The Irrationality of Disagreement

1. The Irrationality of Disagreement Robin Hanson Associate Professor of Economics George Mason University

2. We Disagree, Knowingly • Stylized Facts: • Argue in science/politics, bets on stocks/sports • Especially regarding ability, when hard to check • Less on “There’s another tree” • Dismiss dumber, but not defer to smarter • Disagree not embarrass, its absence can • Given any free pair, find many disagree topics • Even people who think rationals should not disagree • Precise: we can publicly predict direction of other’s next opinion, relative to what we say

3. Aumann 1976 assumed: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie, josh, or misunderstand We Can’t Agree to Disagree Nobel Prize 2005 his most cited paper by x2 Agent 1 Info Set Agent 2 Info Set Common Knowledge Set

4. age 7 here age 2 here John estimates car age E1[x] “It wasn’t shiny” “I’ve never been wrong before” “I can still picture it” “It sounded old” “I had a good viewing angle” “Fred said so” “Mary is blind”

5. age 7 here age 2 here Mary estimates car age E2[x]

6. Agree If Averages Same E1[x] = E2[x] Aumann (1976) Annals Stat. 4(6):1236-9.

7. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

8. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

9. Disagreement Is Unpredictable Hanson (2002) Econ. Lett. 77:365–369.

10. A gets clue on X A1 = A’s guess of X A told Sign(B2-B1) A2 = A’s guess of X Loss (A1-X)2+(A2-X)2 B gets clue on X B told A1 B1 = B’s guess of X B2 = B’s guess of A2 Loss (B1-X)2+(B2-A2)2 Experiment Shows Disagree E.g.: What % of U.S. say dogs better pets than cats? time Example 30% 70% 40% “low” 40% A neglects clue from B B reliably predicts neglect

11. Complexity of Agreement Can exchange 100 bits, get agree to within 10% (fails 10%). Can exchange 106 bits, get agree to within 1% (fails 1%). “We first show that,for two agents with a common prior to agree within ε about the expectation of a [0,1] variable with high probability over their prior, it suffices for them to exchange order 1/ε2 bits. This bound is completely independent of the number of bits n of relevant knowledge that the agents have. … we give a protocol ... that can be simulated by agents with limited computational resources.” Aaronson (2005) Proc. ACM STOC, 634-643.

12. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

13. Generalized Beyond Bayesians • Possibility-set agents: if balanced (Geanakoplos ‘89), or “Know that they know” (Samet ‘90), … • Turing machines: if can prove all computable in finite time (Medgiddo ‘89, Shin & Williamson ‘95) • Ambiguity Averse (maxact minp in S Ep[Uact]) • Many specific heuristics … • Bayesian Wannabes

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

15. Theorem in English • If two Bayesian wannabes • nearly agree to disagree about any X, • nearly agree each thinks himself 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). Hanson (2003) Theory & Decision 54(2):105-123.

16. Wannabe Summary • 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.

17. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

18. Which Priors Are Rational? Prior = counterfactual belief if same min info • Extremes: all priors rational, vs. only one is • Can claim rational unique even if can’t construct (yet) • Common to say these should have same prior: • Different mental modules in your mind now • You today and you yesterday (update via Bayes’ rule) • Common to criticize self-favoring priors in others • E.g., coach favors his kid, manager favors himself • “I (Joe) beat Meg, but if I were Meg, Meg beats Joe” • Prior origins not special => priors same

19. Origins of Priors • Seems irrational to accept some prior origins • Imagine random brain changes for weird priors • In standard science, your prior origin not special • Species-common DNA • Selected to predict ancestral environment • Individual DNA variations (e.g. personality) • Random by Mendel’s rules of inheritance • Sibling differences independent of everything else! • Culture: random + adapted to local society • Turns out you must think differing prior is special! • Can’t express these ideas in standard models

20. Standard Bayesian Model Agent 1 Info Set A Prior Agent 2 Info Set Common Kn. Set

21. An Extended Model Multiple Standard Models With Different Priors

22. Standard Bayesian Model

23. Extending the State Space As event

24. An Extended Model

25. My Differing Prior Was Made Special My prior and any ordinary event E are informative about each other. Given my prior, no other prior is informative about any E, nor is E informative about any other prior.

26. Corollaries My prior only changes if events are more or less likely. If an event is just as likely in situations where my prior is switched with someone else, then those two priors assign the same chance to that event. Only common priors satisfy these and symmetric prior origins.

27. A Tale of Two Astronomers • Disagree if universe open/closed • To justify via priors, must believe: “Nature could not have been just as likely to have switched priors, both if open and if closed” “If I had different prior, would be in situation of different chances” “Given my prior, fact that he has a particular prior says nothing useful” All false for brothers’ genetic priors!

28. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

29. Theory or data wrong? Few know theory? Infeasible to apply? We lie? Exploring issues? Misunderstandings? We not seek truth? Each has prior: “I reason better” ? They seem robust Big change coming? Need just a few adds We usually think not, and effect is linear But we complain of this in others Why Do We Disagree?

30. Our 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, tone of voice, … • Leak less if conscious mind really believes • Beliefs like clothes • Function in harsh weather, fashion in mild • When made to see self-deception, still disagree • So at some level we accept that we not seek truth

31. How Few Meta-Rationals (MR)? Meta-Rational = Seek truth, not lie, not self-favoring-prior, know disagree theory basics • Rational beliefs linear in chance other is MR • MR who meet, talk long, should see are MR? • Joint opinion path becomes random walk • We see no virtually such pairs, so few MR! • N each talk 2T others, makes ~N*T*(%MR)2 pairs • 2 billion ea. talk to 100, if 1/10,000 MR, get 1000 pairs • None even among accept disagree irrational

32. When Justified In Disagree? When others disagree, so must you • Key: relative MR/self-deception before IQ/info • Psychology literature self-deception clues: • Less in skin response, harder re own overt behaviors, older kids hide better, self-deceivers have more self-esteem, less psychopathology/depression • Clues?: IQ/idiocy, self-interest, emotional arousal, formality, unwilling to analyze/consider • Self-deceptive selection of clues use • Need: data on who tends to be right if disagree! • Tetlock shows “hedgehogs” wrong on foreign events • One media analysis favors: longer articles, in news vs editorial style, by men, non-book on web or air, in topical publication with more readers and awards

33. Aumann in 1976: Any information Of possible worlds Common knowledge Of exact E1[x], E2[x] Would say next For Bayesians With common priors If seek truth, not lie or misunderstand Since generalized to: Impossible worlds Common Belief A f(•, •), or who max Last ±(E1[x] - E1[E2[x]]) At core, or Wannabe Symmetric prior origins We Can’t Agree to Disagree

34. Implications • Self-Deception is Ubiquitious! • Facts may not resolve political/social disputes • Even if we share basic values • Let models of academics have non-truth-seekers • New info institution goal: reduce self-deception • Speculative markets do well; use more? • Self-doubt for supposed truth-seekers • “First cast out the beam out of thine own eye; and then shalt thou see clearly to cast out the mote out of thy brother's eye.” Matthew 7:5

35. Common Concerns • I’m smarter, understand my reasons better • My prior is more informed • Different models/assumptions/styles • Lies, ambiguities, misunderstandings • Logical omniscience, act non-linearities • Disagree explores issue, motivates effort • We disagree on disagreement • Bayesian “reductio ad absurdum”