Peter Killworth

Introduction

Peter D. Killworth (27 March 1946 – 28 January 2008) was a British scientist who maintained two largely separate research careers, and was distinguished in both. As a physical oceanographer he published more than a hundred and sixty papers, founded the journal Ocean Modelling, and received the Stommel Research Medal from the American Meteorological Society. As a social network analyst he collaborated for over thirty years with the anthropologist H. Russell Bernard, and co-developed the network scale-up method, a way of estimating the size of populations that cannot be counted directly.

The unusual feature of his career is that the second line of work was done, in effect, part-time. Killworth was never an anthropologist or a psychologist; he was an applied mathematician who kept getting asked to solve problems about people, and who kept solving them.

Early Life and Education

Killworth was born in Birmingham in 1946. He read for his doctorate at Trinity College, Cambridge, completing it in 1972 with a thesis on analytical and numerical models of ocean circulation, supervised by Adrian Gill.

He then spent a year at the Scripps Institution of Oceanography in California, which turned out to be the decisive year of his second career. There, in 1972, he met H. Russell Bernard, an American anthropologist who was studying how the people aboard an oceanographic research vessel knew one another. Killworth suggested applying an algorithm from the "Baltimore traffic problem" to the structure of that network, and the collaboration that followed lasted the rest of his life.

Academic and Professional Career

After Scripps, Killworth returned to Cambridge and spent twelve years in the Department of Applied Mathematics and Theoretical Physics, the latter part as a Research Fellow of Clare Hall, maintaining close ties to the United States and teaching at the Woods Hole Oceanographic Institution.

In 1985 he moved to Oxford to join the Robert Hooke Institute, later the NERC Oceanography Unit, where he was a Research Fellow of Wolfson College and then a Fellow of St Cross College, and built a research group at the forefront of numerical ocean modelling. When the unit closed he moved to Southampton in 1995 and built a second group at the Southampton Oceanography Centre, now the National Oceanography Centre, focused on ocean process modelling. During this period he founded Ocean Modelling and served as its editor-in-chief; by 2005 it had the highest impact factor of any physical oceanography journal.

His honours included election as a Fellow of the American Geophysical Union in 2000, the Fridtjof Nansen Medal of the European Geophysical Society in 2002 (EGU awards record), and the Henry Stommel Research Medal of the American Meteorological Society in 2008, announced shortly before his death (University of Southampton, 2008). He co-chaired the Scientific Steering Group of the World Ocean Circulation Experiment from 1999 to 2002.

Killworth died in Southampton on 28 January 2008 after a long illness with motor neurone disease. The National Oceanography Centre established the Peter Killworth Memorial Fund to support students, in recognition of his commitment to fostering early-career scientists.

Major Contributions to Psychology

The network scale-up method

Killworth's best-known contribution to the social sciences is the scale-up method, developed with Christopher McCarty, H. Russell Bernard, Gene Ann Shelley, and Eugene Johnsen. The idea is simple and clever. Ask a representative sample of respondents how many people they know in each of a list of subpopulations, most of known size and a few of unknown size. Because the known sizes act as a calibration, the responses yield a maximum-likelihood estimate of the total number of people each respondent knows. That estimate can then be used in reverse to back-estimate the size of the populations you cannot count.

The 1998 paper in Evaluation Review applied the method to three such "apparently uncountable populations" in the United States. It estimated 800,000 people living with HIV, 526,000 homeless people, and 194,000 women raped in the previous twelve months. The HIV figure agreed strikingly with independent medical estimates, and the other two fell within the published ranges.

Killworth was insistent about why this mattered. Before deciding how much to spend on a social problem, he argued, you need to know how big the problem is: it may not matter much whether the average American knows 290 people or 2,900, but it matters enormously whether the homeless population is growing or shrinking.

Estimating personal network size

A companion line of work, with Bernard, Eugene Johnsen, and Stephen Robinson, addressed how large an average personal network actually is, and how people's estimates of their own network size diverge from what can be inferred. This work, published in 1989 and 1991, underpinned the scale-up method and also produced estimates of the size of "event subpopulations," people connected by a shared experience rather than by acquaintance.

The small world problem and informant accuracy

Killworth worked with Bernard on the structure of the small world, examining the gap between how many people individuals believe they know and how many they can be shown to know, and on the reliability of informants' reports about who interacts with whom. This strand, beginning in the mid-1970s, established that survey reports of social ties are systematically imperfect, a finding with consequences well beyond anthropology.

Major Publications

Killworth's oceanographic output exceeds a hundred and sixty papers and is not listed here. His principal contributions to social network research include:

Killworth, P. D., McCarty, C., Bernard, H. R., Shelley, G. A., and Johnsen, E. C. (1998), "Estimation of seroprevalence, rape, and homelessness in the United States using a social network approach," Evaluation Review 22(2): 289–308 — the canonical statement of the network scale-up method.
Bernard, H. R., Johnsen, E. C., Killworth, P. D., and Robinson, S. (1991), "Estimating the size of an average personal network and of an event subpopulation: Some empirical results," Social Science Research 20: 109–121 — the network-size estimation work on which the scale-up method depends.
Bernard, H. R., Johnsen, E. C., Killworth, P. D., and Robinson, S. (1989), "Estimating the size of an average personal network and of an event subpopulation," in M. Kochen (ed.), The Small World.
Killworth, P. D. and Bernard, H. R. (1976–1978), the "informant accuracy" series and the reverse small-world experiment — establishing the limits of survey-based network data.
Killworth, P. D. et al. (2006), "Investigating the variation of personal network size under unknown error conditions" — later work on the robustness of these estimates to reporting error.
Ocean Modelling (founded 1999), as founding editor-in-chief.

Impact and Legacy

The network scale-up method is now a standard tool in demography, epidemiology, and official statistics. It has been used by national statistical offices and international agencies to estimate the size of populations, including men who have sex with men, people who inject drugs, and, more recently, casualties in conflicts and emergencies, in settings where no register exists. Killworth's argument that you must size a problem before you can fund a response to it has become routine in that literature.

The method's known weaknesses, however, are substantial and have driven a generation of methodological work intended to fix them. The original estimator assumes that respondents know everything relevant about their contacts, that members of a hidden population are as visible to those who know them as anyone else, and that respondents can accurately count large categories of acquaintance. In practice all three fail to some degree. Transmission error means a respondent may not know that an acquaintance is HIV-positive or homeless. Barrier effects mean some groups are systematically less likely to be talked about, and therefore under-reported. Recall error means large categories are badly under-counted, a problem for which later researchers proposed remedies such as the "known population" corrections and alternative elicitation formats.

The consequence is that the 1998 confidence intervals are widely regarded as too narrow, since they reflect sampling variability but not these structural biases. Where the method has been validated against known populations, it has sometimes performed well and sometimes badly, generally in ways that track whether its assumptions hold. Subsequent methodological work, including the network reporting method and the generalised scale-up estimator, was developed precisely to relax the assumptions the original design required.

His work on informant accuracy has had a similarly double-edged reception. The finding that people's reports of their own social ties correspond poorly to observed behaviour was important, but it is sometimes read as a sweeping scepticism about survey-based network data, a conclusion more radical than Killworth himself drew.

Finally, his influence in the social sciences is limited by the fact that this was his second career. He had no doctoral students in anthropology and no departmental base in the social sciences, and his network work is most often cited as a set of methods rather than as a body of theory.

Learn More

Russell Bernard — his principal collaborator over three decades, and co-author on the network scale-up method.
Stanley Milgram — whose small-world experiments set the problem Killworth and Bernard worked to quantify.