Ethical Rules, Games, and Evolution

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Ethical Rules, Games, and Evolution

• Ted Bergstrom, Economics Dept, UCSB

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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.

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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.

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Two Competing Golden Rules

• Thou shalt love thy neighbor as thyself.
• ---Old Testament Leviticus 1918
• Do unto others as you would have them do unto
  you
• ---New Testament Luke 631
• One rule is an exhortation to extreme sympathy,
  the other to extreme symmetry.
• Questions
• Are these rules different?
• Why are they so extreme?

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Common to many cultures

• Love thy neighbor rulesCommand 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.''

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Hamiltons 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.''

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Who is my neighbor? The Pharisees 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

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Golden Rules and Hamiltons 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 BgtC.
• Hamiltons rule Do it if and only if
• rBgtC (where r is coefficient of relatedness to
  recipient)

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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
• r1/2 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

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Are Golden Rules Unrealistic?

• Believers in Homo Economicus would think so.
• So would believers in Hamiltons Rule.
• Are golden rules just empty preaching?
• Return to this question later.

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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 players action.
• In this environment, the two versions of the
  golden rule are equivalent.
• In more general games, they are not.

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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
• SltPltRltT.
• 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
  players.

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Love-thy-Neighbor in Prisoners Dilemma

• Love thy neighbor can lead to a trap where both
  defect.
• Players care equally about their own and
  neighbors payoff.
• Suppose that TSlt2P.
• 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

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Love-thy-neighbor in Prisoners Dilemma

• Prisoners dilemma as before.
• Players care equally about their own and
  neighbors payoff.
• Suppose that TSgt2R
• 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.

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Hamiltons 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.

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Which Hamiltons 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.

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Is Hamiltons rule too selfish?

• Why might evolution produce more altruism than
  Hamiltons 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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