings, 1/4 for half siblings, 1/8 for

cousins 1/2 for parent and child, 1/4 for grandparent and

child, etc. Nearly 0 for random stranger

Are Golden Rules Unrealistic?

Believers in Homo Economicus would think so.

So would believers in Hamilton’s Rule.

Are golden rules just empty preaching?

Return to this question later.

Ethics in games Subtleties of ethics are better understood in

framework of game theory. Hamilton considered only a special class of

“game” in which both the cost to you and the benefit to the other player of your own action is independent of the other player’s action.

In this environment, the two versions of the golden rule are equivalent.

In more general games, they are not.

An Example: A prisoners’ dilemma game Two strategies, c and d. Payoff function f(x,y) is what you get if you do x

and the other person does y. Let f(c,c)=R, f(d,d)=P, f(d,c)=T, and f(c,d)=S,

where S<P<R<T. Selfish Play: Dominant strategy equilibrium is both

choose d. Do unto others rule. You would like other to

cooperate. So rule demands cooperate. Love thy neighbor rule: Choose the thing that

maximizes the sum of your payoff and other player’s.

Love-thy-Neighbor in Prisoners’ Dilemma Love thy neighbor can lead to a trap where both

defect. Players care equally about their own and neighbor’s

payoff. Suppose that T+S<2P. Then there is a Nash equilibrium where both defect. If other guy is defecting, we will both get P if I

defect. If I cooperate, he will be better off, but his gain T-P is

less than my loss, P-S. There is also an equilibrium where both cooperate,

but this is not unique as it is for Do-unto-others types

Love-thy-neighbor in Prisoners’ Dilemma Prisoners’ dilemma as before. Players care equally about their own and

neighbor’s payoff. Suppose that T+S>2R In equilibrium, one defects and the other

cooperates. Doing the opposite of the other guys action

maximizes sum of payoffs. In this case, love-thy-neighbor results in

higher joint return than Do-unto-others.

Hamilton’s rule for general games. Two possibilities: Corresponding to Love-thy-neighbor

Love thy neighbor r times as well as thyself. Act as if your payoff is H(x,y)=f(x,y)+rf(y,x)

Corresponding to Do-unto-others Semi-Kantian rule: Act as if the probability is r that

your neighbor will copy you Act as if your payoff is V(x,y)=(1-r)f(x,y)+rf(x,y)

In simple additive games considered by Hamilton, these two rules yield same behavior.

In general, they do not.

Which Hamilton’s rule is right? Do we expect to see evolution of “love for relatives”

of of more abstract semi-Kantian behavior? For sexual diploids and symmetric games, the semi-

Kantian rule is predicted by the most common model of resistance to dominant mutant alleles.

For asymmetric role-playing games, either rule could be appropriate, depending on the details of genetics and cross-over.

For games with “concave payoff functions” predictions of the two theories predict the same behavior.

Maybe love is easier to evolve.

Is Hamilton’s rule too selfish? Why might evolution produce more altruism

than Hamilton’s rule predicts? Common reproductive interest of partners

mated for life. Repeated interactions between any two

people. If repeated encounters mean that you will

usually wind up playing with somebody who plays as you do, then a “semi-Kantian” preference with high r may be the most successful under evolutionary pressure.

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