1. Cognition and Strategy: A Deliberation Experiment
Eric Dickson (NYU),
Catherine Hafer (NYU),
and Dimitri Landa (NYU)

2. 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

3. 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 didn’t bark in the night”
Sherlock Holmes: realizes this implies the crime was not a burglary
Dr. Watson: didn’t realize that the dog’s silence could be informative
Do people use such indirect information in updating policy judgments?
And do they anticipate that others might do so?

4. 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
Individual’s known fragment a: “active fragment”
Individual’s unknown fragment l: “latent fragment”

5. 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

6. 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|

7. 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 j’s true number
…37 must be j’s true number

8. 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

9. 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

10. Experimental Setup: Different Deliberative Situations
Distributions of Active Fragments
ABB (or CCD)
ABC (or BCD)
Different probability orderings
Pr(BC|B) > Pr(AB|B)
Pr(BC|B) < Pr(AB|B)
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

11. 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 US$26.56

12. 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 Don’t Matter: Between ABB and ABC; Between A and C role in ABC; Specific Values of Fragments or Probabilities

13. 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)

14. 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.
Voting Prediction: Votes correctly as moderate in Listening Case (ABB) upon receiving foreign fragment.

15. Experimental Results III: Individual-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)

16. Experimental Results IV: Watsonians 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).

17. 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”