Networks & Collective Behavior

If each voter is more likely right than wrong and votes independently, majority accuracy rises with group size.

Condorcet proved it in 1785. It requires competence above chance and independence, and the independence assumption is what fails in practice — correlated errors destroy the result entirely.

In practice

• A jury of twelve is more accurate than any one juror, provided they deliberate on the evidence and not on each other.
• A prediction market beats individual forecasters until everyone starts trading on the same widely shared model, at which point the accuracy collapses.

Attributed to

Marquis de Condorcet

Further reading

Wikipedia

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Cognitive limits cap stable social relationships at roughly 150, with tighter layers of about 5, 15, and 50.

The layers are the robust finding: about 5 intimates, 15 close friends, 50 friends, 150 acquaintances, each roughly tripling. The specific number and the neocortex explanation are both contested.

In practice

• A department of 40 knows everyone; at 200 the same organisation invents a directory, an org chart and an all-hands, because nobody can hold it any more.
• A community group that ran on a WhatsApp thread for years needs a committee and minutes once it passes about 150 members.

Attributed to

Robin Dunbar

Also called

The rule of 150

Possible explanations

One explanation Dunbar offered is cognitive: tracking who stands in what relation to whom costs attention that grows with group size. Another is time, since relationships need maintenance and the hours available cap how many can be kept warm.

In its favour

The layered structure appears in several independent datasets, including personal networks, Christmas card lists and the sizes of military units.

Against it

A 2021 reanalysis of the primate data found the estimate so imprecise as to be consistent with anything from a few dozen to several hundred, and the neocortex argument it rests on is disputed.

Standing

Layer sizes vary by method and the neocortex argument is contested.

Further reading

Wikipedia

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A community's norms cannot survive a permanent influx of newcomers too large to acculturate.

Named for the annual September influx of students onto Usenet, which the community absorbed each year until AOL opened access in 1993 and the influx never stopped.

In practice

• A moderated forum with careful norms is linked from a large site and is unrecognisable within six weeks.
• A neighbourhood pub with a regular crowd is reviewed in a national paper and loses the crowd within a season.

Attributed to

Usenet

Further reading

Wikipedia

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In any shared system, some participants derive value from degrading others' experience rather than from the system's purpose.

The design consequence is that moderation is structural rather than remedial. Any system open enough to be worth joining is open enough to be degraded for sport, and it must be built expecting that.

In practice

• An online game must design for the player who wants to ruin the round, because that player exists in every population.
• A public consultation must be designed for the respondent submitting four hundred identical objections, not only the sincere ones.

Attributed to

Online gaming culture

Standing

A design constraint rather than an anomaly, and the reason moderation is structural.

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Ties form disproportionately between similar people, so networks segregate without anyone intending it.

McPherson's summary: birds of a feather flock together. Segregated networks require no prejudice at all, only mild preference, which is why integration does not follow automatically from contact opportunity.

In practice

• A hiring pipeline built on referrals reproduces the existing team's background without a single biased decision.
• A book club that grows by members inviting friends reads a narrower range each year and nobody chose the narrowing.

Attributed to

Lazarsfeld & Merton

Also called

Birds of a feather

Further reading

Wikipedia

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Scale-free networks tolerate random failures well but fragment under targeted removal of their hubs.

Albert, Jeong and Barabási's 2000 result, called robust yet fragile. The internet survives random router failures and would fragment under attack on the largest few, which is why hub protection is a distinct security problem.

In practice

• A payments network survives thousands of merchant outages and stops entirely when one clearing house fails.
• A supply chain absorbs a dozen small supplier failures and halts when the single certifying laboratory closes.

Attributed to

Albert, Jeong & Barabási

Also called

Robust yet fragile

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Most members of a large population are linked by short chains of acquaintance, popularly six steps.

Of 296 initiated chains in the full 1969 study, 64 reached the target, and among those completed chains the mean was 5.2 intermediaries, about six links. The high attrition means this is not a direct estimate that every arbitrary pair of people is six steps apart.

In practice

• Milgram's completed chains averaged about six steps, and only a quarter of the letters arrived.
• A supplier introduction sought through three intermediaries usually arrives, which is why professional networks function without anyone mapping them.

Attributed to

Milgram (1967); Travers & Milgram (1969)

Also called

Six degrees of separation

Possible explanations

The explanation is that a few long-range ties collapse the distance across an otherwise clustered network, so short chains exist even when almost all ties are local.

In its favour

The structural result is solid, has been reproduced in large digital networks where whole graphs can be measured, and the original experiment was an ingenious attempt at a hard measurement.

Against it

Only about a fifth of the 1969 chains completed, and completion was correlated with the target's accessibility, so the mean of the completed chains is not an estimate for arbitrary pairs and the famous six is not what the study showed.

Standing

About 22% of chains completed, so the mean of the completed chains is not an estimate for arbitrary pairs.

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Two people with a mutual acquaintance are unusually likely to connect, which closes networks into clusters.

Simmel's insight, and the reason social networks cluster rather than spreading evenly. It is also why introducing two friends changes your relationship with both.

In practice

• Two colleagues introduced at a leaving do are working together within the year, and the person who introduced them is in neither conversation.
• A newcomer to a village is invited to one supper and knows fourteen people by Christmas, because each introduction pulls in the rest of the table.

Attributed to

Georg Simmel

Further reading

Wikipedia

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A belief gains credence through repetition in public discourse rather than through evidence, and becomes self-reinforcing.

Kuran and Sunstein's cases include the 1989 Alar apple scare, which reduced apple sales sharply on evidence that did not support the alarm. Each repetition raises the cost of public scepticism.

In practice

• A neighbourhood becomes known as dangerous through repetition on a local group, and the repetition is the whole of the evidence.
• A management fad appears in three conference talks, then in a board paper as established practice, having acquired no new support in between.

Attributed to

Kuran & Sunstein

Further reading

Wikipedia

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Adoption is driven by innovators responding to outside influence plus imitators responding to prior adopters.

Bass published it in 1969, and it forecast colour television adoption well enough to become standard in market research. The two parameters separate advertising-driven from word-of-mouth-driven uptake.

In practice

• A new payroll system is adopted by two divisions on the finance director's insistence and by eleven more because those two adopted it.
• A neighbourhood app spreads to three streets through leaflets and to the rest of the town because three streets are on it.

Attributed to

Frank Bass

Further reading

Wikipedia

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Costly or contested behaviours spread only with reinforcement from several contacts, unlike simple information.

Centola's experiments found health behaviours needed several independent contacts to spread, unlike news, which needs one. It means the network structure that spreads information fails at spreading practice.

In practice

• A safety procedure spreads through a plant only when four separate colleagues are seen using it, not when the poster goes up.
• A payment app is downloaded because a friend mentions it; it is actually used because three friends already are.

Attributed to

Damon Centola

Further reading

Wikipedia

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Collective action takes off only once a small, highly motivated core has absorbed the initial cost.

Oliver and Marwell's finding: the core absorbs disproportionate cost, and only after they have does the majority find participation cheap. It is why movements look futile until abruptly they do not.

In practice

• Three people start a monthly reading group and carry it for a year at real cost before it becomes something people join casually.
• A neighbourhood recycling scheme is unusable until enough households join to justify the collection, and the first households get the worst service.

Attributed to

Oliver, Marwell & Teixeira

Further reading

Wikipedia

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The most moderate members leave a group first, so each departure radicalises the remainder and prompts the next.

Yudkowsky's 2007 term. The mechanism is selection: whoever is least committed finds each successive position hardest to accept, so departures are ordered by moderation.

In practice

• A campaign group's most pragmatic organiser resigns, which makes the next meeting less pragmatic, which prompts the next resignation.
• A book club that reads increasingly demanding texts loses its casual members, which frees it to choose harder texts.

Attributed to

Eliezer Yudkowsky

Standing

The belief-dynamics counterpart of the Dead Sea effect.

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Subcultures that define themselves by inclusion lose the ability to exclude anyone, including those who damage the group.

Suileabhain-Wilson's 2003 essay. The first fallacy — that ostracism is always wrong — leaves a group unable to remove anyone, so its tolerance is captured by whoever exploits it.

In practice

• A volunteer group that cannot expel a member who drives others away loses six members to keep one.
• A community forum where every ban is treated as a betrayal of openness ends up with only the people willing to tolerate the worst behaviour.

Attributed to

Michael Suileabhain-Wilson

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Once enough others have chosen, individuals rationally ignore private information and copy, so early accidents lock in.

Bikhchandani, Hirshleifer and Welch's 1992 model. Restaurant queues are the everyday case: after three people join, the fourth ignores their own information, and the queue no longer carries any.

In practice

• A hiring panel that hears the first two interviewers' scores before forming their own converges, and the interview order determined the outcome.
• A consultation where early responses are published shapes the later ones, and the total looks like consensus.

Attributed to

Bikhchandani, Hirshleifer & Welch

Also called

Herding

Further reading

Wikipedia

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Adoption of innovation follows a bell curve: innovators, early adopters, majority, laggards.

Rogers's 1962 curve, built from Ryan and Gross's study of hybrid seed corn adoption in Iowa. Tarde described the same S-curve in 1890, seventy years earlier.

In practice

• A tool spreads through two enthusiast teams, stalls, and then arrives everywhere at once when procurement standardises on it.
• A neighbourhood's solar panels appear on three roofs, then nothing for two years, then eleven in one summer.

Attributed to

Everett Rogers

Also called

Diffusion of innovations; adoption curve

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The value of a network is claimed to grow roughly with the square of the number of connected users.

Network value can grow faster than user count, but the specific n-squared valuation is a heuristic rather than an established law, and models such as n log n fit better in many settings. It nonetheless drove much of the valuation logic of the dot-com era.

In practice

• A messaging app is useless with three users and indispensable with three hundred, and no feature changed in between.
• A jobs board with fifty employers and no candidates has neither, and the first thousand of each are the whole difficulty.

Attributed to

Robert Metcalfe

Also called

Network value law

Possible explanations

The explanation is combinatorial: the number of possible pairs of users grows with the square of their number, and the law treats every pair as equally valuable.

In its favour

Network value does grow faster than user count, which is the durable point, and the law captured why early network businesses were worth building before they were profitable.

Against it

Users do not value all connections equally, so the square overstates it; models closer to n log n fit measured data better, and the law was used to justify valuations in the dot-com period that did not survive.

Standing

The n-squared form is a heuristic rather than an established law; alternatives such as n log n fit better in many settings. Compare Odlyzko's law.

Further reading

Wikipedia

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If errors are independent and unbiased, a largely uninformed electorate can still produce accurate collective judgements.

It fails exactly when errors are correlated, which is the usual case where media supply a common frame. The miracle requires independence, and shared information destroys it.

In practice

• A referendum on a technical question can still aggregate well if the errors are scattered.
• A poll taken the morning after every outlet ran the same headline reflects the headline, and the average of many wrong answers is still wrong.

Attributed to

Public opinion research

Standing

Fails when errors are correlated, which researchers of media environments find is common there.

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Dense networks in which one's contacts also know each other support trust, monitoring and norm enforcement, at the cost of access to new information.

Coleman argued in 1988 that a closed network can enforce obligations because everyone can observe everyone, so reputation is unavoidable and sanctions are cheap. Burt's structural holes argument runs the other way: the advantage lies in bridging the unconnected. The disagreement is real and largely resolved by asking what the network is for.

In practice

• A trade where every supplier knows every other needs no contracts and produces no new methods.
• A tightly knit team catches errors quickly and hears about a competing approach eighteen months late.

Attributed to

James Coleman

Also called

Closed networks; Coleman's social capital

Possible explanations

The explanation is observability: in a network where one's contacts know each other, behaviour is visible from several directions at once, so reputation is unavoidable and sanctions are cheap to apply.

In its favour

Closure is measurably associated with trust, norm enforcement and lower monitoring costs, which is what the theory predicts.

Against it

It stands in direct opposition to the structural holes account, which values exactly the gaps closure fills, and both have empirical support, so the useful question is which conditions favour which, not which is right.

Standing

Stands in direct opposition to the structural holes account, which values exactly the gaps closure fills. Both have empirical support, and which pays depends on whether the task needs trust or novelty.

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A product or service gains value as more people use it.

Vail's insight at AT&T, formalised by Rohlfs in 1974. The one-sided version is direct; the two-sided version — where buyers attract sellers and vice versa — is what platform economics is built on.

In practice

• A payment app is useless to the first user and indispensable to the millionth.
• A recruitment marketplace needs employers to attract candidates and candidates to attract employers, and the first year is spent solving that.

Attributed to

Theodore Vail; formalised by Jeffrey Rohlfs

Also called

Demand-side economies of scale

Further reading

Wikipedia

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Network value grows closer to n log n than n squared, because most users value only a few connections.

Odlyzko and Tilly's 2005 correction to Metcalfe. The n log n form is why a network of a billion is not a million times more valuable than one of a thousand, and why the dot-com valuations failed.

In practice

• A messaging app with ten thousand users in one city is worth more to each of them than one with ten million spread thinly across forty.
• A professional network's hundredth connection adds far less than its tenth, and the pricing that assumed otherwise did not survive.

Attributed to

Odlyzko & Tilly

Also called

Briscoe–Odlyzko–Tilly law; n log n law

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Connectivity across a network appears abruptly at a critical density of links rather than gradually.

Percolation explains why a rumour, a disease or a blackout spreads not at all below a density and everywhere above it. There is no gradual middle, which is why containment thresholds matter so much.

In practice

• A firm's internal referral scheme produces nothing at 200 staff and floods the pipeline at 400, and no incentive changed.
• A vaccination programme achieves nothing measurable at 55% coverage and eliminates transmission at 82%, with no gradual middle.

Attributed to

Broadbent & Hammersley

Further reading

Wikipedia

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People misstate private views under social pressure, so a regime that looks stable can collapse without warning.

Kuran's 1995 argument. It explains why the 1989 collapses surprised everyone including participants: private opposition was widespread and invisible, so nobody could estimate how many others would move.

In practice

• A ballot on an unpopular policy passes unanimously, and the anonymous survey a month later finds two-thirds against.
• A team where nobody will say the deadline is impossible produces a plan every member privately rejects, and the collapse looks sudden from outside.

Attributed to

Timur Kuran

Also called

The emperor's new clothes

Standing

The dictator's dilemma is the ruler's side of the same problem.

Further reading

Wikipedia

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New links attach disproportionately to already well-connected nodes, producing heavy-tailed degree distributions.

Barabási and Albert's 1999 model. The rich-get-richer mechanism produces the heavy tails seen in citations, web links, wealth and city sizes without anyone designing the outcome.

In practice

• A blog with 400 subscribers grows slowly; the same blog after one large share grows on the strength of having grown.
• A conference speaker with a reputation is invited because they are invited elsewhere, and the first invitation was closer to chance than anyone admits.

Attributed to

Barabási & Albert

Also called

Rich-get-richer; Barabási–Albert model

Further reading

Wikipedia

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The utility of large networks scales exponentially with size, especially for social networks.

Reed's 1999 claim of two-to-the-n growth from subgroup formation. It is the most optimistic of the network-value laws and the least defended — Odlyzko's n log n is the better-supported estimate.

In practice

• A platform argues that its value grows with the number of groups its users could form, and prices its funding round on that arithmetic.
• The groups people actually maintain number a dozen or so however large the platform becomes, and the valuation rested on the ones nobody formed.

Attributed to

David Reed

Further reading

Wikipedia

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Networks of trust and reciprocity function as a productive asset, and their decline degrades collective capacity.

Coleman and Putnam's concept. Putnam argued in Bowling Alone in 2000, using multiple indicators, that American civic participation and social connectedness had declined. The measurement of social capital, the aggregation of bonding and bridging ties, and the causal consequences all remain debated.

In practice

• The critique is that the measures conflate different things: bridging and bonding capital have opposite effects.
• A tightly bonded community with no bridging ties has high social capital by one measure and is closed to outsiders by any other.

Attributed to

Coleman; Putnam

Also called

Bowling alone

Possible explanations

One explanation is information: networks carry knowledge of who can be trusted, which lowers the cost of cooperating. Another is enforcement, since reputation within a dense network punishes defection without courts.

In its favour

Measured associations between civic participation and outcomes such as health, crime and government performance are consistent across many studies.

Against it

Measurement is disputed, bonding and bridging ties are often pooled when they behave differently, and the causal direction is hard to establish, since prosperous and stable places may produce civic life rather than the reverse.

Standing

The measurement of social capital, the pooling of bonding and bridging ties, and the causal consequences all remain debated.

Further reading

Wikipedia

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Novel information and job leads travel through weak acquaintances, because strong ties already share what you know.

Granovetter's 1973 paper, from a study of how people found jobs: most heard through acquaintances rather than close friends, because close friends already know what you know.

In practice

• A job that was never advertised is filled by someone the hiring manager met once at a conference.
• A researcher's most useful reference comes from someone in an adjacent field they meet twice a year.

Attributed to

Mark Granovetter

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Advantage accrues to whoever bridges otherwise disconnected clusters and brokers across the gap.

Burt's 1992 argument. The broker's advantage is informational and controlling at once: they see combinations nobody else sees and they choose what passes between the clusters.

In practice

• A project manager who is the only person attending both the clinical meeting and the procurement meeting becomes indispensable without acquiring a single new skill.
• Two suppliers who never meet are quoted against each other by the buyer who knows both, and the buyer's margin is the gap between them.

Attributed to

Ronald Burt

Further reading

Wikipedia

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A small, inflexible minority can impose its preferences on a flexible majority, because the majority can accommodate it cheaply and the minority will not accommodate the majority.

Taleb set it out in a 2016 essay and in Skin in the Game (2018). His example is food: if a small share of a population will eat only kosher or halal food and the rest do not mind, producers find it simpler to make everything compliant. The asymmetry of preferences, not the size of the group, decides the outcome.

In practice

• Ten friends choosing a restaurant end up, every time, where the one vegan can eat.
• A company makes its whole product line meet the strictest single market's rules rather than run two versions.

Attributed to

Nassim Nicholas Taleb

Also called

The most intolerant wins

Possible explanations

One explanation is cost: accommodating an inflexible minority costs the flexible little, while ignoring it loses the minority altogether. Another is tipping: a committed minority above a threshold can shift a convention.

In its favour

Consistent with experiments in which a committed minority of about a quarter changed a group's social convention (Centola and colleagues, 2018), and with the regulatory spread known as the Brussels effect.

Against it

Taleb's examples are mostly anecdotal, and many inflexible minorities impose nothing because accommodating them is costly. The threshold at which a minority tips a group varies widely.

Standing

Compare complex contagion and the tipping point.

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Small increments accumulate with little visible effect until the system flips rapidly to a new state.

Grodzins's tipping in neighbourhood racial composition, popularised by Gladwell in 2000. The mechanism is the threshold model, and the popularised version often skips the mechanism entirely.

In practice

• Small increments accumulate with little visible effect until the system flips.
• A neighbourhood's shops change one at a time for a decade and the character changes in a single year, which is when residents notice.

Attributed to

Grodzins; popularised by Gladwell

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Rewiring a few links in a regular lattice collapses path length while leaving clustering intact, which is why real networks are both clustered and short-pathed.

Watts and Strogatz's 1998 model, and the formal counterpart to Milgram's empirical finding. A few long-range links do almost all the work of shortening paths.

In practice

• A firm's departments each talk mostly among themselves, and the three people who sit on two committees are why a question can cross the building in a day.
• A conference that flies in six outsiders changes more connections than a year of internal away-days, because the internal links were already dense.

Attributed to

Watts & Strogatz

Standing

The formal model behind Milgram's empirical small-world finding.

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Adding capacity to a network can worsen overall performance when users independently optimise their own routes.

Braess's 1968 result, confirmed when Seoul demolished the Cheonggyecheon expressway in 2003 and traffic improved. New York closing 42nd Street on Earth Day 1990 produced the same effect.

In practice

• A city opens a new bypass and finds journey times unchanged, because drivers who had avoided the route return to it.
• A team adds a second checkout queue and the total wait rises, because the queue is now worth joining.

Attributed to

Dietrich Braess

Further reading

Wikipedia

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Most people's friends have more friends than they do, because popular people appear in more friend lists.

Feld's 1991 result, and it is a mathematical necessity rather than a psychological finding. Popular people appear in more friendship lists, so sampling by friendship oversamples them.

In practice

• A conference organiser concludes attendance is disappointing because everyone she asks knows people who went to a bigger one.
• A gym member feels unusually unfit because the people at the gym are the fit ones, and the unfit are at home.

Attributed to

Scott Feld

Further reading

Wikipedia

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A minority view can look like the majority when its holders are well connected, distorting perceived norms.

Lerman, Yan and Wu's 2016 result. If a well-connected minority holds a view, most people's local sample shows it as the majority — so perceived norms can invert actual ones without anyone lying.

In practice

• A team where three well-connected members hold a view finds every member believes it is the majority position, and it is not.
• A neighbourhood group where the loudest ten people oppose a development produces a consultation response that misrepresents the street.

Attributed to

Lerman, Yan & Wu

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An anonymous and endlessly revised list of numbered maxims about online behaviour, of which the best known say that there are no real rules, that nothing is to be taken seriously and that Anonymous never forgives.

The list began in discussion on Anonymous-related chat channels. An entry reached Encyclopedia Dramatica in late 2006, archived on 10 January 2007, and a version of 50 rules was posted to 4chan on 15 February 2007. No author is named, and asked about them at ROFLcon in 2007 the 4chan founder moot joked that they had been invented by Gaia and did not exist. There is no authoritative text. Counts have run from 18 in the first archived entry to 50 on 4chan, 100 on Urban Dictionary in 2008, 47 on Encyclopedia Dramatica by 2012 and over 900 on one wiki. In one widely circulated version the best known are Rule 5, Anonymous never forgives; Rule 8, there are no real rules about posting; Rule 9, there are no real rules about moderation either; Rule 12, anything you say can and will be used against you; Rule 14, do not argue with trolls, because it means they win; Rule 20, nothing is to be taken seriously; Rule 21, original content is original only for a few seconds before getting old; Rule 25, relation to the original topic decreases with every single post; Rule 32, you must have pictures to prove your statements; and Rule 33, lurk moar. Numbering and wording differ between editions, and the rules about sex and gender are left out here.

In practice

• A company wiki opened to everyone with no editorial rules and no moderator fills with stale and contradictory pages, and its careful contributors drift away.
• A veteran of a support forum tells a new member to read for a week before posting, and the member's first post is better for it.

Attributed to

Anonymous (disputed)

Also called

Anonymous's rules; the Rules

Possible explanations

Read as folk social science, the better-known rules restate patterns that research has studied, and each generalises beyond the Internet. Rule 5 says that where offenders are anonymous and no further dealings are expected, grievances are kept rather than settled. Its research counterparts are the Online Disinhibition Effect, the SIDE Model, the Discontinuity Effect and Generous Tit-for-Tat, which shows why forgiveness matters wherever mistakes are common. Rule 33 says newcomers should watch before they speak, which is Legitimate Peripheral Participation, while the 90-9-1 Rule describes how few go on to contribute. Rules 8 and 9 describe an unmanaged commons, treated by the Tragedy of the Commons and Ostrom's Design Principles, with the Law of Rule Proliferation as the opposite failure. Rule 12 is Context Collapse. Rule 14 rests on Brandolini's Law, with Sealioning and the Gish Gallop as its tactics. Rule 20 makes Poe's Law inevitable, since a statement that nothing is serious cannot be told from one that is. Rule 25 echoes Parkinson's Bicycle Shed, and Godwin's Law names a common end point. Rule 32 is the Burden of Proof, Hitchens's Razor and the Sagan Standard. In organisations the same patterns appear in anonymous feedback channels, open chat rooms and unmoderated wikis.

In its favour

Bernstein and colleagues' 2011 analysis of the 4chan board /b/ found that its content was overwhelmingly anonymous and extremely short-lived, which fits the spirit of Rules 21 and 25. Rule 33 matches later research on lurking, such as Preece, Nonnecke and Andrews's 2004 survey, which found that many lurkers read first to learn a group's ways.

Against it

The list is not a data set. It has no author, no fixed text and a self-undermining premise, since Rules 1 and 2 forbid talking about the board that produced it. Gabriella Coleman and other scholars of Anonymous describe it as a leaderless and shifting label, so no body existed that could hold or enforce rules. Whitney Phillips has argued that trolling mirrors mainstream culture rather than standing outside it, which cuts against reading the list as the private law of a separate tribe.

Standing

There is no canonical version. The generalisations are paraphrases of established research, not named laws. Compare Eternal September, Godwin's Law and Poe's Law.

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