For Bayesian Wannabes, Are Disagreements Not About Info?

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For Bayesian Wannabes, Are Disagreements Not
About Info?

• Robin Hanson
• Economics, GMU

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The Puzzle of Disagreement

• Persistent disagreement ubiquitous
• Speculative trading, wars, juries,
• Argue in science, politics, family,
• Theory seems to say this irrational
• Possible explanations
• Were just joshing
• Infeasible epistemic rationality
• Fixable irrationality all will change!
• Other rationality truth not main goal

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My Answer We Self-Deceive

• We biased to think better driver, lover,
• I less biased, better data analysis
• Evolutionary origin helps us to deceive
• Mind leaks beliefs via face, voice,
• Leak less if conscious mind really believes
• Beliefs like clothes
• Function in harsh weather, fashion in mild

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We Cant Agree to Disagree

• Aumann in 1976
• Re possible worlds
• Common knowledge
• Of exact E1x, E2x
• Would say next
• For Bayesians
• With common priors
• If seek truth, not lie

• Since generalized to
• Impossible worlds
• Common Belief
• A f(, ), or who max
• Last (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

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Generalize to Bounded Rationality

• Bayesians (with common prior)
• Possibility-set agents balanced (Geanakoplos
  89), or Know that they know (Samet 90),
• Turing machines prove all computable in finite
  time (Medgiddo 89, Shin Williamson 95)
• Many more specific models

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Consider Bayesian Wannabes
Pure Agree to Disagree?
Disagree Sources

• Prior
• Info
• Errors

Yes No Yes

Either combo implies pure version!
Ex E1p _at_ 3.14, E2p _at_ 22/7
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Theorem in English

• If two Bayesian wannabes
• nearly agree to disagree about any X,
• nearly agree that both think they nearly
  unbiased,
• nearly agree that one agents estimate of others
  bias is consistent with a certain simple
  algebraic relation
• Then they nearly agree to disagree about Y, one
  agents average error regarding X.
• (Y is state-independent, so info is
  irrelevant).

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Notation
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More Notation
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Still More Notation
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Let 1,2 Agree to Disagree Re X
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Theorems
1
2
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Theorem in English

• If two Bayesian wannabes
• nearly agree to disagree about any X,
• nearly agree that both think they nearly
  unbiased,
• nearly agree that one agents estimate of others
  bias is consistent with a certain simple
  algebraic relation
• Then they nearly agree to disagree about Y, one
  agents average error regarding X.
• (Y is state-independent, so info is
  irrelevant).

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Consider Bayesian Wannabes
Pure Agree to Disagree?
Disagree Sources

• Prior
• Info
• Errors

Yes No Yes

Either combo implies pure version!
Ex E1p _at_ 3.14, E2p _at_ 22/7
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Conclusion

• Bayesian wannabes are a general model of
  computationally-constrained agents.
• Add minimal assumptions that maintain some
  easy-to-compute belief relations.
• For such Bayesian wannabes, A.D. (agreeing to
  disagree) regarding X(w) implies A.D. re Y(w)Y.
• Since info is irrelevant to estimating Y, any
  A.D. implies a pure error-based A.D.
• So if pure error A.D. irrational, all are.