marketing cascades

Threshold cascades for marketing

Charlie BrummittUniversity of California, Davis

Graduate Group in Applied MathPresenting work by others and joint work with

K.-M. Lee, K.-I. Goh (Korea University)

Soundbites

1. Target the easily influenced.

2. Targeting influentials probably not worth it.

3. Use new media. (Even a little bit.)

Threshold cascade model• A large group of individuals must make a

decision between two choices A, B.

• Examples:Do I buy an Android instead of Apple phone?Do I use Charles Schwab or not?

• Probability a person i chooses B over A increases with # of i’s contacts who have chosen B.

Reasoning: utility increases with # users, compatible technology, recommendations, influence.

Evidence for threshold model

• Kotler (2000): 60% of 7000 European consumers influenced to buy a new brand by family and friends

• Jupiter Communications (1999): 57% of people visit a new website due to personal recommendation (highest influence)

Live Journal DVD purchases

Example: Joe buys an iPhone once ≥ 20% of his friends have

Joe activates

Common choice: hard

thresh-olds

3 of 5 friends chose B

Joe

3

5> 20%

1. Start with a social network(e.g., everyone has ≈ 5 friends, chosenrandomly)

(or use a real social network)

2. Initially activate a few random people (seeds)

“early adopters” “given free copies”

3. Run the cascade dynamictill no one can activate

4. Final cascade size

here: 70%

How cascades

work

Example: Joe buys an iPhone once ≥ 20% of his friends have

Joe activates

Common choice: hard

thresh-olds

3 of 5 friends chose B

Joe

3

5> 20%

What affects cascade size:

1. threshold: % of friends

needed

2. Number of friends

What affects cascade size:

1. threshold: % of friends

needed

2. Number of friends

2 4 6 8 10z = average

number of friends

1cascade size r

need enough interactions

too many interactions: difficult to get enough of your friends to activate

cascade window

2 4 6 8 10z = average

number of friends

1cascade size r no cascades

z = 1 z = 3 z = 7 z = 9

average

Conclusion: more ads & influence → harder to

convince them

Influentials hypothesis

= influentials = people who influence their friends (not celebrities, formal leaders)

two-step flow of communication from media to influentials to everyone else

(Katz, Lazarsfeld 1955)

cascades driven by a critical mass of easily influenced people

Influentials not that importantDefine influentials: top 10% of influence

Influentials not that importantDefine influentials: top 10% of influence

Watts, D.J. & Dodds, P.S. Influentials, networks, and public opinion formation. Journal of Consumer Research (2007).

relative influence

relative cascade

size

influentials trigger slightly larger cascades

but not as much as their relative influence suggests.

Conclusion: don’t overspend on tiny fraction. Target the easily influenced.

Cascades are driven by “easily influenced people influencing other easily influenced people.”

few interactions, low threshold

Hyperinfluentials, communitiesConsider hyperinfluentials, who

influence way more people

But these hyperinfluentials are difficult to convince.

Hyperinfluentials, communitiesConsider hyperinfluentials, who

influence way more people

But these hyperinfluentials are difficult to convince.

People belong to groups. Many of our friends are friends.

But influential people tend to interact with influential people (assortativity)

and are difficult to influence.

Focus on easily influenced people.

Conclusions on influentials hypothesis

Watts, D.J. & Dodds, P.S. Influentials, networks, and public opinion formation. Journal of Consumer Research (2007).

• Influentials less important than generally supposed

• A critical mass of easily influenced people

• The particular people who cause cascades are likely due to chance.

• Marketers: if social influence is important, target easily influenced people.

colleagues friends

family

• 4 of your contacts bought a Windows 7 smartphone

• How likely will you buy it, too?

Multiple kinds of influence

• Different social spheres

Brummitt, Lee, Goh (2011) arXiv:1112.0093

k1 = 3,m1 = 1 k2 = 4,m1 = 2

max{13

,1

2

} > R ?

work colleaguesTwitter friends

Go out for drinks with colleagues. 2 of 4 bought a

Windows 7 phone. Will I buy it too?

Rule: I’ll buy it if large enough % of colleagues have. Or enough friends, enough Twitter followers, etc.

Multiple kinds of influence

Effect: large cascades easier.

Tool for marketers:Advertise even a little in new media

Facebook is crowded.

Tool for marketers:Advertise even a little in new media

Facebook is crowded.

Add another way to interact (e.g., Instagram).

Sparse layer can spark a cascade in the dense

layer

→ Viral marketing campaigns more effective with each new medium: Google AdWords, Twitter, blogs, forums, iPads, Pandora...

Stubborn people

• What if people aren’t so easily influenced by just one social sphere?

• Example: I won’t buy a Windows 7 phone unless >10% of my friends and >10% of bloggers whom I follow buy one.

• Suppose a fraction q of people are easily influenced (need just one social sphere), 1-q of people are stubborn (need all social spheres)

Discontinuous jump in cascade size. Explosively viral.

0.0 0.2 0.4 0.6 0.8 1.0q

0.2

0.4

0.6

0.8

1.0q•H1L = q•H2L

0.0 0.2 0.4 0.6 0.8 1.0q

0.2

0.4

0.6

0.8

1.0q•H1L = q•H2L

z = 1 z = 4

q

ρ

average cascade size

fraction of easily influenced people

few friends many friends

Many interactions → abrupt jump in

cascade size

jump

Implications of

• Well-connected networks attain suddenly large cascades as people become easier to persuade (increase q)

• Viral campaigns either fail or flourish. Hard to predict.

• Example: qsmartphone app ≫ qcar, apps go viral more easily than Priuses.

• Globalization, technology → more connections & ways to connect → more explosively viral

• - Does the success of your marketing campaigns change smoothly or abruptly?- Is adoption more viral/explosive in electronic media?- How does adding new media affect marketing success?

0.0 0.2 0.4 0.6 0.8 1.0q

0.2

0.4

0.6

0.8

1.0q•H1L = q•H2L

q

ρjump

Thank you!

Charlie Brummittcbrummitt@math.ucdavis.eduwww.math.ucdavis.edu/~cbrummitt/

Collaborators:Kyu-Min Lee, Kwang-Il Goh (Korea University)