Complex Sociotechnical Lecture Three Systemspdodds/teaching/courses/2012-07liparisummer... ·...

Transcript of Complex Sociotechnical Lecture Three Systemspdodds/teaching/courses/2012-07liparisummer... ·...

ComplexSociotechnicalSystems

A Very DismalScience

Contagion

Winning: it’s not foreveryone

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Lecture ThreeStories of Complex Sociotechnical Systems:Measurement, Mechanisms, and Meaning

Lipari Summer School, Summer, 2012

Prof. Peter Dodds

Department of Mathematics & Statistics | Center for Complex Systems |Vermont Advanced Computing Center | University of Vermont

Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://www.uvm.edu/~pdodds/teaching/courses/2012-07Lipari-http://www.uvm.edu/~pdodds/teaching/courses/2012-07Lipari-http://www.uvm.edu/~pdoddshttp://www.uvm.edu/~cems/mathstat/http://www.uvm.edu/~cems/complexsystems/http://www.uvm.edu/~vacc/http://www.uvm.eduhttp://www.uvm.eduhttp://www.uvm.edu/~cems/complexsystems/http://www.uvm.edu/~vacc/http://www.uvm.edu/~pdoddshttp://www.uvm.edu/~pdodds


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Outline

A Very Dismal Science

Contagion

Winning: it’s not for everyone

Social Contagion ModelsGranovetter’s modelNetwork versionGroups

Simple disease spreading models

References

http://www.uvm.eduhttp://www.uvm.edu/~pdodds


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Economics, Schmeconomics

Alan Greenspan (September 18, 2007):

“I’ve been dealing with these bigmathematical models of forecasting theeconomy ...

If I could figure out a way to determinewhether or not people are more fearfulor changing to more euphoric,

I don’t need any of this other stuff.

I could forecast the economy better thanany way I know.”

http://wikipedia.org

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://wikipedia.org


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Economics, SchmeconomicsGreenspan continues:“The trouble is that we can’t figure that out. I’ve been inthe forecasting business for 50 years. I’m no better than Iever was, and nobody else is. Forecasting 50 yearsago was as good or as bad as it is today. And the reasonis that human nature hasn’t changed. We can’t improveourselves.”

Jon Stewart:

“You just bummed the @*!# out of me.”

wildbluffmedia.com

I From the Daily Show (�) (September 18, 2007)I The full inteview is here (�).

http://www.uvm.eduhttp://www.uvm.edu/~pdoddswildbluffmedia.comhttp://www.thedailyshow.comhttp://www.thedailyshow.com/video/index.jhtml?videoId=102970&title=alan-greenspan


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Jon Stewart:


wildbluffmedia.com




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Jon Stewart:


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Jon Stewart:


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Jon Stewart:


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Jon Stewart:


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James K. Galbraith:NYT But there are at least 15,000 professional

economists in this country, and you’re saying onlytwo or three of them foresaw the mortgage crisis?

[JKG] Ten or 12 would be closer than two or three.

NYT What does that say about the field of economics,which claims to be a science?

[JKG] It’s anenormous blot on the reputation of the profession.There are thousands of economists. Most of themteach. And most of them teach a theoreticalframework that has been shown to be fundamentallyuseless.

From the New York Times, 11/02/2008 (�)

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://www.nytimes.com/2008/11/02/magazine/02wwln-Q4-t.html


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economists in this country, and you’re saying onlytwo or three of them foresaw the mortgage crisis?

[JKG] Ten or 12 would be closer than two or three.






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economists in this country, and you’re saying onlytwo or three of them foresaw the mortgage crisis?[JKG] Ten or 12 would be closer than two or three.






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NYT What does that say about the field of economics,which claims to be a science? [JKG] It’s anenormous blot on the reputation of the profession.

There are thousands of economists. Most of themteach. And most of them teach a theoreticalframework that has been shown to be fundamentallyuseless.




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NYT What does that say about the field of economics,which claims to be a science? [JKG] It’s anenormous blot on the reputation of the profession.There are thousands of economists. Most of themteach.

And most of them teach a theoreticalframework that has been shown to be fundamentallyuseless.




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NYT What does that say about the field of economics,which claims to be a science? [JKG] It’s anenormous blot on the reputation of the profession.There are thousands of economists. Most of themteach. And most of them teach a theoreticalframework that has been shown to be fundamentallyuseless.




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Collective Cooperation:

I Standard frame:

Locally selfish behavior→ collective cooperation.

I Different frame:

Locally moral/fair behaviour→ collective bad actions.

I So why do we study frame 1 instead of frame 2?I Tragedy of the Commons is one example of frame 2.I Better question:

Who is it that studies frame 1 over frame 2. . . ?



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I Standard frame:


I Different frame:






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I Standard frame:


I Different frame:






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I Standard frame:


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I Standard frame:


I Different frame:






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Homo Economicus

I ‘What makes people think like Economists?Evidence on Economic Cognition from the “Survey ofAmericans and Economists on the Economy” ’ [8]

Bryan Caplan, Journal of Law and Economics, 2001

People behave like Homo economicus:1. if they are well educated,2. if they are male,3. if their real income rose over the last 5 years,4. if they expect their real income to rise over the next 5

years,5. if they have a high degree of job security,6. but not because of high income nor ideological

conservatism.



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Homo Economicus

I ‘What makes people think like Economists?Evidence on Economic Cognition from the “Survey ofAmericans and Economists on the Economy” ’ [8]

Bryan Caplan, Journal of Law and Economics, 2001

People behave like Homo economicus:1. if they are well educated,2. if they are male,3. if their real income rose over the last 5 years,4. if they expect their real income to rise over the next 5

years,5. if they have a high degree of job security,6. but not because of high income nor ideological

conservatism.



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Wealth distribution in the United States:

Questions used in a recent study by Norton andAriely: [29]

I What percentage of all wealth is owned byindividuals grouped into quintiles?

I How do people believe wealth is distributed?I How do people believe wealth should be distributed?



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This is a Collateralized Debt Obligation:


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Contagion

A confusion of contagions:I Was Harry Potter some kind of virus?I What about Vampires?I Did Sudoku spread like a disease?I Language? The alphabet? [17]

I Religion?I Democracy...?



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NaturomorphismsI “The feeling was contagious.”I “The news spread like wildfire.”I “Freedom is the most contagious virus known to

man.”—Hubert H. Humphrey, Johnson’s vice president

I “Nothing is so contagious as enthusiasm.”—Samuel Taylor Coleridge



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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass.

Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.

I Hoffer (�) was an interesting fellow...

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://en.wikipedia.org/wiki/Eric_Hoffer


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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke

sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,

and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter,

swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison,

hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation,

there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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Social contagion

Eric Hoffer, 1902–1983There is a grandeur in the uniformity of the mass. Whena fashion, a dance, a song, a slogan or a joke sweepslike wildfire from one end of the continent to the other,and a hundred million people roar with laughter, swaytheir bodies in unison, hum one song or break forth inanger and denunciation, there is the overpoweringfeeling that in this country we have come nearer thebrotherhood of man than ever before.




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The spread of fanaticism

Hoffer’s acclaimed work: “The True Believer:Thoughts On The Nature Of Mass Movements” (1951) [20]

Quotes-aplenty:I “We can be absolutely certain only about things we

do not understand.”I “Mass movements can rise and spread without belief

in a God, but never without belief in a devil.”I “Where freedom is real, equality is the passion of the

masses. Where equality is real, freedom is thepassion of a small minority.”



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Imitation

despair.com

“When people are freeto do as they please,they usually imitateeach other.”

—Eric Hoffer“The Passionate Stateof Mind” [21]

http://www.uvm.eduhttp://www.uvm.edu/~pdoddsdespair.com


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The collective...

despair.com

“Never Underestimatethe Power of StupidPeople in LargeGroups.”

http://www.uvm.eduhttp://www.uvm.edu/~pdoddsdespair.com


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Contagion

DefinitionsI (1) The spreading of a quality or quantity between

individuals in a population.I (2) A disease itself:

the plague, a blight, the dreaded lurgi, ...I from Latin: con = ‘together with’ + tangere ‘to touch.’I Contagion has unpleasant overtones...I Just Spreading might be a more neutral wordI But contagion is kind of exciting...



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Examples of non-disease spreading:

Interesting infections:I Spreading of buildings in the US... (�)

I Viral get-out-the-vote video. (�)

Lavf50.5.0

Convertified by iSquint - http://www.isquint.org

walmartspread.mp4Media File (video/mp4)

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://www.youtube.com/watch?v=EGzHBtoVvpchttp://www.cnnbcvideo.com/?nid=VWB8OWHr.GqH2kYkPxOMwTQ1NDIxODA-


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Examples of non-disease spreading:

Interesting infections:I Spreading of buildings in the US... (�)

I Viral get-out-the-vote video. (�)

Lavf50.5.0

Convertified by iSquint - http://www.isquint.org

walmartspread.mp4Media File (video/mp4)

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://www.youtube.com/watch?v=EGzHBtoVvpchttp://www.cnnbcvideo.com/?nid=VWB8OWHr.GqH2kYkPxOMwTQ1NDIxODA-


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Contagions

Two main classes of contagion1. Infectious diseases

:tuberculosis, HIV, ebola, SARS, influenza, ...

2. Social contagion

:fashion, word usage, rumors, riots, religion, ...



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2. Social contagion




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Contagions

Two main classes of contagion1. Infectious diseases:

tuberculosis, HIV, ebola, SARS, influenza, ...

2. Social contagion




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Contagions

Two main classes of contagion1. Infectious diseases:

tuberculosis, HIV, ebola, SARS, influenza, ...

2. Social contagion:fashion, word usage, rumors, riots, religion, ...



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Where do superstars come from?I Rosen (1981): “The Economics of Superstars”

Examples:I Full-time Comedians (≈ 200)I Soloists in Classical MusicI Economic Textbooks (the usual myopic example)

I Highly skewed distributions (again)...



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Where do superstars come from?I Rosen (1981): “The Economics of Superstars”

Examples:I Full-time Comedians (≈ 200)I Soloists in Classical MusicI Economic Textbooks (the usual myopic example)

I Highly skewed distributions (again)...



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Superstars

Rosen’s theory:I Individual quality q maps to reward R(q)I R(q) is ‘convex’ (d2R/dq2 > 0)I Two reasons:

1. Imperfect substitution:

A very good surgeon is worth many mediocre ones

2. Technology:

Media spreads & technology reduces cost ofreproduction of books, songs, etc.

I No social element—success follows ‘inherent quality’



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Superstars


1. Imperfect substitution:

A very good surgeon is worth many mediocre ones

2. Technology:

Media spreads & technology reduces cost ofreproduction of books, songs, etc.




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Superstars


1. Imperfect substitution:A very good surgeon is worth many mediocre ones

2. Technology:Media spreads & technology reduces cost ofreproduction of books, songs, etc.




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Superstars


1. Imperfect substitution:A very good surgeon is worth many mediocre ones

2. Technology:Media spreads & technology reduces cost ofreproduction of books, songs, etc.




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Superstars

Adler (1985): “Stardom and Talent”

I Assumes extreme case of equal ‘inherent quality’I Argues desire for coordination in knowledge and

culture leads to differential successI Success is then purely a social construction



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Dominance hierarchies

Chase et al. (2002): “Individual differences versus socialdynamics in the formation of animal dominancehierarchies” [11]

The aggressive female Metriaclima zebra (�):

Pecking orders for fish...

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://en.wikipedia.org/wiki/Metriaclima


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Dominance hierarchies

I Fish forget—changing of dominance hierarchies:

(one-sided binomial test: n ! 22, P " 0.001 and P " 0.03,respectively). In this light, 27% of the groups with identicalhierarchies is very small.

Discussion. When we rewound the tape of the fish to form newhierarchies, we usually did not get the same hierarchy twice. Thelinearity of the structures persisted and the individuals stayed thesame, but their ranks did not. Thus our results differ considerablyfrom those predicted by the prior attributes hypothesis. The factthat more identical hierarchies occurred than expected by chancealone supports the hypothesis that rank on prior attributesinfluences rank within hierarchies but not the hypothesis that

rank on prior attributes of itself creates the linear structure of thehierarchies. Although 50% of the fish changed ranks from onehierarchy to the other, almost all the hierarchies were linear instructure. Some factor other than differences in attributes seemsto have ensured high rates of linearity. In the next experiment,we tested to determine whether that factor might be socialdynamics.

It might seem possible that ‘‘noise,’’ random fluctuations inindividuals’ attributes or behaviors, could account for the ob-served differences between the first and second hierarchies.However, a careful consideration of the ways in which fluctua-tions might occur shows that this explanation is unlikely. Forexample, what if the differences were assumed to have occurredbecause some of the fish changed their ranks on attributes fromthe first to the second hierarchies? To account for our results,this assumption would require a mixture of stability and insta-bility in attribute ranks at just the right times and in just the rightproportion of groups. The rankings would have had to have beenstable for all the fish in all the groups for the day or two it tookthem to form their first hierarchies (or we would not have seenstable dominance relationships by our criterion). Then, in three-quarters of the groups (but not in the remaining one-quarter)various numbers of fish would have had to have swapped rankson attributes in the 2-week period of separation so as to haveproduced different second hierarchies. And finally, the rankingson attributes for all the fish in all the groups would have had tohave become stable once more for the day or two it took themto form their second hierarchies.

Alternatively, instead of attribute rank determining domi-nance rank as in the prior attribute model, dominance in pairsof fish might be considered to have been probabilistic, such thatat one meeting one might dominate, but at a second meetingthere was some chance that the other might dominate. Theproblem with this model is that earlier mathematical analysisdemonstrates that in situations in which one of each pair in agroup has even a small chance of dominating the other, theprobability of getting linear hierarchies is quite low (34). Andeven in a more restrictive model in which only pairs of fish thatare close in rank in the first hierarchies have modest probabilitiesof reversing their relationships, such as the level (0.25) weobserved in this experiment, the probability of getting as manylinear hierarchies as we observed is still very low (details areavailable from the authors).

We know of only one other study (47) in which researchersassembled groups to form initial hierarchies, separated theindividuals for a period, and then reassembled them to form asecond hierarchy (but see Guhl, ref. 48, for results in whichgroups had pairwise encounters between assembly and reassem-bly). Unfortunately, their techniques of analysis make it impos-sible to compare results, because they examined correlationsbetween the frequency of aggressive acts directed by individualsin pairs toward one another in the two hierarchies rather thancomparing the ranks of individuals. With these techniques it ispossible to get a positive correlation and thus a ‘‘replication’’ ofan original hierarchy in situations in which several animalsactually change ranks from the first to the second hierarchies.

Table 1. Percentage of groups with different numbers of fishchanging ranks between first and second hierarchies (n ! 22)

No. of fish changing ranks Percentage of groups

0 27.32 36.43 18.24 18.2

Fig. 1. Transition patterns between ranks of fish in the first and secondhierarchies. Frequencies of experimental groups showing each pattern areindicated in parentheses. Open-headed arrows indicate transitions of rank.Solid-headed arrows show dominance relationships in intransitive triads; allthe fish in an intransitive triad share the same rank.

5746 ! www.pnas.org"cgi"doi"10.1073"pnas.082104199 Chase et al.

(one-sided binomial test: n ! 22, P " 0.001 and P " 0.03,respectively). In this light, 27% of the groups with identicalhierarchies is very small.

Discussion. When we rewound the tape of the fish to form newhierarchies, we usually did not get the same hierarchy twice. Thelinearity of the structures persisted and the individuals stayed thesame, but their ranks did not. Thus our results differ considerablyfrom those predicted by the prior attributes hypothesis. The factthat more identical hierarchies occurred than expected by chancealone supports the hypothesis that rank on prior attributesinfluences rank within hierarchies but not the hypothesis that

rank on prior attributes of itself creates the linear structure of thehierarchies. Although 50% of the fish changed ranks from onehierarchy to the other, almost all the hierarchies were linear instructure. Some factor other than differences in attributes seemsto have ensured high rates of linearity. In the next experiment,we tested to determine whether that factor might be socialdynamics.

It might seem possible that ‘‘noise,’’ random fluctuations inindividuals’ attributes or behaviors, could account for the ob-served differences between the first and second hierarchies.However, a careful consideration of the ways in which fluctua-tions might occur shows that this explanation is unlikely. Forexample, what if the differences were assumed to have occurredbecause some of the fish changed their ranks on attributes fromthe first to the second hierarchies? To account for our results,this assumption would require a mixture of stability and insta-bility in attribute ranks at just the right times and in just the rightproportion of groups. The rankings would have had to have beenstable for all the fish in all the groups for the day or two it tookthem to form their first hierarchies (or we would not have seenstable dominance relationships by our criterion). Then, in three-quarters of the groups (but not in the remaining one-quarter)various numbers of fish would have had to have swapped rankson attributes in the 2-week period of separation so as to haveproduced different second hierarchies. And finally, the rankingson attributes for all the fish in all the groups would have had tohave become stable once more for the day or two it took themto form their second hierarchies.

Alternatively, instead of attribute rank determining domi-nance rank as in the prior attribute model, dominance in pairsof fish might be considered to have been probabilistic, such thatat one meeting one might dominate, but at a second meetingthere was some chance that the other might dominate. Theproblem with this model is that earlier mathematical analysisdemonstrates that in situations in which one of each pair in agroup has even a small chance of dominating the other, theprobability of getting linear hierarchies is quite low (34). Andeven in a more restrictive model in which only pairs of fish thatare close in rank in the first hierarchies have modest probabilitiesof reversing their relationships, such as the level (0.25) weobserved in this experiment, the probability of getting as manylinear hierarchies as we observed is still very low (details areavailable from the authors).

We know of only one other study (47) in which researchersassembled groups to form initial hierarchies, separated theindividuals for a period, and then reassembled them to form asecond hierarchy (but see Guhl, ref. 48, for results in whichgroups had pairwise encounters between assembly and reassem-bly). Unfortunately, their techniques of analysis make it impos-sible to compare results, because they examined correlationsbetween the frequency of aggressive acts directed by individualsin pairs toward one another in the two hierarchies rather thancomparing the ranks of individuals. With these techniques it ispossible to get a positive correlation and thus a ‘‘replication’’ ofan original hierarchy in situations in which several animalsactually change ranks from the first to the second hierarchies.

Table 1. Percentage of groups with different numbers of fishchanging ranks between first and second hierarchies (n ! 22)

No. of fish changing ranks Percentage of groups

0 27.32 36.43 18.24 18.2

Fig. 1. Transition patterns between ranks of fish in the first and secondhierarchies. Frequencies of experimental groups showing each pattern areindicated in parentheses. Open-headed arrows indicate transitions of rank.Solid-headed arrows show dominance relationships in intransitive triads; allthe fish in an intransitive triad share the same rank.

5746 ! www.pnas.org"cgi"doi"10.1073"pnas.082104199 Chase et al.

I 22 observations: about 3/4 of the time, hierarchychanged



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26 of 137

Music Lab Experiment

48 songs30,000 participants

multiple ‘worlds’Inter-world variability

I How probable is a social state?I Can we estimate variability?

Salganik et al. (2006) “An experimental study of inequality andunpredictability in an artificial cultural market” [33]



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Experiment 1 Experiments 2–4



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112243648

1

12

24

36

48

Experiment 1

Rank market share in indep. world

Ran

k m

arke

t sha

re in

influ

ence

wor

lds

112243648

1

12

24

36

48

Experiment 2

Rank market share in indep. worldR

ank

mar

ket s

hare

in in

fluen

ce w

orld

s

I Variability in final rank.



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0

0.2

0.4

0.6

Social Influence Indep.

Gin

i coe

ffici

ent G

Experiment 1

Social Influence Indep.

Experiment 2

I Inequality as measured by Gini coefficient:

G =1

(2Ns − 1)

Ns∑i=1

Ns∑j=1

|mi −mj |



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0

0.005

0.01

0.015

SocialInfluence

Independent

Unp

redi

ctab

ility

U

Experiment 1

SocialInfluence

Independent

Experiment 2

I Unpredictability

U =1

Ns(Nw

2

) Ns∑i=1

Nw∑j=1

Nw∑k=j+1

|mi,j −mi,k |



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Sensible result:I Stronger social signal leads to greater following and

greater inequality.

Peculiar result:I Stronger social signal leads to greater

unpredictability.

Very peculiar observation:I The most unequal distributions would suggest the

greatest variation in underlying ‘quality.’I But success may be due to social construction

through following.I ‘Payola’ leads to poor system performance.



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greater inequality.


unpredictability.






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greater inequality.


unpredictability.






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greater inequality.


unpredictability.






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greater inequality.


unpredictability.






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33 of 137

Music Lab Experiment—Sneakiness

0 400 7520

100

200

300

400

500

Dow

nloa

ds

Exp. 3

Song 1

Song 481200 1600 2000 2400 2800

Exp. 4

Subjects

Song 1

Song 1

Song 1

Song 48

Song 48Song 48

Unchanged worldInverted worlds

0 400 7520

50

100

150

200

250

Dow

nloa

ds

Exp. 3

Song 2

Song 47

1200 1600 2000 2400 2800

Exp. 4

Subjects

Song 2

Song 2Song 2

Song 47

Song 47Song 47


I Inversion of download countI The ‘pretend rich’ get richer ...I ... but at a slower rate



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0 400 7520

100

200

300

400

500

Dow

nloa

ds

Exp. 3

Song 1

Song 481200 1600 2000 2400 2800

Exp. 4

Subjects

Song 1

Song 1

Song 1

Song 48

Song 48Song 48


0 400 7520

50

100

150

200

250

Dow

nloa

ds

Exp. 3

Song 2

Song 47

1200 1600 2000 2400 2800

Exp. 4

Subjects

Song 2

Song 2Song 2

Song 47

Song 47Song 47





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0 400 7520

100

200

300

400

500

Dow

nloa

ds

Exp. 3

Song 1

Song 481200 1600 2000 2400 2800

Exp. 4

Subjects

Song 1

Song 1

Song 1

Song 48

Song 48Song 48


0 400 7520

50

100

150

200

250

Dow

nloa

ds

Exp. 3

Song 2

Song 47

1200 1600 2000 2400 2800

Exp. 4

Subjects

Song 2

Song 2Song 2

Song 47

Song 47Song 47





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Social Contagion

http://xkcd.com/610/ (�)

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://xkcd.com/610/


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Social Contagion



Contagion



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Social Contagion



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Social Contagion

Examples abound

I fashionI strikingI smoking (�) [13]

I residentialsegregation [34]

I ipodsI obesity (�) [12]

I Harry PotterI votingI gossip

I Rubik’s cubeI religious beliefsI leaving lectures

SIR and SIRS contagion possibleI Classes of behavior versus specific behavior

: dieting

http://www.uvm.eduhttp://www.uvm.edu/~pdoddshttp://content.nejm.org/cgi/content/short/358/21/2249http://content.nejm.org/cgi/content/full/357/4/370


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Social Contagion

Examples abound







: dieting



Contagion



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37 of 137

Social Contagion

Examples abound







: dieting



Contagion



Network version

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37 of 137

Social Contagion

Examples abound






SIR and SIRS contagion possibleI Classes of behavior versus specific behavior: dieting



Contagion


Social ContagionModelsGranovetter’s mod

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