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 Theres 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
  others next opinion, relative to what we say

3
We Cant Agree to Disagree
Nobel Prize 2005
his most cited paper by x2
Agent 1 Info Set

• Aumann 1976 assumed
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• Would say next
• For Bayesians
• With common priors
• If seek truth, not lie, josh, or misunderstand

Agent 2 Info Set
Common Knowledge Set
4
John estimates car age E1x
Ive never been wrong
before
It wasnt shiny
I can still picture it
It sounded old
I had a good viewing angle
Fred said so
Mary is blind
5
Mary estimates car age E2x
6
Agree If Averages Same
E1x E2x
Aumann (1976) Annals Stat. 4(6)1236-9.
7
We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

8
We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

9
Disagreement Is Unpredictable
Hanson (2002) Econ. Lett. 77365369.
10
Experiment Shows Disagree
E.g. What of U.S. say dogs better pets than
cats?
time
Example

• A gets clue on X
• A1 As guess of X
• A told Sign(B2-B1)
• A2 As guess of X
• Loss (A1-X)2(A2-X)2

• B gets clue on X
• B told A1
• B1 Bs guess of X
• B2 Bs guess of A2
• Loss (B1-X)2(B2-A2)2

30
70
40
low
40
A neglects clue from B
B reliably predicts neglect
11
Sample Percent Questions

• What percent of people in the U.S. agree with
  this opinion? God created humans in basically
  their present form in the last 10,000 years.
  (Gallup,1999)
• What percent of people in the U.S. agree with
  this opinion? The U.S. government is hiding
  that it knows of the existence of aliens. (CNN
  1994)
• By weight, what percent of cheddar cheese is
  protein? (U.S. Department of agriculture)
• What percent of the population of India is
  literate? (Nation of India)

12
Experiment Features

• All answers integers in 0,100, either real or
  XA XB, each from 6s dice 0,10,20,30,40,50
• All by hand, subjects roll dice first, for
  credibility
• Subjects told all after each round, to help
  learning
• Zipper design, to minimize strategic interactions
• Lottery payoff, to reduce risk aversion
• Double dice, for easy squared-error penalty
• Only tell B-sign, to reduce signaling ability

13
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 e about the expectation of
a 0,1 variable with high probability over their
prior, it suffices for them to exchange order
1/e2 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.
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We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

15
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 EpUact)
• Many specific heuristics
• Bayesian Wannabes

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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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Notation
18
More Notation
19
Still More Notation
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Let 1,2 Agree to Disagree Re X
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Theorems
1
2
22
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 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).

Hanson (2003) Theory Decision 54(2)105-123.
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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.

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We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

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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 cant 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 gt priors same

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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 Mendels rules of inheritance
• Sibling differences independent of everything
  else!
• Culture random adapted to local society
• Turns out you must think differing prior is
  special!
• Cant express these ideas in standard models

27
Standard Bayesian Model
Agent 1 Info Set
A Prior
Agent 2 Info Set
Common Kn. Set
28
An Extended Model
Multiple Standard Models With Different Priors
29
Standard Bayesian Model
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Extending the State Space
As event
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An Extended Model
32
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.
33
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.
34
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!

35
We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

36
Why Do We Disagree?

• 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

37
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

38
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 NT(MR)2 pairs
• 2 billion ea. talk to 100, if 1/10,000 MR, get
  1000 pairs
• None even among accept disagree irrational

39
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/depres
  sion
• 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

40
We Cant Agree to Disagree

• Aumann in 1976
• Any information
• Of possible worlds
• Common knowledge
• Of exact E1x, E2x
• 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 (E1x - E1E2x)
• At core, or Wannabe
• Symmetric prior origins

41
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 75

42
Common Concerns

• Im 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

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Counter Example

• P(y) exp(-by)
• Asodpf