Social Choice and Social Norms

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Social Choice and Social Norms

• Anabela Botelho, Glenn W. Harrison, Ligia C.
  Pinto, and me

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Theory of Public Goods and Voluntary Contributions

• Max U(x, ?y) s.t. px x py y Y
• x private good
• y public good
• ?y total contributions by everyone
• Assume linear utility MUxMUy
• and px 1 pygt1
• MUx/ px gt MUy / py
• Prediction nobody will contribute to y
• Social return from contributions depend on number
  of participants
• MSy nMUy
• MUx/ px gt MSy / py

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Experimental design

• Initial endowment for spendings on x and y 10
  tokens
• MU(x)MU(y)
• px1 and py1/0.61.67
• If everyone contributes all tokens, utility for
  each individual is n10/1.67, for n4 it is 24
• If nobody contributes all tokens, utility is 10,
  obviously less
• What comparative statics could be investigated?
• Theory prediction is independent of the parameter
  values
• Testing theory comparing decisions over two
  private goods to those over one private and one
  public
• Auxiliary factors
• Propensity to signal and cooperate should be
  decreasing in n since it is harder to generate
  and sustain cooperation in larger groups
• Return to risky action of signaling and
  cooperating is increasing in n since total gain
  is larger
• Return is also decreasing in py
• Confounds
• Identify the first and second effects of n

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Treatments

• Increase n keeping nE/py constant (i.e. decrease
  E or increasy py)
• Increase n keeping E and py constant
• Increase py keeping n and E constant
• Provision points?

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Phenomena

• Reject the standard theory prediction
• Voluntary contributions significantly higher than
  0 particularly in early rounds
• Contributions decay over rounds
• Contributions do not disappear
• How can we reject that subjects are not just
  picking choices randomly?
• On average half of tokens should be contributed
  if risk neutral
• If risk averse should contribute less than half
  since contributions are riskier than private
  account
• Alternative hypotheses?
• Extend the theory

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Extensions to theory

• Reciprocity U(y,ry-i)
• Altruism U(y,a)
• Inequality aversion Ua(y-y-i)b(y-i-y)
• b gt a
• b is envy
• a is guilt
• Random choice plus risk aversion
• Maximize expected earnings
• Max EU(Y) where Yx?y and
• E(?y) increasing in y
• If preferences are based on reciprocity they
  should generate actions such as Punishments and
  Rewards if they are allowed

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Theory with VCM and punishment

• Max U(x, ?y,r(y-i)) s.t. px x py y prrY
• r is the punishment action
• MU(r)gt0 if y-i0
• MU(r)0 if y-igt 0 for all others

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Experimental design

• Reciprocity vs. random choice, or altruism, or
  inequality aversion
• The latter do not generate utility from
  punishment and prediction should be zero
  punishment
• Use same VCM design
• Add a subsequent stage where each subject has a
  choice to punish, but this is a costly act

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Phenomena
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New Question

• Contributions are higher and more sustained when
  voluntary punishments are allowed
• So what?
• Is society better because contributions are
  higher?
• Punishment is costly in terms of net resources
  perhaps we are worse off

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State Hypothesis

• In societies with voluntary punishments
• Voluntary contributions will be higher and more
  sustained
• The cost of punishment will exceed the benefits
  of the contributions
• When given a choice participants will prefer the
  institution with higher earnings, not higher
  contributions
• Than in societies that lack punishment
  opportunities
• Will punishments work as well when there is no
  perceived repeated game effect?

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Design

• What to keep from previous designs?
• VCM mechanism
• Punishment mechanism the same
• Remove repeated game effects
• Necessitates small groups
• Groups of 2
• Vary returns as before
• Add a stage to elicit preferences over societies
  with and without punishment
• What information or experience is needed when
  giving them the choice?

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Our design

• 10 rounds of no punishment
• 10 rounds with punishment
• Matching rule?
• Majority vote over these two options
• One more round at 10 times the payoffs
• Training and instructions?