Cognition and Strategy: A Deliberation Experiment

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Cognition and StrategyA Deliberation Experiment

• Eric Dickson (NYU),
• Catherine Hafer (NYU),
• and Dimitri Landa (NYU)

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Deliberative Considerations

• Different considerations may be seen as
  relevant by different people.
• At a given point in time, individuals may not
  have in mind all considerations they would find
  to be relevant
• Considerations perceived as (potentially)
  relevant induce policy preferences
• Deliberation as argumentation
• provable messages
• non-common veridicality (considerations relevant
  for some need not be for others)
• Endogenous deliberation roles
• speaking to affect the considerations perceived
  as relevant by others VS.
• listening to receive arguments made by others or
  to withhold arguments from others

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Persuasion vs Alienation

• Imagine collective choice between leftist
  policy (induced under complete information by
  considerations (A),(B)) and a centrist policy
  (induced by (B),(C))
• Suppose you have active consideration (B), and
  a left-winger makes an argument trying to
  activate consideration (A)
• If (A) is a latent consideration of yours, (A)
  is brought to mind
• You become more likely to favor the leftist
  policy
• If (A) is not a latent consideration of yours,
  no new consideration is brought to mind
• However, an introspective listener might use this
  failure to persuade to update in favor of the
  centrist policy
• The dog that didnt bark in the night
• Sherlock Holmes realizes this implies the crime
  was not a burglary
• Dr. Watson didnt realize that the dogs silence
  could be informative
• Do people use such indirect information in
  updating policy judgments?
• And do they anticipate that others might do so?

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Model of Deliberation Information Structure

• Set of true numbers AB,BC,CD is commonly
  known (e.g., 13,37,79)
• Unconditional probabilities of each of the true
  numbers is commonly known
• Each individual knows a fragment of his or her
  true number (e.g., 3 or 7 if true number is 37)
• Set of fragments known to group members is common
  knowledge
• Pair of social alternatives x1, x2 is common
  knowledge
• Individuals known fragment a active fragment
• Individuals unknown fragment l latent fragment

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Model of Deliberation Deliberation Stage

• Individuals simultaneously choose a mode of
  deliberative participation ? ? 0,1
• ? 0 speaking (to all members of the group
  who are listening)
• ? 1 listening (to all members of the group
  who are speaking)
• Communication from i to j takes place iff i
  speaks and j listens
• If this is true (?i 0 and ?i 1)
• The message received, mj ai if and only if ai ?
  aj lj
• Otherwise mj You have received a foreign
  fragment. (that is, listener is told they have
  received a fragment that is not part of their
  true number)
• Receiving your latent fragment hearing a
  convincing argument of which you were not already
  aware
• Receiving your active fragment hearing a
  convincing argument of which you were already
  aware
• Receiving a notice of a foreign fragment
  hearing an unconvincing argument

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Model of Deliberation Voting Stage

• Once deliberation is complete, individuals vote
  for one of x1, x2
• x is the winner by simple majority rule
• Payoffs are assigned ui(x, xi) c - xi - x

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Example 1 Foreign Fragments Can Be Informative

• Commonly known set of true numbers is 13,37,79
• Group members active fragments are 1,3,3
• An individual j with active fragment 3 may have
  true number 13 or 37
• Suppose j chooses to listen, and receives notice
  of a foreign fragment
• This foreign fragment must have come from the
  individual with active fragment 1
• 1 must not be part of js true number
• 37 must be js true number

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Example 1a Strategic Incentive to Speak

• Commonly known set of true numbers is 13,37,79
• Group members active fragments are 1,3,3
• Social alternatives in voting stage 13,37
• 37 has higher unconditional probability than 13.
• An individual j with active fragment 3 may have
  true number 13 or 37
• This individual will vote for 37 in the absence
  of further information
• The individual i with active fragment 1 has a
  weakly dominant strategy to speak
• If those with active fragment 3 speak, decision
  is of no consequence
• If at least one of those with active fragment 3
  listens, speaking may convince listener to vote
  for 13 (if message of 1 is received) better
  for the speaker.
• Speaking can help but cannot hurt

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Example 1b Strategic Incentive not to Speak

• Commonly known set of true numbers is 13,37,79
• Group members active fragments are 1,3,3
• Social alternatives in voting stage 13,37
• 13 has higher unconditional probability than 37.
• An individual j with active fragment 3 may have
  true number 13 or 37
• This individual will vote for 13 in the absence
  of further information
• The individual i with active fragment 1 has a
  weakly dominant strategy to listen
• If those with active fragment 3 speak, decision
  is of no consequence
• If at least one of those with active fragment 3
  listens, speaking may convince listener to vote
  for 37 (if message indicating foreign fragment is
  received) worse for the speaker.
• Speaking can hurt but cannot help

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Experimental Setup Different Deliberative
Situations

• Distributions of Active Fragments
• ABB (or CCD)
• ABC (or BCD)
• Different probability orderings
• Pr(BCB) gt Pr(ABB)
• Pr(BCB) lt Pr(ABB)
• Agents with A and C active fragments know ex ante
  which social alternative they prefer
• Agents with B active fragments do not
• A and C agents extremists (one issue-voters,
  more extreme ex ante policy preference) B
  agents moderates
• Speaking Case A and C agents with an incentive
  to speak
• Listening Case A and C agents with an incentive
  to listen

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Experimental Instantiation

• z-tree software at Center for Experimental Social
  Science, New York University
• Two experimental sessions of 18 subjects each,
  web-based recruitment
• Each session consisted of 30 periods (period 1
  play of entire deliberation game)
• Instructions were distributed to subjects and
  also read aloud in an effort to induce common
  knowledge
• Subjects interacted anonymously through computers
  and were randomly rematched into new groups each
  period
• Different values of fragments, probabilities each
  period
• Exposure to ABB vs ABC, Speaking Case vs
  Listening Case, spread throughout experiment
• Periods 1-12 inexperienced Periods 13-30
  experienced
• Sessions lasted 90 minutes, average pay to
  subjects US26.56

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Experimental Results I Aggregate Level
Deliberation Data

• Conclusion 1 Extremists Speak More, Moderates
  Listen More
• Conclusion 2 Extremists Speak More in Speaking
  Case than in Listening Case, but barely. In
  particular there is far too much over-speaking
  in Listening Case.
• Conclusion 3 Strategically Irrelevant
  Distinctions Dont Matter Between ABB and ABC
  Between A and C role in ABC Specific Values of
  Fragments or Probabilities

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Experimental Results II Aggregate Level Voting
Data

• Conclusion 4 Subjects Almost Always Use Dominant
  Voting Strategies When Receiving their Latent
  Fragment or Receiving No Signal
• Conclusion 5 But Often Fail to Learn from
  Informative Foreign Fragments that Indicate They
  Should Vote Against their Prior Belief (Listening
  Case-ABB)
• Violation of Negative Introspection (Failure to
  learn from what does not happen or from what one
  does not know)

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Disaggregating by Behavioral Types

• Watsonian
• Violates Negative Introspection. For purposes of
  deliberation, imagines that others are also
  Watsonians.
• Deliberative Prediction Speaks as Extremist in
  Listening Case and Speaking Case
• Voting Prediction Votes incorrectly as moderate
  in Listening Case (ABB) upon receiving foreign
  fragment.
• Unreflective Bayesian
• Does Not Violate Negative Introspection. But
  fails to account for possibility that others may
  be negatively introspective.
• Deliberative Prediction Speaks as Extremist in
  Listening Case and Speaking Case
• Voting Prediction Votes correctly as moderate in
  Listening Case (ABB) upon receiving foreign
  fragment.

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Experimental Results IIIIndividual-Level Data

• Conclusion 6 The bulk of subjects can be
  classified as Watsonian/Unreflective Bayesian.
• Conclusion 7 At the individual level,
  classification in the deliberation stage is
  correlated with extent of negative introspection
  in the voting stage.
• Deliberators classified as Bayesian vote
  correctly upon receiving a foreign fragment in
  Listening Case (ABB) 100 of time (4/4)
• Deliberators classified as Watsonian/Unreflective
  Bayesian vote correctly in this situation 57.9
  of the time (11/19)
• Deliberators classified as Deviant vote
  correctly in this situation 28.6 of the time
  (2/7)

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Experimental Results IVWatsonians and
Unreflective Bayesians

• Conclusion 8 There is a significant presence of
  both Watsonian and Unreflective Bayesian Types
• Subjects classified as Watsonian/Unreflective
  Bayesian based on deliberative choices vote
  correctly 57.9 of the time (11/19) in Listening
  Case (ABB)
• If they were all Watsonians would be 0
• If they were all UB would be 100.
• Post-experiment questionnaire responses are
  broadly consistent with these conclusions
• How did you decide when to send vs receive?
• Did your choice of sending vs. receiving vary
  depending on circumstances? If so, how?
• Did communication often help you decide how to
  vote - and if so, how?
• Pattern of responses is Bayesian for a small
  of subjects is Watsonian for a large of
  subjects and is Bayesian with respect to
  voting but not deliberative choices for some (UB).

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Alternative Hypothesis

• Everyone is Bayesian, but believes others are a
  deviant type that will vote randomly unless they
  know both fragments of their true number (in
  which case they will vote correctly).
• But
• Quiz Questions people understand probability
  structure of game
• Voting Behavior people vote correctly when
  they receive no message
• Questionnaire Questions people thought that the
  game was easy and believed that others also
  found it easy