Uncommon Priors Require Origin Disputes Robin Hanson George Mason University ProLogic 2005

Clarifying “Objective” Beliefs Regarding belief as truth estimate –vs. as expression of individuality, or what provokes intellectual progress Yes, distinguish possible topics of beliefs –what theory to apply now, vs. theory closest to ultimate truth, vs. mix of topics to focus research now Normative, not positive, claim –Clearly real people with similar info often disagree –But big scientists in big episodes may be wrong Need not know how to explicitly construct –Constraints: ≥0, Σ=0, update via Bayes’ rule, more? –If enough constraints, result must be unique

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! –Non-epistemic rationality – truth not goal

We Can’t Agree to Disagree Aumann in 1976 Any information 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

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 When see our self-deception, still disagree –So at some level we accept that we not seek truth

Two Faces of Priors Prior help tell us what to believe We have beliefs about prior origins/causes –Can this help constrain rational priors?

Origins of Priors Seems irrational to accept some priors –Imagine random brain changes for weird priors In standard theories, your prior is 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 But you must think differing prior special! Can’t express these ideas in standard models

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

An Extended Model Multiple Standard Models With Different Priors

Standard Bayesian Model

Extending the State Space As event

An Extended Model

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.

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.

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 different prior contains no info” All false if they are brothers!