Reaching beyond Dunbar's Number

When the participants in encounters reach beyond Dunbar's number, a human being can no longer have knowledge of the personal identities and motivations of all the others, nor what happens to them. The participants in encounters with more members than Dunbar's number are not only self-interested in varying degrees but have private information and private ambitions unknown to some of the others. The knowledge required for arranging, scheduling, and forecasting is not known.

"The economic problem of society is not merely a problem of how to allocate 'given' resources...It is rather a problem of how to secure the best use of resources known to any of the members of society, for ends whose relative importance only these individuals know. ...it is a problem of the utilization of knowledge not given to anyone in its totality."

So wrote Friedrich Hayek, a Nobel laureate in economy, in 1945 in an important paper entitled "The Use of Knowledge in Society." The only additions we need to make to the core of this paper is that its theses begin to apply when Dunbar's number is reached:

A low degree of familiarity is typical among people working in a bureaucracy, or by people who participate in a market. It is an attribute of a Gesellschaft, not a Gemeinschaft.

The Hayek thesis is clause (a) of the proposition of The Limit of Knowledge about Others. More concretely, it holds that the price system in a market can aggregate vast amounts of information much more efficiently than a centralized bureaucracy can do.

It is often said with reference to Hayek's work that unplanned consequences of large-scale planned actions are a predictable curse of all social engineering of large systems. This unpredictability is enhanced by clause (b) in our proposition.

Oskar Lange, a socialist economist, had argued that there were no reasons to believe that anonymous market forces would make better allocations of investment capital than would trained central planners (Lange 1938). He became one of Hayek's adversaries. Lange discovered, however, when he was a chief economic planner in Communist Poland, that he regularly received beautified and doctored reports from the field that reported more production and fewer problems with disturbances and inequalities than there were in reality. He started a vain search for mechanisms that could overcome dishonest reporting in national planning.

Clause (b) of the proposition of The Limit of Knowledge says in effect that deceits are endemic in large organizations and networks. This can be read between the lines in some of Hayek's writings, but became more explicit in the work of Leonid Hurwicz, also a Nobel laureate, when he studied design mechanisms to make the economy more efficient. He had escaped from Hitler by moving from Poland to the United States. Here Lange's problem was also familiar, but as a reporting problem in capitalist corporations with many subsidiaries and in public administrations such as the FBI with many local branches. Local units of a central organization may not be in the habit of outright lying in their reporting to the top, but they may withhold relevant information and overly emphasize information favorable to their budgets, promotions, and remunerations. 

Hurwicz' first postulate is that participants have direct information only about themselves, not about other persons. It is worth noting that he studied designs for decentralization and honesty prior to the discovery of Dunbar's number. Several of his cases rest on an analysis of transactions between only two parties. Designs that overcome unpredictability and dishonesty might work well in small durable settings with few participants, what we called the small social worlds (N<≈15). Parents know that when two children are bickering over how to divide a cake you should rule that one child cuts and the second child chooses. Only if the first child cut as evenly as possible will he get a maximum share. The rule works among siblings who are very familiar with one another, and also with two children who are strangers to one another. This is a setting in a small social world, and the critical point is that both children have full information.

Problems of Lange's sort need something that would work in larger networks and groups (15<≈N>≈150), and also in the great populations beyond Dunbar's number (N>≈150). These three group sizes behave somewhat differently.

To be able to achieve designs for efficiency in complex and decentralized cases, Hurwicz must introduce restrictions on the number of messages to be exchanged, on the degree of diversity of the environment of the participants, and on the compatibility of the incentives of the participants. The construction of designs to improve the efficiency of imperfect markets can then be systematic and scientific. As these restrictions are applied, however, the success of the designs in terms of human honesty remains questionable. The shortcut conclusion is pessimistic: in large decentralized organizations and networks, no incentive scheme, no matter how intelligent, can assure that people always tell the truth, the whole truth, and nothing but the truth.

There is much evidence supporting this pessimism outside the equations of the economists as well.

An American, who will never cheat at cards played in the socially small world, will without much ado accept unearned money to which he is not entitled from a public crib known as the "Gover'ment" and located in the big world. A giant case of abuse in the United States affected the pension system introduced after the Civil War. It was originally designed for crippled soldier and for orphaned children. In 1890 a revision in the Federal pension law removed the link between pensions and service-related injuries, allowing any veteran who had served honorably to qualify for a pension, if at some time he had became too disabled to perform manual labor. By 1906 old age alone became sufficient justification to receive a pension. Shrewd work by pension lawyers could make virtually any male citizen eligible who had been a teenager or older during the war. And numerous still younger persons were found to have fathers who had fought in the Civil War.

Fortunately, the abuse had a natural end in that the abusing generations died out. The United States, in the meantime, had received a long-lasting vaccination against copying the big European government-run welfare systems (Skocpol 1992). The United States got very little of what Bismarck started in Germany in the 1890s and Lord Beaverbrook designed for Britain, which was enacted after World War II. Not to speak of the openings in Scandinavia toward governmental payments for non-work, which are beyond the horizon of American imagination; I call them “the gestation of a citizen's wage." They became common around the millennium in Scandinavia, providing work-free income to a large proportion of the population of working age.

Gunnar Myrdal (1978), another Nobel laureate, observed the dishonesty phenomenon in the tax system. The large-scale Swedish welfare systems were paid for by exceptionally high taxes, and he concluded that this system had created “a nation of small crooks” who cheated on taxes. Later we have learned that the Swedes also cheat a great deal to get welfare benefits.

At best, we can follow Hurwicz and find or create situations in which everyone has a main strategy to tell the truth. For example, in the lifearea of science, truth will emerge if research is conducted according to the scientific method in a field where all findings are checked and confirmed by other researchers. Truth telling in science is also supported by the knowledge that cheating in research is a sure way to end a career. Prior to the advent of science as a full-fledged lifearea of society, the beliefs within some religions in an almighty God who sees and knows everything and keeps track of it, could also promote strategies of truth-telling — but one could never be quite sure that some people were not seduced by the devil to lie.

Honest Knowledge about Large Populations

You know that your neighbor soon will buy a new car. In the cold mornings you hear that his old car takes a long time to start. You know from talking to him that he is fond of a car of this make, and he usually keeps his models as long as he can. So you assume that his new car will be of the same make. This you know, but how many people in the country are like your neighbor? You have no idea of how many will become repeat buyers of this make during the coming year. But the car manufacturer has a marketing department that has a good estimate of how many new cars will be sold and how many of them will be sold to repeat customers. They have market surveys and calculations that forecast the future annual sale. They have overcome Dunbar's limit and Hayek's restricted knowledge, but not necessarily the problem of dishonesty.

Social scientists have long looked at the large numbers. The father of quantitative social science and the standard setter for census bureaus, the Belgian statistician Adolphe Quetelet (1796-1874), found his safety in large numbers. Among 100,000 young Frenchmen appearing in front of draft boards, the individual measurements of their length grouped themselves in a bell-shaped curve, symmetrically around a stable mean. Armed with this mathematical curve Quetelet could conclude that about 2,000 men had escaped service by somehow shortening themselves just below the minimum length required for a soldier.

In this instance, large numbers were needed to reach a reliable conclusion about the dishonesty in the presentations by recruits of themselves. But in other contexts, such as in the number of interviews in a public opinion poll, there is no self-evident safety in large numbers.

Sample Surveys

The sample survey is a modern method to cope with the limit of knowledge a decision-maker has of people beyond Dunbar's number. It is used in a variety of fields, production controls in engineering, symptom diversion in medicine, satisfaction with government services, images of corporation, et cetera.

In the 1930s a well-established magazine Literary Digest in the United States used to tell its readers how elections were going by mailing millions of questionnaires to subscribers and people in the phone book and automobile registry. (United States has never had a total population registry and its civil servants and researchers depend on other registers.) In the 1936 election the Digest had reported that Roosevelt would lose, 56 percent to 44 percent. Many pundits agreed: Roosevelt seemed helpless to stop the Great Depression, too free-spending, too controversial not only in the business community, but in the broad middle classes.

George Gallup’s data in 1936 included questionnaires from three thousand people. Gallup's sample was not statistically ideal; he did not start using probability sampling until after the failure to forecast the 1948 election when Truman unexpectedly beat Dewey. But his 1934 sample was more representative of the electorate as a whole than the one used by the Literally Digest. He had selected a small number of voting areas with names and addresses of voters drawn from election rolls when available, and otherwise from telephone directories. Like the Digest he mailed them questionnaires. More important, he asked the sample how they had voted in the election 1932 as well as how they would vote in the election 1936. His sample was hand-counted in his small Princeton office of six employees; the first IBM card sorter did not arrive in the office until the following year. The questionnaires were sorted into piles to reflect the 1932 election outcome. The procedure was called “adjustment of the sample,” and it eventually became subsumed under the heading “post-stratification” in the vocabulary of statisticians, a procedure that under some assumptions can improve results from samples.

The Digest did not reach all the eligible voters, or a good sample of them. However, the gap between the presidential candidates was considerable, and it is possible that the Literary Digest might also have been able to call the right winner in the 1936 election, if they had made a similar adjustment as Gallup used of their sample. On Election Day, Roosevelt's Republican opponent, Al Landon, won a total of two states. Roosevelt swept the rest of the nation, the greatest landslide to that date in presidential history. Literary Digest stopped publishing election forecasts; eventually it stopped publishing altogether.

A branch of mathematics, the theory of sampling, has become an intellectual basis to overcome the limitation set by Dunbar's number and Hayek's theorem. The general tenet of statistical sampling is simple: by studying the response in a randomly selected sample of the population we can, with known probability, estimate the response of the entire population. We often use a similar approach in daily life. A cook need not consume a whole pot of sauce in order to know how it tastes. He need only stir the sauce (randomize) and taste a spoonful (sample) of it. If the sample has too little spice, the whole sauce has too little spice. This can be concluded with a known degree of conviction expressed as statistical confidence limits.

The statistical "margins of error" do not mean that that researchers have done something in error, but rather that the readers or users of the findings would be wrong in assuming that the reported numbers are exact representations of reality rather than indications of likely intervals. The measures obtained from correctly constructed samples apply to the entire population, with the allowance of the "margin of error." The deviations from the true value form the same kind of bell-shaped distribution that Quetelet had worked with. The correct answer most probably lies within calculable margins. This margin is chosen somewhat differently, depending on the topic at hand and on the use to be made of the research. An advertising agency testing the recall of copy about a brand may be satisfied with a lower margin of error than a court of law that shall rule on an alleged infringement of someone's established brand name. In much medical and social research a tolerable minimum to call a finding "statistically significant" is a probability of 95 percent. In other words, if the survey samples were to be repeated over and over again until the entire population had been measured, 95 out of 100 results would lie within these margins. In the language of the experts you then have a "statistical significance" at the 5 percent level. At the level of 1 percent they may say "high statistical significance." 

One must never forget that the figures in sample surveys represent approximate values, not exact numbers, but the beauty of correct sampling is that we can calculate the likely limits of the deviation. The proper use of these calculations is restricted to samples that do not deviate from the sampling plan of random or known selection in every step. If this deviation is large, the statistics no longer represent the population to be measured. The discrepancy between the planned sample and the achieved sample is therefore necessary information. It is usually called "completion rate" (or “response rate” in interview surveys) and can be expressed as a percentage.

The widespread use of the sample survey instrument in market research has led to an increasing reluctance to respond to questionnaires by the general public. In the second half of the twentieth century the response rate for opinion surveys in the advanced countries declined from 80-90 percent to 50-60 percent. In this way surveys become ineffective as a provider of reliable statistics about the entire population. This means that public opinion polling cannot count on support from mathematical statistics. Unless the relation between non-responses and the topic studied is known in advance, which is rare, the present models for calculating confidence intervals require high response rates.

The calculations of margins of error in samples with poor response rates do not reveal the range in which the true value is found with 95 percent probability, as is often claimed in press releases of opinion polls. It does tell us that repeats of the samples with the same inadequate response rate in 95 cases of 100 would render results within this range. In this way we may understand why different polls differ slightly from one another in their results, but not how they differ from the true value in the entire population studied.

Public Opinion Polls as a Social Innovation

A critical task in all public opinion polling on issues is the choice of topics for the questionnaire. It is important to ask questions revealing the public’s concerns, and not only questions that interest the pollsters or their editors or sponsors. Gallup solved this problem in the late 1930s by regularly asking: “What is the most important problem facing the country today?” He did not want to define all issues by himself, or to have his editors take all the initiatives. In the ideal issue poll, his respondents, the general public, should have the main say in defining the issues! Their views on the issues should be known to the public and to the leaders of the public through the media without any filters or restrictions. The full measure of Gallup’s contribution is not only a scientific application of sampling, interviewing, and calculation of percentages of responses into majorities and minorities. He also made a social innovation, that is, polling of the public, on the issues defined by the public, for the benefit of the public (Gallup & Ray, 1940).

Gallup himself and other serious pollsters discovered the hard way the power of Hurwicz's thesis that people's accounts of themselves may be dishonest. This applies also to nationwide interviewing. No scheme can induce respondents in a short encounter with an interviewer to tell the truth at all times. Poststratification based on party choice in a previous election is a tricky procedure that easily can result in wrong pre-election polls (Busch & Zetterberg 1976). There are times when people are not motivated to truthfully disclose how they voted in an election some years ago. Political trends, events, and scandals may make them embarrassed to tell how they voted. Or, if they recently have converted to a another party, they may on the day the pollster calls be tempted to present themselves as smart in the past as today, and say that voted for their new party in the previous election as well.