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An Experimental Test of Agreeing to Disagree

An Experimental Test of Agreeing to Disagree. ICES Brown Bag, Mar.1, 2002 Robin Hanson, G.M.U., presenting William Nelson, SUNY Buffalo. Agreeing to Disagree Theory.

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An Experimental Test of Agreeing to Disagree

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  1. An Experimental Test of Agreeing to Disagree ICES Brown Bag, Mar.1, 2002 Robin Hanson, G.M.U., presenting William Nelson, SUNY Buffalo

  2. Agreeing to Disagree Theory • E1[x] = E2[x] if x is r.v., finite space, Bayesian, common prior, common knowledge of exact current values E1[x], E2[x] (Aumann 76) • exact values → sep. point (Sebenius & Geanakoplos 83), monotone stat. (McKelvey & Page 86), who has max value (Hanson 98a) • Bayesian → balanced (Geanakoplos 89), know that they know (Samet 90), Turing machine (Medgiddo 89), Bayesian wannabe (Hanson 98b)

  3. Agreeing to Disagree Theory II • finite → infinite state space (Samet 92) • =,c.k. →≈,common belief (Monderer & Samet 89) • current values → eventually if finite, last values honestly said (Geanakoplos & Polemarchakis 82) • E1t[x] = E1t[E2t+s[x]] if finite space, Bayesian, common prior, common knowledge that 2 hears 1 honestly say if E1t[x] ≥ E1t[E2t+s[x]] (Hanson 02) (Should generalize to infinite space, common belief, Bayesian wannabes)

  4. Comparing Theory to Reality • Humans seem to disagree constantly, seem well aware of this, even those know theory • So we not seek truth? (Cowen & Hanson 01) • But many question if theory ever tested GOAL: a more direct agreeing to disagree test

  5. A gets clue XA 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 XB B told A1 B1 = B’s guess of X B2 = B’s guess of A2 Loss (B1-X)2, (B2-A2)2 Dice Game X = XA + XB time

  6. 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 told A1 B1 = B’s guess of X B2 = B’s guess of A2 Loss (B1-X)2, (B2-A2)2 Percent Game time E.g.: What % of U.S. say dogs better pets than cats?

  7. Percent Forms

  8. 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)

  9. 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

  10. Results • * = 5%, ** = 1%, *** = .2% • Exclude B-sign=0 • Really B-sign*(A1-X) … • In both games, A2 neglects info in B-sign, and B2 accurately anticipates this. • In percent game, B1 neglects info in A1 • No correlation with self-deception measure, question emotion level

  11. Where go from here? • Do we need more data of same form? • Should we see degree of signaling by also paying on estimates never show others? • Should see degree of common belief via auctions pay off on subject test error rate?

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