Social Learning and Consumer Demand

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Social Learning and Consumer Demand

• Markus Mobius (Harvard University and NBER)
• Paul Niehaus (Harvard University)
• Tanya Rosenblat (Wesleyan University and IAS)
• 28 April, 2006

2
Introduction

• We seed a known social network with information
  by
• distributing new products randomly to some
  members.
• Methodology How can we measure the influence of
  treated agents on their friends?

3
Introduction

• We seed a known social network with information
  by
• distributing new products randomly to some
  members.
• Methodology How can we measure the influence of
  treated agents on their friends?
• Results How does social influence decline
  with distance?

4
Methodology

• We build a simple model to infer the interaction
  probability between a treated agent and any of
  her social neighbors.
• During an interaction the treated agents
  knowledge is transferred to the neighbor.
• Interaction probabilities vary by social
  distance.
• Our model has the advantage that it can be easily
  estimated and that it can deal with treatment
  overlaps.

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Methodology

• Interaction probabilities are convenient to
  measure
• influence.
• Example Assume that an agent has 10 direct
  friends and
• 60 indirect friends and the interaction
  probabilities are
• and . Then on average the agent
  transfers knowledge
• to 1 direct friends and 3 indirect friends. In
  this example the
• agent affects knowledge in the network mainly by
  influencing
• indirect friends rather than direct friends
  because the interaction
• probability decreases less strongly than the
  network grows.

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Basic Design

• Stage 1 Measure Social Network
• Stage 2 Baseline Survey
• Stage 3 Distribute Products
• Stage 4 Track Social Learning

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• 1. Measuring the Social Network

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Measuring the Network

• Rather than surveys, agents play in a trivia game
• Leveraged popularity of www.thefacebook.com
• Membership rate at Harvard College over 90
• 95 weekly return rate

Data provided by the founders of thefacebook.com
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• Markus
• His Profile
• (Ad Space)
• His Friends

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Trivia Game Recruitment

• On login, each Harvard undergraduate member of
  thefacebook.com saw an invitation to play in the
  trivia game.
• Subjects agree to an informed consent form now
  we can email them!
• Subjects list 10 friends about whom they want to
  answer trivia questions.
• This list of 10 people is what were interested
  in (not their performance in the trivia game)

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Trivia Game Trivia Questions

• Subjects list 10 friends this creates 10N
  possible pairings.
• Every night, new pairs are randomly selected by
  the computer
• Example Suppose Markus listed Tanya as one of
  his 10 friends, and that this pairing gets
  picked.

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Trivia Game Example

• Tanya (subject) gets an email asking her to log
  in and answer a question about herself
• Tanya logs in and answers, which of the
  following kinds of music do you prefer?

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Trivia Game Example (cont.)

• Once Tanya has answered, Markus gets an email
  inviting him to log in and answer a question
  about one of his friends.
• After logging in, Markus has 20 seconds to answer
  which of the following kinds of music does Tanya
  prefer?

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Trivia Game Example (cont.)

• If Markus answer is correct, he and Tanya are
  entered together into a nightly drawing to win a
  prize.

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Trivia Game Summary

• Subjects have incentives to list the 10 people
  they are most likely to be able to answer trivia
  questions about.
• This is our (implicit) definition of a friend
• Answers to trivia questions are unimportant
• ok if people game the answers as long as the
  people its easiest to game with are the same as
  those they know best.
• Roommates were disallowed
• 20 second time limit to answer
• On average subjects got 50 of 4/5 answer
  multiple choice questions right and many were
  easy

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Recruitment

• In addition to invitations on login,
• Posters in all hallways
• Workers in dining halls with laptops to step
  through signup
• Personalized snail mail to all upper-class
  students
• Article in The Crimson on first grand prize
  winner
• Average acquisition cost per subject 2.50

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Participation

• Consent 2932 out of 6389 undergrads (46), and
  50 of upperclassmen
• 10 friends 2360 undergraduates (37)
• Participation by year of graduation

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Participation

• By residential house (upperclassmen)

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Network Data

• 23,600 links from participants
• 12,782 links between participants
• 6,880 of these symmetric (3,440 coordinated
  friendships)
• Similar to 2003 results
• Construct the network using or link definition
• 5576 out of 6389 undergraduates (87)
  participated or were named
• One giant cluster
• Average path length between participants 4.2
• Cluster coefficient for participants 17
• Lower than 2003 results because many named
  friends are in different houses

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Growth of Neighborhoods
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Methods in Comparison

• 2003 House Experiment in 2 undergraduate houses
• Email-data Sacerdote and Marmaris (2004)
• Mutual-friend methods with facebook data?
  (Glaeser, Laibson, Sacerdote 2000)

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• 2. Baseline Survey

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Goals of Baseline

• We want to predict valuations of subjects for our
  products without telling them which products we
  will distribute.
• This allows us to test whether subjects with a
  higher valuations are more influenced.
• We treat a product as a vector of attributes
  which span a space containing the specific
  product.

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Choice of Products

• We want new products to maximize the potential
  for social learning.

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Choice of Products

• We want new products to maximize the potential
  for social learning.
• We want some products where subjects have to talk
  to exchange information (such as newspaper
  subscription) and some products whose use is
  conspicuous (such as cell phone).

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Public Products
T-Mobile Sidekick II
Philips Key019 Digital Camcorder
Philips ShoqBox
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Private Products
Student Advantage Discount Card (1 year)
Baptiste Studios Yoga Vouchers (5)
Qdoba Meal Vouchers (5)
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Configurators

• We identified 5 or 6 salient features for each of
  the six products.
• For example, a product might be a general type of
  discount card for students.
• Particular features of the card could be (i)
  provides a discount on textbooks (ii) provides a
  discount on Amtrak/ Greyhound etc.
• We elicit a baseline valuation from subjects plus
  a valuation for each feature (assumes additive
  separability of valuations over features).

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Feature descriptions
Feature bids
Baseline bid
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Constructed Bids

• We constructed an implicit bid B from subjects
  responses
• BidBaseline Value Sum over Feature Values (for
  existing features)
• Subjects were told that they could submit a
  second in the followup survey and that either
  this bid or the followup bid would be entered
  with equal probability into a uniform-price
  auction.

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Constructed Bids

• We constructed an implicit bid B from subjects
  responses
• BidBaseline Value Sum over Feature Values (for
  existing features)
• Subjects were told that they could submit a
  second in the followup survey and that either
  this bid or the followup bid would be entered
  with equal probability into a uniform-price
  auction.

Subjects are provided with incentives for
truth-telling.
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(20)
(50)
(35)
(150)
(150)
(250)
(Price)
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Distributions of Imputed Bids

• Imputed valuations look sensible.
• In each case market prices lie between median bid
  and upper tail.

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• 3. Distribution of Products

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Randomized Product Trials

• Private Products
• 1 year Student Advantage cards
• 5 yoga vouchers
• 5 meal vouchers
• Public products
• Try out for approximately 4 weeks during end of
  term

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Randomization

• Only subjects with imputed bids above the median
  were eligible. We then offered products to about
  100 subjects for each product.
• Blocked by year of graduation, gender, and
  residential house.
• Email invitations to come pick up samples
• Invitation times varied to vary strength of
  exposure (April 26th May 3rd)

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Response Rates
Overall 57
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Info Treatments

• Varied information communicated verbally by
  workers doing distribution
• Information treatments correspond to product
  features in our configurators (5 or 6 features
  for each product).
• Reinforced this information treatment with
  reminder emails
• Each treatment given with 50 probability to each
  subject

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Other Treatments

• We also provided randomized online and print ads
  to subjects who did not receive products (not
  reported in this talk).

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• 4. Track Social Learning

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Followup Survey

• We measure both subjective and objective
  knowledge of all subjects.

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Followup Survey

• We measure both subjective and objective
  knowledge of all subjects.

Subjective Knowledge Stated probability that
subject can answer any Yes/No question correctly.
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Followup Survey

• We measure both subjective and objective
  knowledge of all subjects.

Subjective Knowledge Stated probability that
subject can answer any Yes/No question correctly.
Objective Knowledge Average number of actual
correct Yes/No questions in subsequent quiz.
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Eliciting Confidence Levels

• Meet Bob the Robot and his clones Bob 1 Bob
  100
• Subjects are randomly paired with an (unknown)
  Bob
• Subjects indicated a cutoff Bob at which they
  are indifferent about who should answer the
  question
• If assigned Bob is better than the cutoff, Bob
  answers the question otherwise we use subjects
  answer
• Incentive-compatible mechanism to elicit
  subjects belief that he/she will get the
  question right

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Final Valuations

• Also asked for a second bid for each product.
• Asked subjects about the valuations of other
  randomly selected subjects.

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Analysis

• Model

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Model

• An untreated (uninformed) subject has a
  probability p of interacting with some treated
  (informed) subject.
• The interaction probability p depends on the
  social distance between uninformed and informed
  subject.
• We distinguish three types of social distances
  room mates (M), direct friends (NW1) and indirect
  friends (NW2).

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Model

• We define knowledge as the subjective or
  objective probability of answering a question
  about the product correctly.
• If an informed and uninformed subject interact
  the knowledge of the informed subject is
  transferred to the uninformed subject (informed
  treated with a product).

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Model

• We define knowledge as the subjective or
  objective probability of answering a question
  about the product correctly.
• If an informed and uninformed subject interact
  the knowledge of the informed subject is
  transferred to the uninformed subject (informed
  treated with a product).

After interacting the uninformed subject has the
same probability of answering a question
correctly as the informed subject.
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Model

• Assume that the knowledge of an informed subject
  is and the knowledge of an uninformed
  subject is .
• Assume that the uninformeds probability of
  interacting with some informed subject is X.
  Then we can express the final expected knowledge
  of the uninformed agent as

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What is X?

• Assume that the uninformed agent has
  room mates who were offered a product,
  direct friends and indirect friends.
  Then we can express X as

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What is X?

• Assume that the uninformed agent has
  room mates who were offered a product,
  direct friends and indirect friends.
  Then we can express X as

The probability of interacting with some informed
subject is 1 minus the probability of interacting
with none of them.
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Model

• We obtain

• We observe and in the
  followup survey.

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Model

• We obtain

• We observe and in the
  followup survey.
• We do not observe because we
  cannot do a baseline quiz without revealing the
  product.

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Model

• We obtain expression ()

• We observe and in the
  followup survey.
• However, we do not observe
  because we cannot do a baseline quiz without
  revealing the product.
• Moreover, we expect the information of
  uninformed agents to vary with the number of
  eligible neighbors (and hence the number of
  neighbors who were offered a treatment) due to
  selection.

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We instead compare agents in similar cells
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We instead compare untreated agents in similar
cells
We say the green subject lives in a (1,4,4) cell
to indicate that she has one treated room-mate,
and four treated NW1 and NW2 friends AND she has
at least one more eligible (but non-treated) NW1
friend (indicated by plus sign).
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For example, compare a (1,4,4) cell with a
(1,5,4) cell



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For example, compare a (1,4,4) cell with a
(1,5,4) cell



The green agent on the right faces the same
neighborhood as the agent on the left but the
randomization turned one eligible, untreated
agent into a treated agent.
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Model

• By dividing expression () for all agents in cell
  (1,5,4) by expression () for all agents in cell
  (1,4,4) we obtain the marginal impact of
  treating one more NW1 neighbor

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Model

• By dividing expression () for all agents in cell
  (1,5,4) by expression () for all agents in cell
  (1,4,4) we obtain the marginal impact of
  treating one more NW1 neighbor

Since we only have finitely many observations per
cell we get an estimate for p. For each marginal
comparison between two neighboring cells we get a
new estimate. From this we can construct an
estimate for p and a confidence interval.
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Model

• By dividing expression () for all agents in cell
  (1,5,4) by expression () for all agents in cell
  (1,4,4) we obtain the marginal impact of
  treating one more NW1 neighbor

By comparing neighboring cells we are essentially
differing out the unobserved knowledge of the
uninformed agent.
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Analysis

• Results

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Results

• We are estimating the interaction probabilities
  separately for each product.
• We use both subjective knowledge (What is the
  probability that you can answer a Yes/No question
  correctly?) and objective knowledge (Actual
  share of correctly answered questions in the
  quiz).

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Results - Card
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Results - Card
SE (0.16) (0.21)
(0.02) (0.04)
(0.09) (0.03)
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Results - Yoga
SE (0.19) (0.23)
(0.04) (0.03)
(0.03) (0.05)
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Results Restaurant
SE (0.03) (0.08)
(0.03) (0.04)
(0.02) (0.01)
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Results Camcorder
SE (0.02) (0.02)
(0.02) (0.03)
(0.02) (0.02)
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Results MP3
SE (0.06) (0.07)
(0.03) (0.04)
(0.02) (0.01)
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Results PDA
SE (0.04) (0.07)
(0.03) (0.04)
(0.02) (0.02)
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Results

• For private products the interaction
  probability for NW2 neighbors is usually
  insignificant.
• For public products the NW2 effect is small but
  significant.
• NW2 neighborhoods are also 7-times as large as
  NW1 neighborhoods! Therefore, the expected number
  of influenced NW2 agents can be large.

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Results

• We would expect that agents with higher implied
  bids (from baseline survey) should have
• greater incentive to learn about the product
• higher probability of being talked to by treated
  guys (assuming that treated agents know the
  interests of their friends)

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Results

• We would expect that agents with higher implied
  bids (from baseline survey) should have
• greater incentive to learn about the product
• higher probability of being talked to by treated
  guys (assuming that treated agents know the
  interests of their friends)

We therefore repeat the previous analysis and
only compare high-implicit-bid agents across
cells.
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Results - Card
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Results - Yoga
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Results Restaurant
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Results Camcorder
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Results MP3
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Results PDA
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Results

• Generally, the interaction probability is greater
  towards high-value subjects.

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Results

• Generally, the interaction probability is greater
  towards high-value subjects.

This is consistent with the idea that high-value
agents either pay more attention to social
learning or are talked to more often by product
owners who know their interests.
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Who is influenced the most by social learning
(close or distant neighbors)?(expected number of
interactions taking Nhood size into account
subjective knowledge and significant
probabilities only)
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Who is influenced the most by social learning
(close or distant neighbors)?(expected number of
interactions taking Nhood size into account
subjective knowledge and significant
probabilities only)
Although there is a greater probability to
interact with close agents the expected number of
interactions increases with distance.
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Summary

• Novel design
• Hedonic analysis using configurators
• Measure of confidence using the Bobs
• Simple model of social learning provides
  interpretable interaction probabilities.