The many and the few

The many and the few

An idea is only as successful as the number of people who know about it, says Sanjeev Goyal – so what should firms and governments be doing to enlarge their spheres of influence?

We often have to make a choice between alternatives without full knowledge of their consequences – whether it is which stocks to invest in (Google or Unilever), which career to pursue (investment banking or engineering), which party to vote for (Labour or Conservative), which crop to plant (cassava or pineapple) or which medicine to prescribe for the treatment of an ailment such as Parkinson’s disease (pramipexole or levodopa). In arriving at a decision, we make use of our own experience, talk to experts, read reports and use the experience of others, especially those who are close to us.

In a series of pioneering studies in the 1950s, Elihu Katz and Paul Lazersfeld identified a key feature of social communication: the fact that a very small fraction – about 20% – of the population, which consisted of so-called ‘opinion leaders’, served as the primary source of information for the rest. In the intervening decades, a number of studies on information and communication have confirmed that this is a robust feature of our social networks; we rely on a relatively small subset of our social group for information. Malcolm Gladwell calls this the ‘law of the few’.

What are the implications of the law of the few for attitudes and behaviour? Does it facilitate an open, resilient and dynamic society? How can firms and governments make use of these opinion leaders? What can they do to shape networks so that they may better serve private and social objectives? 

The law of the few has far-reaching consequences for a number of social and economic phenomena. Let us consider a simple example to illustrate its implications for the choice between two technologies: one well understood, old technology and one poorly understood, new technology. The new technology may be better or worse than the old technology.

Suppose that the new technology is, in fact, better and that everyone in this community is optimistic enough to start using it. In the long term, people are more likely to be better off with it than with the old technology. As with most new technologies, however, there is a small chance that something will not work right away and the outcome will be poor. So repeated trials of the new technology may be needed to ascertain its true quality – but trials are costly, so people must remain optimistic and be willing to try it out. Their beliefs about the new technology will depend not only on personal experience but also on what they see and hear about it. In other words, their beliefs – and the fate of the new technology – will depend on their network of social communication.

Consider a society in which the law of the few holds, where everyone talks to two friends and, in addition, observes a group of five opinion leaders. It is possible that, due to chance, all the opinion leaders will be unlucky when they try the new technology. Each person can observe a maximum of three good outcomes with the new technology (their own experience and the experience of their two immediate neighbours), while they all observe the poor experience of five opinion leaders. Thus, in net terms, everyone observes at least two negative outcomes with the new technology. This could well push them below their belief threshold and lead them to switch to the old technology. Once everyone switches to the old technology, no further information about the new technology can be generated. The social group is locked into using an inferior technology.

Now consider a society in which everyone relies only on local information and there are no opinion leaders. Since the new technology is superior, on average it will outperform the old technology. In particular, there are strings of people who will each have a good experience with the new technology. In this case, the person in the middle of the string is insulated from the negative experiences of others. By the time negative information from outside the string reaches this person, he/she will have had some time to accumulate knowledge about the new technology and convince himself/herself that it is in fact a better option. In other words, the middle person is insulated from premature exposure to negative information. Indeed, research shows that the successful adoption of new technology in large groups – sometimes referred to as the ‘wisdom of crowds’ – is predicated on the absence of opinion leaders.

What is it about the opinion leaders that leads to the failure of the new technology? The key reason is an asymmetry in observation: opinion leaders observe only a few others, while almost everyone observes them. This leads to the mass adoption of ideas and technologies whose desirability is contradicted by large amounts of locally collected information. Moreover, due to the broad adoption of such actions, the generation of information about alternatives is seriously inhibited, so the lack of experimentation can persist for a long time.

These findings may be interpreted in the light of Mark Granovetter’s celebrated ‘strength of weak ties’ hypothesis. Granovetter visualises society as comprising groups of individuals who have many internal links but only a few cross-group links. Our research suggests that strong ties within groups sustain experimentation, while weak, cross-group ties carry valuable information across a broader network, thereby sustaining technological dynamism in a society.

Influencing the influencers

The availability of online networking data and other recent advances in information technology now make it possible for us to collect and process detailed data on large and evolving social networks. Practical interest has centred on a number of questions, such as which product categories and behaviour are susceptible to network effects, which people to target for maximal reach and influence in a social network, and how much we should be willing to pay to acquire information about social networks.

As advertising budgets have grown, so has concern about the effectiveness of traditional marketing methods. Can the use of social networking lead to smaller budgets and more effective advertising? Perhaps the best known example of the power of ‘social networks’ marketing is Hotmail. Individuals who received an email message from someone with a Hotmail account could themselves sign up for Hotmail by simply clicking on the link at the bottom of the message. Almost 12 million people signed up for Hotmail within 18 months of its launch. The advertising budget was a mere $500,000 (£330,000).

The spread of information through word of mouth in social networks makes advertising more attractive to firms, as any information they send to one person becomes available to more people. But by making it possible for consumers to be indirectly informed, social networks also render direct advertising by firms less necessary. Thus the effects of social networks on advertising budgets are unclear.

Recent research demonstrates that the answer depends on the current level of advertising: if it is already extensive, many people are being informed directly. More active use of social networks will lead to more people getting information from their informed friends. So an increase in network connectivity reduces the need for direct advertising. The converse is true if a firm initially undertakes little or no advertising. Since the network multiplier makes advertising more profitable, a greater reliance on networks could encourage greater spending.

Targeted spending

A simple way to make advertising and social information campaigns more effective is to target people more accurately. Highly connected nodes in a social network are a natural target for firms and governments, as they offer quick, indirect access to a large number of people. This raises the question: how can a firm or a government locate highly connected nodes in a large social network? Recent research suggests a simple method for locating such ‘hubs’: pick a random sample of people and ask them to enumerate their friends. Now make these friends the target of the information campaign. It is logical to target these friends because a more popular person is more likely to be a friend of a randomly picked individual than a person with only an average number of connections.

Finally, how much should someone be willing to pay to learn about a network? If a firm or a government expects the network to be homogenous, then there is little to be gained from learning its details. However, if the network is very unequal – with a few highly connected nodes – then knowing about its structure can greatly enhance the effectiveness of advertising and social information campaigns. The law of the few thus provides us with good reasons for investing in network data collection.

Given the significant effects that networks can have on attitudes and behaviour, it is natural to wonder what steps governments can take to shape networks in ways that promote social and economic objectives. The economic theory of network formation highlights the role of costs and benefits in the formation of links and networks. Government interventions can alter these costs and benefits and thereby shape networks.

Collaborative benefits

Consider government subsidies for inter-firm collaboration. When two firms form a research alliance, they compare their own costs and benefits. But such a link may also alter their market position vis-à-vis competitor firms. Thus, linking activity is purposeful and a tie between two entities has indirect effects on third parties. Leading firms in many industries increasingly rely on a combination of in-house and collaborative research to remain competitive. For instance, Daimler-Chrysler has independently obtained a series of patents in the area of gear-change transmissions for motor vehicles. At the same time, it has engaged in collaborative research with BMW and Volkswagen on processes and systems that aim to reduce the emissions of internal combustion engines. Such alliances lower the cost of production and so improve the company’s competitive position in the market.

The incentives to create an additional link are greater for highly linked firms than for those that are poorly linked. For a highly linked firm, the next link will lead to lower costs for a larger total production and hence raise profits more than for a firm with fewer links. Moreover, as a firm forms additional links with new partners, the non-partner firms lose market share and sell less in the market. This will lower their return from the creation of another link. Individual firms do not usually take this negative effect on other firms into account. Thus, firms will create more links among themselves than is in their collective interest – something that governments should always keep in mind when weighing up the economic grounds for subsidising research collaborations among firms. 

What about government funding for interdisciplinary research? Consider a community of researchers from different disciplines, all studying social networks. They have their own local subject links with students and collaborators. When an economist goes to an interdisciplinary conference on networks, he/she may run into a computer scientist. This contact gives him/her access to valuable new ideas and research in computer science, as well as creating an indirect link between the communities of economists and computer scientists. When the economist compares the costs and benefits of going to the interdisciplinary meeting, he/she may not assign sufficient weight to these indirect benefits. He/she may then choose not to take part in meetings, even though the social value of doing so may be considerably greater than the private cost. To the extent that the economist cannot fully appropriate the gains that flow to the two communities, he/she is likely to under-provide links relative to what is socially desirable. This may provide a justification for publicly subsidising interdisciplinary academic meetings. 

Finally, consider the creation of local social networks. The internet is a network in which the law of the few holds sway. The vast majority of web pages receive a few incoming links, but some receive hundreds of thousands. The preceding discussion shows how the diffusion of information and new technology may be inefficient in such networks and highlights the need for greater reliance on local communication. Recently, a number of governments, international development agencies and charitable organisations have launched programmes to activate local social networks. Community empowerment and greater involvement in local public affairs is often cited as the argument behind such initiatives; our research shows that active local social networks may facilitate greater experimentation and thereby sustain more dynamic societies.



Sanjeev Goyal is professor of economics at the University of Cambridge and a Fellow of Christ’s College, Cambridge. His book, Connections: an introduction to the economics of networks, is published by Princeton University Press