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For Savvy Bayesian Wannabes, Disagreements Are Not About Information

For Savvy Bayesian Wannabes, Disagreements Are Not About Information. Robin Hanson RWJF Health Policy Scholar U.C. Berkeley. Correctable Mental Mistakes. “Men have above average IQ. So do women.” “Win or lose, I’ll be disappointed.” “Let’s cooperate in this zero-sum game.”

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For Savvy Bayesian Wannabes, Disagreements Are Not About Information

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  1. For Savvy Bayesian Wannabes,Disagreements Are Not About Information Robin Hanson RWJF Health Policy Scholar U.C. Berkeley

  2. Correctable Mental Mistakes “Men have above average IQ. So do women.” “Win or lose, I’ll be disappointed.” “Let’s cooperate in this zero-sum game.” “We agree to disagree on that.”

  3. Who Can’t Agree to Disagree • Bayesians (with common prior):given • common knowledge of exact opinions (Aumann ‘76), separating point (Sebenius & Geanakoplos ‘83), monotone statistic (McKelvey & Page ‘86) • common belief of such (Monderer & Samet ‘89) • 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)

  4. The Puzzle of Disagreement • Persistent disagreement seems ubiquitous • Speculative trading • Disputes in science, business, politics, juries • Arguments among friends, family • Possible explanations • Not real: persuasion, signal ability/association • Fixable irrationality: world will change • Infeasible rationality

  5. Prior Info Errors Consider Bayesian Wannabes Pure Agree to Disagree? Disagree Sources Yes No Yes Either combo implies pure version! Ex: E1[p] @ 3.14, E2[p]@ 22/7

  6. Theorem in English • If two Bayesian wannabes • nearly agree to disagree about any X, • nearly agree that the conclusion of a theorem holds, • presumably because the assumptions of this theorem hold: • both agents consider themselves well-calibrated regarding X, • one agent’s estimates are consistent with another theorem, and • she estimates both are rarely mistaken about whether they agree, • Then they nearly agree to disagree about Y, one’s average calibration error regarding X. (Y is state-independent, so information is irrelevant).

  7. Notation

  8. More Notation

  9. Still More Notation

  10. Let 1,2 Agree to Disagree

  11. Main Theorem

  12. Conclusion • Bayesian wannabes are a general model of computationally-constrained agents. • “Savvy” means has self-respect, maintains certain other easy-to-manage constraints on estimates. • For savvy Bayesian wannabes, A.D. (agreeing to disagree) regarding X(w) implies A.D. re Y(w)=Y. • Since information is irrelevant to estimating Y, any A.D. implies a pure error-based A.D. • So if pure error A.D. is irrational, all A.D. are.

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