Eliciting Honest Feedback

1. Eliciting Honest Feedback Minimum Payments that Reward Honest Feedback (Jurca, Faltings) Eliciting Honest Feedback: The Peer-Prediction Model (Miller, Resnick, Zeckhauser) Nikhil Srivastava Hao-Yuh Su

2. Eliciting Feedback • Fundamental purpose of reputation systems • Review: general setup

3. Eliciting Feedback • Fundamental purpose of reputation systems • Review: general setup • Information distributed among individuals about value of some item • external goods (NetFlix, Amazon, ePinions, admissions) • each other (eBay, PageRank) • Aggregated information valuable for individual or group decisions • How to gather and disseminate information?

4. Challenges • Underprovision • “inconvenience” cost of contributing • Dishonesty • niceness, fear of retaliation • conflicting motivations

5. Challenges • Underprovision • “inconvenience” cost of contributing • Dishonesty • niceness, fear of retaliation • conflicting motivations • Reward systems • motivate participation, honest feedback • monetary (prestige, privilege, pure competition)

6. Overcoming Dishonesty • Need to distinguish “good” from “bad” reports • explicit reward systems require objective outcome, public knowledge • stock, weather forecasting • But what if … • subjective? (product quality/taste) • private? (breakdown frequency, seller reputability)

7. Overcoming Dishonesty • Need to distinguish “good” from “bad” reports • explicit reward systems require objective outcome, public knowledge • stock, weather forecasting • But what if … • subjective? (product quality/taste) • private? (breakdown frequency, seller reputability) • Naive solution: reward peer agreement • Information cascade, herding

8. Peer Prediction • Basic idea • reports determine probability distribution on other reports • reward based on “predictive power” of user’s report for a reference rater’s report • taking advantage of proper scoring rules, honest reporting is a Nash equilibrium

9. Outline • Peer Prediction method • model, assumptions • result: • underlying intuition through example • Extensions/Applications • primary practical concerns • (weak) assumptions: sequential reporting, continuous signals, risk aversion • (Strong) assumptions • Other limitations

10. Information Flow - Model announcement a PRODUCT type t CENTER (a) signal S transfer 

11. Information Flow - Model announcement a PRODUCT type t CENTER (a) signal S transfer  PRODUCT type t CENTER (a) signal S announcement a transfer 

12. Information Flow - Example h h l PLUMBER type ={H, L} signal = {h (high), l (low)} h h l $1 $1 $0 h h l (a) “agreement”

13. Assumptions - Model PRODUCT type t {1, …, T} f (s | t) • common prior: distribution p(t) • common knowledge: distribution f(s|t) • linear utility - stochastic relevance - fixed type - finite T

14. Stochastic Relevance • Informally • same product, so signals dependent • certain observation (realization) should change posterior on type p(t), and thus on signal distribution f(s | t) • Rolex v. Faux-lex • generically satisfied if different types yield different signal distributions

15. Stochastic Relevance • Informally • same product, so signals dependent • certain observation (realization) should change posterior on type p(t), and thus on signal distribution f(s) • Rolex v. Faux-lex • generically satisfied if different types yield different signal distributions • Formally • Sistochastically relevant for Sj iff: • distribution (Si | Sj) different for different realizations of Sj • there is sj such that

16. Assumptions - Example • finite T: plumber is either H or L • fixed type: plumber quality does not change • common prior: p(t) • p(H) = p(L) = .5 • stochastic relevance: need good plumber’s signal distribution to be different than bad’s • common knowledge: f(s|t) • p(h | H) = .85, p(h | L) = .45 • note this gives p(h), p(l)

17. Definitions - Model • T types, M signals, N raters • signals: S = (S1, …, SN), where Si = {s1, …, sM} • announcements: a = (a1, …, aN), where ai= {s1, …, sM} • transfers: (a) = (1 (a), …, N(a)) • announcement strategy for player i: ai = (ai1, … aiM) (a)

18. Definitions - Example h h l h h l T(a) $1 $1 $0 PLUMBER type ={H, L} signal = {h, l} • 2 types, 2 signals, 3 raters • signals: S = (h, h, l) • announcements: a = (h, h, l) • transfers: (a) = (1 (a), 2(a), 3(a)) • announcement strategy for player 2: a2 = (a2h, a2l) • total set of strategies: (h, h), (h, l), (l, h), (l, l)

19. Best Responses - Model T(a) • Each player decides announcement strategy ai • ai is a best-response to other strategies a-i if: • Best-response strategy maximizes rater’s expected transfer with respect to other raters’ signals … conditional on Si = sm • Nash equilibrium if equation holds for all i

20. Best Responses - Example t1(a1, a2) t2 (a1, a2) PLUMBER • Player 1 receives signal h • Player 2’s strategy is to report a2 • Player 1 reporting signal h is a best-response if h or l a2 T(a) S1 = h S2 = ?

21. Peer Prediction • Find reward mechanism that induces honest reporting • where ai = Si for all i is a Nash equilibrium • Will need Proper Scoring Rules

22. Proper Scoring Rules • Definition: • for two variables Si and Sj, a scoring rule assigns to each announcement ai of Si a score for each realization of Sj • R ( sj | ai ) • proper if score maximized by the announcement of the true realization of Si

23. Applying Scoring Rules • Before: predictive markets (Hanson) • Si = Sj = reality, ai = agent report • R ( reality | report ) • Proper scoring rules ensure honest reports: ai = Si • stochastic relevance for private info and public signal • automatically satisfied • What if there’s no public signal?

24. Applying Scoring Rules • Before: predictive markets (Hanson) • Si = Sj = reality, ai = agent report • R ( reality | report ) • Proper scoring rules ensure honest reports: ai = Si • stochastic relevance for private info and public signal • automatically satisfied • What if there’s no public signal? Use other reports • Now: predictive peers • Si = my signal, Sj = your signal, ai = my report • R ( your report | my report )

25. How it Works • For each rater i, we choose a different reference rater r(i) • Rater i is rewarded for predicting rater r(i)’s announcement • *i (ai , ar(i) ) = R( ar(i), ai ) • based on updated beliefs about r(i)’s announcement given i’s announcement • Proposition: for any strictlyproper scoring rule R, a reward system with transfers *imakes truthful reporting a strict Nash equilibrium

26. Proof of Proposition • If player i receives signal s*, he seeks to maximize his expected transfer • Since player r(i) is honestly reporting, his report a equals his signal s • since R is proper, score is uniquely maximized by announcement of true realization of Si • uniquely maximized for ai = s* • Si is stochastically relevant for Sr(i), and since r(i) reports honestly Si is stochastically relevant for ar(i) = sr(i)

27. Peer Prediction Example PLUMBER p(H) = p(L) = .5 a1 = {h, l} a2 = s2 • Player 1 observes low and must decide a1 = {h, l} • Assume logarithmic scoring • t1(a1, a2) = R(a2 | a1) = ln[ p(a2 | a1 )] • What signal maximizes expected payoff? • Note that peer agreement would incentivize dishonesty (h) t1(a1, a2) T(a) S1 = l S2 = ? p(h | H) = .85 p(h | L) = .45

28. Peer Prediction Example PLUMBER p(H) = p(L) = .5 a1 = {h, l} a2 = s2 • Player 1 observes low and must decide a1 = {h, l} • Assume logarithmic scoring • t1(a1, a2) = R(a2 | a1) = ln[ p(a2 | a1 )] t1(a1, a2) T(a) S1 = l S2 = ? p(h | H) = .85 p(h | L) = .45 • a1 = l (honest) yields expected transfer: -.69 • a1 = h (false) yields expected transfer: -.75

29. Things to Note • Players don’t have to perform complicated Bayesian reasoning if they: • trust the center to accurately compute posteriors • believe other players will report honestly • Not unique equilibrium • collusion

30. Primary Practical Concerns • Examples • inducing effort: fixed cost c > 0 of reporting • better information: users seek multiple samples • participation constraints • budget balancing

31. Primary Practical Concerns • Examples • inducing effort: fixed cost c > 0 of reporting • better information: users seek multiple samples • participation constraints • budget balancing • Basic idea: • affine rescaling (a*x + b) to overcome obstacle • preserves honesty incentive • increases budget … see 2nd paper

32. Extensions to Model • Sequential reporting • allows immediate use of reports • let rater i predict report of rater i + 1 • scoring rule must reflect changed beliefs about product type due to (1, …, i - 1) reports

33. Extensions to Model • Sequential reporting • allows immediate use of reports • let rater i predict report of rater i + 1 • scoring rule must reflect changed beliefs about product type due to (1, …, i - 1) reports • Continuous signals • analytic comparison of three common rules • eliciting “coarse” reports from exact information • for two types, raters will choose closest bin (complicated)

34. Common Prior Assumption • Practical concern - how do we know p(t),? • needed by center to compute payments • needed by raters to compute posteriors • define types with respect to past products, signals • types t = {1,…,9} where f(h | t) = t/10 • for new product, p(t) based on past product signals • update beliefs with new signals • note f(s | t) given automatically

35. Common Prior Assumption • Practical concern - how do we know p(t)? • Theoretical concern - are p(t), f(s|t) public? • raters trust center to compute appropriate posterior distributions for reference rater’s signal • rater with private information has no guarantee • center will not report true posterior beliefs • rater might skew report to reflect appropriate posteriors • report both private information and announcement • two scoring mechanisms, one for distribution implied by private priors, another for distribution implied by announcement

36. Limitations • Collusion • could a subset of raters gain higher transfers? higher balanced transfers? • can such strategies: • overcome random pairings • avoid suspicious patterns • Multidimensional signals • economist with knowledge of computer science • Understanding/trust in the system • complicated Bayesian reasoning, payoff rules • rely on experts to ensure public confidence

37. Discussion • Is the common priors assumption reasonable? • How might we relax it and keep some positive results? • What are the most serious challenges to implementation? • Can you envision a(n online) system that rewards feedback? • How would the dynamics differ from a reward-less system? • Is this paper necessary at all? • Predominance of honesty from fairness incentive cost of reporting, “coarse” reports, common priors, collusion, multidimensional signals, trust in system