Diffusion of innovation ( PDFDrive ).pptx

Diffusion of innovation
– a physicist’s perspective
Katarzyna Sznajd-Weron
DPCN2016, 8.01.2016

Agenda
• What is diffusion of innovation?
• Examples and questions
• How to model diffusion of innovation?
• ABM of innovation diffusion
• How to model opinion dynamics?
• The role of networks

Innovations – iPhone, iPad, etc.
Long queues: Consumers eager to get their hands on
Apple's new iPhone in Glasgow's Buchanan Street
© HEMEDIA / SWNS Group

Diffusion of innovation
• Diffusion of innovation
– a process in which an innovation is communicated
through certain channels over time among the
members of a social system
• Innovation
– an idea, practice, object
that is perceived as new
Everett M. Rogers (1931 –2004)
known for originating the diffusion
of innovations theory (1962)

Typical pattern for a successful innovation

Example 1: A new practice
• A two-year water-boiling campaign conducted in
Los Molinas (Peru)
– Public health service encouraged to boil drinking
water
– All sources of water were
subject to pollution
– Nelida made several
visits to every home
– Among 200 families only
11 adopted

Q1 – Who adopted?
• Who adopted?
– Mrs. A “sickly one” for other (wrong) reason
– Individuals who were not
integrated into local networks
• Strong social norms

Example 2: QWERTY keyboard – preventing jam
on a mechanical keyboard
A Hermes typewriter (~1910)

Dvorak keyboard
• About 70 percent of typing is done on the home row,
• 22 percent on the upper row,
• 8 percent on the lower row.

Diffusion of innovation is an important,
fascinating and highly interdisciplinary subject
QWERTY
Dvorak
http://www.patrick-wied.at/
projects/heatmap-keyboard/

Q2: Why failed? Why took so long?
• Most of us are used to the QWERTY design
• Considerable effort (training) is required to become
proficient on a Dvorak keyboard
• Technological innovations are not always diffused
and adopted rapidly

Example 3: Scott Paper in 1966
• The world’s largest manufacturer & marketer
of sanitary tissue products (22 countries)
• Scott Paper was founded in 1879 in
Philadelphia by Scott brothers
• Probably the first to market
toilet paper sold on a roll
• An idea for a new market
- paper garments for hospitals

Paper dresses by Scott Paper (1966)
• The colorful A-line frock
was meant to be thrown
away after one use
– “After all, who is going
to do laundry in space?”
• The biggest fashion craze
of the Space Age
• Half a million dresses sold
in the first 5 months!

Q3: Why failed after a promising start?
• Immediately other
brands offered their own
version of the paper
minidress
• By 1968, paper clothing
had disappeared from
the market
• Any idea?

Similar pattern (Bruno Goncalves)
Photo: Universal Studios / Land of the Dead

Example 4: Hush Puppies
• The Hush Puppies brand was founded in 1958
• The classic American brushed-suede shoes with
the lightweight crepe sole
• 1994 – sales of Hush Puppies were down to
30,000 pairs a year
• And suddenly …

• Hush Puppies had suddenly become hip in the
clubs and bars of downtown Manhattan
• By the fall of 1995 several designers wanted to
use them in their Spring collections
• In 1995, the company sold 450,000 pairs of the
classic Hush Puppies

• How did that happen?
• The first few kids were not deliberately
trying to promote Hush Puppies
• They were wearing them because
no one else would wear them
• No one was trying to make
Hush Puppies a trend

Q4: Why succeed without trying?
• Tipping point
• Critical mass
• Initially – anticonformity

Example 5: Intention-behavior gap
• Value-action gap, attitude-belief gap
(Godin et al. 2005; Fennis et al. 2011; Sheeran 2002; Zhang, Nuttall 2011; Ozaki
2011; Blake 1999; Kollmuss, Agyeman 2002; Gadenne et al. 2011; Rogers 2003)
• Discrepancy between attitude and behavior:
– In Italy, 70% of respondents are willing to increase energy
savings, but only 2% are reducing their energy use
(Pongilione 2011)
• Possible reasons for the intention-behavior gap
(Diaz-Rainey, Tzavara 2012)
– Consumer confusion
– Unstable opinions

Example 5: How can we get people
to save electricity?

How can we get people to save electricity?
• Behavioral experiment run in a hot summer in San
Marcos, CA
• 4 different messages:
– ¼ of the homes received a message that said: Did you know
that you can save $54 a month this summer? Turn off your
air conditioning and turn on your fan
– “Save the planet”
– “Be a good citizen and prevent blackouts”
• They had no impact on energy consumption!

It’s social pressure stupid!
• 77% of your neighbors said that they turned off their air
conditioning and turned on their fans. Please join them by
turning off your air conditioning and turning on your fan

What is the question?
• How new products or ideas spread in the
society?
• Why does it take sometimes so long?
• Why does it fail sometimes (valley of death)?
• Why does it fail after a promising start?
• What helps it to diffuse? The network?
• How and why is the critical mass reached?
• Why does the intention-behavior gap appear?

How to model diffusion of innovation?
Agent-based
models (ABM)
Mathematical models
Analytical
(aggregate)
Simple decision
rules
Opinion
dynamics
Contagious spread
of information
Threshold
models
Deterministic Stochastic
Conceptual models
Reservation
price
More
sophisticated and
less parsimonious
E. Kiesling et al., Agent-based
simulation of innovation diffusion:
A review, CEJOR 20 (2012) 183-230

Rogers’ conceptual model
• External influence
– mass media, advertisement
• Internal influence
– word-of-mouth (social)
• Five archetypic types
of individuals
Critical mass
The tipping point

1. Knowledge stage – gain knowledge
of an innovation
2. Persuasion stage – form an attitude towards it
3. Decision stage – decide to adopt it or reject it
4. Implementation stage – implement it
5. Confirmation stage – confirm the decision
Innovation adoption process

Aggregate (analytical) models
F.M. Bass, A New Product Growth Model for Consumer Durables, Management Science 15 (1969) 215
• Based on differential equations
• One of ten most influential papers in the first
50 years of Management Science (Hopp, 2004)
• Contagious process driven by
– external influence (e.g. advertising, mass media)
– internal influence (e.g. word-of-mouth)
• Specify the flow(s) between susceptible
(non-adopted) and the infected (adopted)

Bass model (1969)
𝑛 𝑡
𝑑𝑡
=
𝑑𝑁(𝑡)
= 𝑝 + 𝑞
𝑁(𝑡)
𝑀
𝑀 − 𝑁(𝑡)
Number of adopters until
time t (aggregated number)
Word-of-mouth
Innovation factor,
external influence
Potential number
of adopters
Number of adopters
at time t

Bass model (1969)
p – innovation
q – imitation

Why go beyond the Bass model?
• Phenomenological model – is not aimed at
explaining the mechanisms (‘How?’ not ‘Why?’)
• Does not reproduce the complexity of
real-world diffusion (e.g. innovation failures)
• Can be reformulated in terms of ABM
• Adoption does not propagate as a contagion
process!
– Weiss et al., Physical Review X 4 (2014) 041008

Agent-based models (ABM)
• Microscopic (Statistical physics)
• Bottom-up
• Agent (individual)
– Person, animal, plant, particle
– Organization, society, population
– One or several types in one model
– Individual traits
• Interactions
• Environment (space, network)

1. Knowledge stage – gain knowledge
of an innovation
2. Persuasion stage – form an attitude towards it
3. Decision stage – decide to adopt it or reject it
4. Implementation stage – implement it
5. Confirmation stage – confirm the decision
Innovation adoption - opinion formation

Cellular automata: Bass and threshold
(Goldenberg et al. 2010)
𝑝𝑟𝑜𝑏 𝑡 = { 1 − 1 − 𝑎 1 − 𝑏 𝑚𝑖(𝑡) 𝑖𝑓
𝜒 𝑡
𝑁
> ℎ𝑖
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝜒 𝑡 – cumulative number of adopters
at time t
𝑁 – market potential
𝑎 – prob. of influence by external factors
𝑏 – prob. of influence by interactions
ℎ𝑖 – individual threshold
𝑚𝑖(𝑡) – adopters in the personal network
probability of not being adopted

The distribution of thresholds
• Lack of empirical evidence – what is the distribution?
• Usual assumption – thresholds are normally
distributed in the population (Valente, 1995)
• “Negative” thresholds can be assumed to be zero
(Granovetter, 1978)

Who is influencing whom?
(Watts and Dodds, 2007)
• No clear empirical evidence regarding the structure
of influence networks
• No empirical studies in which individuals have been
shown to influence over 100 others directly
• B. Latané et al., Distance Matters: Physical Space and
Social Impact, Pers Soc Psychol Bull 21 (1995) 795-805
– Studies of college students and citizens of south Florida,
United States, students in Shanghai, China
– Social influence, measured by the frequency of memorable
interactions, is heavily determined by distance

Why seemingly successful products fail after
a promising start? (Moldovan, Goldenberg, 2004)
• Word-of-mouth (w-o-m) communications play
a key role in new product adoption but …
• Limited attention has been
given to the negative w-o-m
• Negative forces are less visible,
leaving no traces in sales data

Negative w-o-m and reversibility of decisions
Leonard-Barton (1985)
• More than 70% of dentists tried or adopted
a specific innovation
• Over 20% rejected its use completely, at the
advice of experts
• There is no qualitative distinction between
negative w-o-m and positive w-o-m
• Some evidence indicating that negative
interactions are more dominant

A strange infection!
You should
go jogging!
Why?
Jogging isn’t good
for your knees!

Models of opinion dynamics
good
hard to say
Social mood:
Is the situation in our country getting better or worse?
bad

The micro and macro levels …
© Marcin Weron

Why diffusion of innovation?
• Important, fascinating and interdisciplinary
– medicine, marketing, sociology, anthropology, etc.
• Simple agents SPINSON=SPIN+PERSON
• Clear initial conditions
not adopted adopted

How to model
individual opinions?
• The diamond model of social response
– elegant and comprehensive
– unambiguous operational definitions
of basic types of social response
– a ready recipe for a microscopic model of opinion dynamics
– supported by social experiments
Paul Nail
Social psychology
(U. Central Arkansas)
Social
psychology
Sociology

The diamond model: Single trial
Nail et al. (2000)
P. Nail, K. Sznajd-Weron, Rethinking the Diamond Model: Theory and Research Support
Self-Anticonformity as a Basic Response and Influence Process, Nova Publishers (2016)

Conformity
• Conformity – the main mechanism of collective
actions
– Informational: “when in doubt, imitate”
– Normative: “when in Rome, do as the Romans do”
Aversion to standing
out in the crowd
conformity
anticonformity

How to model conformity?
Ising at T=0 Threshold model (T=1)
Majority (Galam, Redner)
q-voter

How to model conformity?
Majority rule Threshold models Q-voter
group of influence all neighbors group of influence
absolute majority majority above T unanimity

The power of social validation
• Milgram, Bickman & Berkowitz, 1969
• Results of experiments: 1  4%, 4-5  80%
• Robert B. Cialdini: Social Validation –
the fundamental way of decision making

Asch’s Experiment
• Normative Influence
• Asch (1956) „visual perception”
53

0%
10%
20%
30%
40%
conformity
Asch (1956)
1 2 3 4 5 6 7 8 9 10
The size of the group
The size of the group is important …
0 15
0
0
6
4
2
80
0
0
conformity
(%)
Milgram et al (1969)
5 10
the size of the group

Unanimity is the key!
• The presence of a social supporter reduced the total
number of yielding responses from 32% to 5.5%!
• Participants were far more independent when they
were opposed by
– a 7-person majority and had a partner
– than when they were opposed by a 3-person majority and
did not have a partner
56

Conformity and the group size
• The threshold value of the group size varies between
3 and 5
• Review on the theory and experiments (Bond, 2005)
– The size of the group cannot be too small, i.e., has to be of
a sufficient size to invoke the social pressure
– The size of the group cannot be too large
• All experiments with unanimous majority
• Therefore we use the q-voter model

Do we really need unanimity?
77% of your neighbors said …

Anticonformity or independence?
(c) P
. Nyczka, 2014
C. Castellano, M. A. Munoz, R. Pastor-Satorras,
Nonlinear q-voter model,
Phys. Rev. E 80, 041129 (2009)

The mean-field approach
(c) P
. Nyczka, 2014
𝑐 𝑡
𝑁
=
𝑁+(𝑡)
,
𝑁
𝑖
=1
𝑁
𝑖
𝑚 𝑡 =
1
∑ 𝑆 𝑡 = 1 − 𝑐(𝑡)
𝛾+ = 𝑃𝑟𝑜𝑏 𝑐 → 𝑐 +
1
𝑁
𝛾− = 𝑃𝑟𝑜𝑏 𝑐 → 𝑐 −
1
𝑁
𝛾0 = 𝑃𝑟𝑜𝑏 𝑐 → 𝑐 = 1 − 𝛾+ −𝛾−

The mean-field approach for 𝑵 → ∞
Model A: anticonformity
𝛾+ = 1 − c (1 − 𝑝)cq + p 1 − c q
𝛾− = 𝑐 (1 − 𝑝)(1 − c)q+p𝑐q
Model B: independence
𝛾+ = 1 − c (1 − 𝑝)cq + p𝑓
𝛾− = 𝑐 (1 − 𝑝)(1 − c)q+𝑝𝑓
Time evolution
𝑐 𝑡 +
1
= 𝑐 𝑡 +
1
𝛾+ − 𝛾−
𝑁 𝑁

Type of non-conformity matters
Nyczka et al. (2012, PRE)
z=0 (no independence) z=1 (no anticonformity)
(c) P
. Nyczka, 2015

Conformity and non-conformity
1. P
. Nyczka, K. Sznajd-Weron, Journal of Statistical Physics 151 (2013)
2. P
. Nyczka, K. Sznajd-Weron, J. Cislo, Phys. Rev. E 86, 011105 (2012)

Responses to social influence
– person or situation?
P.R.Nail et al., Psychological Bulletin 126 (2000) 454-470

Question
• Debate important for psychologists
• Is it important from the macroscopic (societal)
point of view?
• Do the modeling assumptions on social
interactions (personal traits vs. situation)
have impact on the system as a whole?
• Answer within the q-voter model
– C. Castellano, M.A.Muoz, R.Pastor-Satorras (2009) Phys. Rev. E 80, 041129
– P. Nyczka, K. Sznajd-Weron, J. Cislo (2012) Phys. Rev. E 86, 011105
– K. Sznajd-Weron, J. Szwabiński, R. Weron (2014) PLoS ONE 9(11)

Conformity and non-conformity
conformity
anticonformity
independence
1-f
f

Person-situation debate
Two types of spinsons:
• permanently independent
• always susceptible to group
pressure
Homogenous spinsons:
• The level of independence
is the same for every spinson

Person vs. situation
Heterogeneous spinsons:
< 𝑝 > = 0.2
Homogenous spinsons:
< 𝑝 > = 0.2
K. Sznajd-Weron, J. Szwabiński, R. Weron (2014) PLoS ONE 9(11), e112203

Person approach – independent
1-f
f
Independent
𝑆𝑖 𝑡 + 1 = −𝑆𝑖 𝑡 with probability 𝑓
𝑆𝑖 𝑡 + 1 = 𝑆𝑖 𝑡 with probability 1 − 𝑓

Person approach– conformist
Conformist
Follow unanimous group

Situation
1
2
3
1-p
p(1-f)
pf
Independence with probability p:
• 𝑆𝑖 𝑡 + 1 = −𝑆𝑖 𝑡 with probability 𝑓
• 𝑆𝑖 𝑡 + 1 = 𝑆𝑖 𝑡 with probability 1 − 𝑓
Conformity with probability 1-p: follow unanimous group

The mean field approach
𝑁𝗍 𝑡
𝑁
= 𝑐(𝑡)
1
𝑐 𝑡 + 1 = 𝑐 𝑡 +
𝑁
𝑝𝑓 1 − 2𝑐 𝑡
1
+
𝑁
(1 − 𝑝) 𝑐𝑞 𝑡 1 − 𝑐 𝑡 − 1 − 𝑐 𝑡
𝑞
𝑐(𝑡)
probability of up-spin
independence
conformity

𝑁↓ 𝑡 + 𝑁𝗍 𝑡
1 1 = 𝑝𝑁
1 1
𝑁↓ 𝑡 𝑁𝗍 𝑡
𝑁 𝑁
𝑁𝗍 𝑡 + 1 = 𝑁𝗍 𝑡 + 1
𝑓 − 1
𝑓
2 2
𝑁↓ 𝑡
𝑁
𝑁𝗍 𝑡 + 1 = 𝑁𝗍 𝑡 + 2
𝑐𝑞 𝑡 − 2
𝑁𝗍 𝑡
𝑁
1 − 𝑐 𝑡
𝑞
𝑁𝗍 𝑡 + 𝑁𝗍 𝑡
𝑁
1 2
= 𝑐(𝑡)
Two groups
𝑁1 + 𝑁2 = 𝑁
Independent
𝑁1 = 𝑝𝑁
The mean field approach – person

Person or situation?
𝑁𝗍 𝑡
𝑁
= 𝑐 𝑡 , 𝑐 0 = 1, 𝑐(∞) ≡ 𝑐
Scaling

Diffusion of innovation – general model

Our model – conformity and independence
• K. Sznajd-Weron, M. Tabiszewski
and A. Timpanaro, EPL (2011)
• P
. Nyczka, K. Sznajd-Weron and
J. Cislo, Phys. Rev. E 86, 011105
(2012)
f 1-f

Model (opinion dynamics)
𝑝𝑓
𝑝 1 − 𝑓
1 − 𝑝
1 − 𝑝 ℎ
1 − 𝑝
1 − ℎ
independence
conformity
external field

Let’s look at the evolution of the system
P
. Przybyła, K. Sznajd-Weron, R. Weron,
Advances in Complex Systems 17 (2014) 1450004

919 MCS 1011 MCS 1088 MCS 1138 MCS
593 MCS 671 MCS
1209 MCS 1932MCS
1610MCS
646 MCS 850 MCS
1173MCS

The role of the external field

Single trajectories
Empirical data
Based on: Karl Hartig poster for the
Wall Street Journal Classroom Edition, 1998
(data sources: A.C. Nielsen Company,
Broadcasting & Cable Yearbook 1996)
Monte Carlo simulations
100x100, p=0.1, h=0.09

Average and median over 1000 trajectories
𝑝 = 0.1,𝑓 = 0.1, 𝑁 = 100 × 100
ℎ = 0.09 ℎ = 0.095

Parameters (p, f, h) and scaling
h = 0.05
h = 0.1839

Some details are important, other not
• Anticonformity or independence?
• Person or situation?
• Sequential or synchronous updating?

Synchronous or sequential update
W
W
W
W
• Sequential:
• Synchronous:
1) B. Skorupa, K. Sznajd-Weron, and R. Topolnicki, Phys. Rev. E 86, 051113 (2012)
2) K. Sznajd-Weron, Phys. Rev. E 82, 031120 (2010)

Rewiring the network. What helps an
innovation to diffuse?
• How does the social network structure
influence the process?
• The role of network structure is still in its
infancy, mainly because of the lack of empirical
data
• In the published studies one can find different
and at times seemingly contradictory results

Time evolution on the SM network
Steven H. Strogatz
Nature 410, 268-276 (2001)

Increasing randomness is good or not?

Is a more dense network better or not?

Conclusions
• The critical value of the external field increases
with β (randomness)
• The critical value of the external field increases
with K (density)
• In the case of uncertainty (high for DI), a more
clustered network will help the diffusion
• When social influence is less important (perfect
information), the diffusion will be easier on a
random graph (shorter path)

Why seemingly successful products, fail, after
a promising start? (Moldovan, Goldenberg, 2004)
• Word-of-mouth (w-o-m) communications play
a key role in new product adoption but …
• Limited attention has been
given to the negative w-o-m
• Negative forces are less visible,
leaving no traces in sales data

Negative w-o-m and reversibility of decisions
Leonard-Barton (1985)
• More than 70% of dentists tried or adopted a
specific innovation
• Over 20% rejected its use completely, at the
advice of experts
• There is no qualitative distinction between
negative w-o-m and positive w-o-m
• Some evidence indicating that negative
interactions are more dominant

Cellular automata modeling of resistance
to innovations
• Positive and negative w-o-m
• Opinion leaders:
– render advice and information about
new products and influence the
attitudes or behaviors of others
– perceived as having greater product
knowledge
– more innovative
– have a higher socio-economic status,
higher educational attainment and
greater public individuation

Heterogeneous consumers
• Consumers belong to one of three groups:
– opinion leaders
– resistance leaders
– main market (ordinary) consumers
• Consumers (in all groups) may be in one of
three states:
– uninformed (do not spread w-o-m)
– adopters (spread positive w-o-m)
– resisters (spread negative w-o-m)

Empirical studies
49 individuals were asked to rate
– their attitude
– purchase intention (low implies product rejection)
– w-o-m intentions (positive or negative)
with respect to 4 new products
Subjects who rejected the innovation showed
significantly stronger intention to spread
negative w-o-m!

Dynamics and parameters (7!)
• Initially – all consumers uninformed:
– opinion leaders (fraction 𝜋𝑂𝐿 )
– resistance leaders (fraction 𝜋𝑅𝐿 )
– ordinary consumers (fraction 1 − 𝜋𝑂𝐿 − 𝜋𝑅𝐿 )
• Consumers become either adopters or resisters by:
– advertising message (prob. 𝛼)
– positive w-o-m by ordinary consumer (prob. 𝛽𝑝)
– negative w-o-m by ordinary consumer (prob. 𝛽𝑛)
– positive w-o-m imparted by an opinion leader (prob. 𝛽𝑂𝐿)
– negative w-o-m imparted by a resistance leader (prob. 𝛽𝑅𝐿)

Further reading
1. K. Sznajd-Weron, J. Szwabiński, R. Weron, "Is the Person-Situation Debate
Important for Agent-Based Modeling and Vice-Versa?" PLoS ONE 9(11), (2014)
doi:10.1371/journal.pone.0112203
2. A. Kowalska-Pyzalska, K. Maciejowska, K. Suszczyński, K. Sznajd-Weron, R. Weron,
"Turning green: Agent-based modeling of the adoption of dynamic electricity
tariffs", Energy Policy 72 (2014) 164-174
3. K. Sznajd-Weron, J. Szwabiński, R. Weron, T.Weron, "Rewiring the network. What
helps an innovation to diffuse?", J. Stat. Mech. (2014) P03007
4. P
. Przybyła, K. Sznajd-Weron, R. Weron, "Diffusion of innovation within an agent-
based model: Spinsons, independence and advertising", Advances in Complex
Systems 17 (2014) 1450004 full article and software WAS
5. P. Nyczka, K. Sznajd-Weron, "Anticonformity or Independence? -Insights from
Statistical Physics", Journal of Statistical Physics 151 (2013)
6. P. Nyczka, K. Sznajd-Weron, J. Cislo, "Phase transitions in the q-voter model with
two types of stochastic driving", Phys. Rev. E 86, 011105 (2012)
7. K. Sznajd-Weron, M. Tabiszewski and A. Timpanaro, "Phase transition in the Sznajd
model with independence", EPL (2011)

The role of opinion leaders
• Katz and Lazarsfeld (1955)
– “two-step flow”
– influence “flows” from the
media through opinion
leaders to their respective
followers
• What is the role of
influentials?
• Are they responsible for
diffusion processes?

The role of opinion leaders
• Binary decisions can be applied to a surprisingly wide
range of real world situations
• Threshold rule – individuals will switch from 0 to 1
only when sufficiently many others have adopted (1)
• 𝑏𝑖 − the fraction of 𝑖’𝑠 sample population that has
adopted
• 𝜙𝑖 − individual threshold
𝑃𝑟𝑜𝑏 → = {1 𝑖𝑓 𝑏𝑖 ≥ 𝜙𝑖
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Who is influencing whom?
• No clear empirical evidence regarding the structure of
influence networks
• Each 𝑖 −th individual influences 𝑛𝑖 others
• 𝑛𝑖 is drawn from an influence
distribution 𝑝 𝑛 , < 𝑛𝑖 >≪
𝑁
• 𝑛𝑖 refers not to how many
others node 𝑖 knows but to
how many others 𝑖 influences
with respect to the particular
issue

Assumptions (Watts and Dodds, 2007)
• Poisson influence distribution 𝑝 𝑛 − little variation
around its average
• Network is random — aside from the distribution of
influence, the network exhibits no other structure
• An influential — an individual in the top 𝑞 = 10% of
the influence distribution 𝑝 𝑛
Pr 𝑋 = 𝑘 =
𝜆𝑘exp(−𝜆)
𝑘!

Dynamics of Influence
• Initial state:
– (𝑁 − 1) individuals are inactive (0)
– 1 initiator activated exogenously (1)
• Initial activation may or may not trigger some
additional endogenous activations
• Newly activated neighbors may activate some of their
own neighbors, etc.
• Cascade – sequence of activations
• Local and global cascades

Dynamics of Influence
• Initial state:
– (𝑁 − 1) individuals are inactive (0)
– 1 initiator activated exogenously (1)
• Initial activation may or may not trigger some
additional endogenous activations
• Newly activated neighbors may activate some of their
own neighbors, etc.
• Cascade – sequence of activations
• Local and global cascades
• Global cascades – critical mass

Modification 1 – go beyond Poisson
• Hyperinfluentials (HI): 𝑝 𝑛
• The presence of HI does affect the size and
prevalence of influence cascades
• Relative impact of HI is greater than influential
• The cascades that are triggered by HI are on
average less successful
• Early adopters are generally less influential
than they are in low-variance networks

Modification 2 – go beyond random
• Random network – not a good approximation of real
social networks
• The presence of group structure changes (support)
the dynamics of influence cascades
• The basic conclusions regarding
influentials continue to hold
• The addition of group structure
appears to diminish their
importance

Modification 3 – beyond the threshold rule
• Individuals only adopt an innovation when some
critical fraction of their neighbors have adopted it
• They have considered a second canonical type of
influence model — a “SIR” (“susceptible” (S),
“infected” (I), and “recovered”(R)) model
• Hyperinfluentials play an important role as early
adopters, when networks are sufficiently sparse, but
not as initiators
• A group structure – impede the effectiveness of
influentials both as initiators and early adopters

Conclusions
• Influentials are less important than is generally
supposed, either as initiators of large cascades or as
early adopters
• HI seems to be more a theoretical possibility than an
empirical reality
• No empirical studies in which individuals have been
shown to influence over 100 others directly

Diffusion of innovation ( PDFDrive ).pptx

Recommandé

Recommandé

Contenu connexe

Similaire à Diffusion of innovation ( PDFDrive ).pptx

Similaire à Diffusion of innovation ( PDFDrive ).pptx (20)

Dernier

Dernier (20)

Diffusion of innovation ( PDFDrive ).pptx