1. For Bayesian Wannabes, Are Disagreements Not About Info? Robin Hanson Economics, GMU

2. The Puzzle of Disagreement  Persistent disagreement ubiquitous Speculative trading, wars, juries, … Argue in science, politics, family, …  Theory seems to say this irrational  Possible explanations We’re “just joshing” Infeasible epistemic rationality Fixable irrationality: all will change! Other rationality – truth not main goal

3. 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

4. We Can’t Agree to Disagree Aumann in 1976  Re possible worlds  Common knowledge  Of exact E 1 [x], E 2 [x]  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 ±(E 1 [x] - E 1 [E 2 [x]]) ® At core, or Wannabe ® Symmetric prior origins

5. 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 …

6. Consider Bayesian Wannabes Prior Info Errors Pure Agree to Disagree? Yes No Yes Ex: E 1 [p] @ 3.14, E 2 [p] @ 22/7 Disagree Sources Either combo implies pure version!

7. 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 agent’s estimate of other’s bias is consistent with a certain simple algebraic relation  Then they nearly agree to disagree about Y, one agent’s average error regarding X. (Y is state-independent, so info is irrelevant).

8. Notation

9. More Notation

10. Still More Notation

11. Let 1,2 Agree to Disagree Re X

12. Theorems 1 2

13. 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 agent’s estimate of other’s bias is consistent with a certain simple algebraic relation  Then they nearly agree to disagree about Y, one agent’s average error regarding X. (Y is state-independent, so info is irrelevant).

14. Consider Bayesian Wannabes Prior Info Errors Pure Agree to Disagree? Yes No Yes Ex: E 1 [p] @ 3.14, E 2 [p] @ 22/7 Disagree Sources Either combo implies pure version!

15. 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.