Eliciting Honest Feedback

1. Eliciting Honest Feedback: The Peer-Prediction Model (Miller, Resnick, Zeckhauser)

2. Minimum Payments that Reward Honest Feedback (Jurca, Faltings)

Nikhil Srivastava Hao-Yuh Su

Eliciting Feedback

• Fundamental purpose of reputation systems

• Review: general setup

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?

Challenges

• Underprovision– “inconvenience” cost of contributing

• Dishonesty– niceness, fear of retaliation– conflicting motivations

Challenges

• Underprovision– “inconvenience” cost of contributing

• Dishonesty– niceness, fear of retaliation– conflicting motivations

• Reward systems– motivate participation, honest feedback– monetary (prestige, privilege, pure competition)

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)

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

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

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

Information Flow - Model

PRODUCT

type t

CENTER

(a)

signal S

announcement a

transfer

Information Flow - Model

PRODUCT

type t

CENTER

(a)

signal S

transfer

PRODUCT

type t

CENTER

(a)

signal S

transfer

announcement a

announcement a

Information Flow - Example

PLUMBER

type = {H, L}

h

h

l

signal =

{h (high), l (low)}

(a)

“agreement”

h

h

l

$1

$1

$0

h

h

l

Assumptions - Model

PRODUCT

type t

{1, …, T}

f (s | t)

- fixed type

- finite T

- common prior: distribution p(t)

- common knowledge: distribution f(s|t)

- linear utility

- stochastic relevance

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

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– Si stochastically relevant for Sj iff:

• distribution (Si | Sj) different for different realizations of Sj

• there is sj such that

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)

Definitions - Model

(a)

• 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, … ai

M)

Definitions - Example

PLUMBER

type = {H, L}

h

h

l

signal = {h, l}

T(a)

$1

$1

$0

h

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, a2

l)– total set of strategies: (h, h), (h, l), (l, h), (l, l)

Best Responses - Model

• 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

T(a)

Best Responses - Example

PLUMBER

S1 = h

S2 = ?

T(a)

t1(a1, a2)

t2 (a1, a2)

h or l

a2

• Player 1 receives signal h• Player 2’s strategy is to report a2

• Player 1 reporting signal h is a best-response if

Peer Prediction

• Find reward mechanism that induces honest reporting– where ai = Si for all i is a Nash equilibrium

• Will need Proper Scoring Rules

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

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?

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 )

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 strictly proper scoring rule R, a reward system with transfers *i makes truthful reporting a strict Nash equilibrium

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)

Peer Prediction Example

• 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)

PLUMBER

p(H) = p(L) = .5S1 = l

S2 = ?

T(a)

t1(a1, a2)a1 = {h, l}

a2 = s2p(h | H) = .85

p(h | L) = .45

Peer Prediction Example

• Player 1 observes low and must decide a1 = {h, l} • Assume logarithmic scoring

– t1(a1, a2) = R(a2 | a1) = ln[ p(a2 | a1 )]

PLUMBER

p(H) = p(L) = .5S1 = l

S2 = ?

T(a)

t1(a1, a2)

p(h | H) = .85

p(h | L) = .45

• a1 = l (honest) yields expected transfer: -.69

• a1 = h (false) yields expected transfer: -.75

a1 = {h, l}

a2 = s2

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

Primary Practical Concerns

• Examples– inducing effort: fixed cost c > 0 of reporting– better information: users seek multiple samples– participation constraints– budget balancing

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

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

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)

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 signalsnote f(s | t) given automatically

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

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

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