[Authors and titles are listed at the end of the review.]
This well-edited volume by Lavan, Jew, and Danon invites ancient economic and social historians to add another tool to their armoury: probabilistic modelling, a tool and wider approach that allows us to deal with uncertainty in our sources mathematically, helping us to resolve (or at least better define) knotty problems of quantification. The contributions in the volume are all individually solid and arrive at interesting conclusions by their application of similar probabilistic methods, but the real value of this book is its subtly pedagogic element, which is done both directly and by demonstration. In fact, the editors should be particularly commended for the coherence of this volume in that respect, amply illustrating the value of probabilistic modelling to writing economic and social history, and making such an approach reasonably accessible to any who wish to follow in their wake, whether they work in Classics or elsewhere.
Myles Lavan & Daniel Jew’s perfectly paced opening chapter clearly and accessibly explains how probabilistic methods work, using a case study from Jew’s own research as the first demonstration of their application: estimating the productive capacity of ancient Attica for the alimentary support of Athens 600-300 BCE. They show for this (already much discussed) case study how key variables such as total land under cultivation, the proportion of that land under cultivation of particular crops, and the average yield of each crop can each be defined as probability distributions rather than single values in order to incorporate our own uncertainty in estimating those values based on our limited sources. Combining these individual probability distributions then brings Lavan & Jew to a ‘final’ probabilistic model which illustrates the full range of final values for the population that Athens’ hinterland could possibly support, with each possible value having an attached probability estimate. Instead of concluding that the land around Athens could support a single given number of people, they have instead shown exactly how certain we can be about any point estimate given our sources, and what range—given that uncertainty—should be given for such figures instead.
They make the compelling argument—one that is echoed by the rest of the volume—that our limited and unreliable sources do not, therefore, have to present a barrier to quantification if instead of attempting to estimate the single ‘right’ answer, we use probabilistic modelling to define the basic problem and find the range of estimates that are ‘most likely’ given our uncertain and unclear sources. The probabilistic approach—a more general approach, rather than just a mathematical tool—becomes a device that allows us to provide a full accounting of historiography on a given topic, and an identification, through sensitivity analyses and computer simulations, of the most significant areas of debate that affect our statistical estimates of key values.
After the opening chapter sets up the volume well with explanations of the key methods and terms, the book then splits off into two sections, with the first (Chapters 2-4) focusing on using probabilistic models to estimate particular values in much the same way that Lavan & Jew do in their Chapter 1 case study.
Emily Mackil (Chapter 2) uses fragmentary historical evidence to show that there was a non-negligible risk of property confiscation in the ancient polis; Bart Danon (Chapter 3) extrapolates from the size of excavated houses in Pompeii to demonstrate that there were almost certainly families who met senatorial wealth requirements there (although he acknowledges there may have been no actual senators given the non-economic elements of such status); and Gilles Bransbourg (Chapter 4) re-evaluates the evidence of coin-hoards to argue that the value of coins in circulation was indeed vast, but was more dominated by silver than previously thought. Each chapter is well-argued, and as a collective clearly demonstrate how the probabilistic methods set out in the opening chapter can be deployed to help us work up from fragmentary evidence towards defining a model that can help us to get a better picture of a wider problem. The models also allow them to begin offering some solutions. While one may disagree with minor elements of their respective methods, all are worth reading not just for their intriguing conclusions, but also for how they use the probabilistic approach as a device to reframe and re-mould historiographical debates on topics as varied as property security, coin circulation, and household wealth. This is best demonstrated by Mackil, whose chapter is focused on tackling these historiographical problems first and foremost, and only comes to the mathematical modelling at the very end. Danon and Bransbourg relegate much of such discussions to (perhaps over-long) appendices, which is a shame.
The second section (Chapter 5-7) focuses on a somewhat different use of the probabilistic method: the definition of an entire population distribution affected by random (‘stochastic’) variations, rather than estimating a single given value. To start, Paul Kelly (Chapter 5) estimates wealth levels among ordinary Egyptian households, who are all subject to random variations in both harvest yields and human fertility and are therefore able to accumulate different amounts of ‘savings’ each year. This affects how well they respond to years of poor harvest, with households who had experienced numerous ‘good’ years having the savings to survive it, but poorer ones possibly having to give up children in order to reduce costs and so escape distress. I found Kelly’s contribution especially compelling, especially given its relevance to the Late Antique context: the Jeme child donations from 7th/8th century Egypt could be seen as a continuation (or re-emergence) of much the same trend he identifies and explains of families giving up children in times of economic hardship. Nicolas Solonakis, Anicet Touré and Mohamed Elhouderi (Chapter 6) use a similar method to examine the survival of urban grain funds, finding that, while some were indeed only viable in the short-term, others could persist for decades if random variation worked in their favour to give them a series of good years (particularly early on) in which surplus could be accumulated.
Both Chapters 5 and 6 show that looking at an ‘average’ example is not as helpful as understanding the full variation within a population, which these probabilistic or ‘stochastic’ models—while simplistic in some of their assumptions—help to show the key features of, and in ways that deterministic estimates of individual households do not. These models can therefore answer problems about financial distress not just by examining whether it existed, but also how it manifested itself and how many were affected at various points.
J. W. Hanson (Chapter 7) then works from the little excavated material we have for the number and size of cities to construct a more general distribution for the size of cities in the 1st and 2nd century CE Roman Empire. In many ways the method is similar to that of Danon’s in Chapter 3, fitting existing data to a given statistical distribution, but the attempt to show how that distribution changes over time appears to me much more speculative given the very limited source-base deployed.
Chapter 8 (Danon, Jew & Lavan), which closes the volume, powerfully restates much of the argumentative thrust of Chapter 1: that these probabilistic methods are helpful tools for the ancient historian, allowing us to find better answers, even if not final ones.
Lavan, Jew, and Danon have not assembled a haphazard collection of loosely linked articles here, but have instead edited a compelling volume of contributions that amply illustrate the value of probabilistic models to writing pre-modern economic and social history. These tools can open up exciting new research horizons for ancient economic and social historians plagued by uncertainty and scarce evidence, but only if they are used properly. Indeed, each contribution demonstrates that the skills of the historian remain key, as various contradictory and fragmentary sources have to be read and interpreted in context to understand how much weight to give their evidence in the final calculations. While some may wince at the subjectivity that this brings to quantification, a supposedly objective field, the editors readily acknowledge this in the opening and closing chapters, and I commend them for so forcefully making the point that these models are not themselves evidence of the truth. Instead, they are merely tools that are themselves dependent upon individual historians’ base assumptions and interpretations concerning the body of evidence. This is a point that is not made as often as it should be about quantitative methods more generally, but is good to see highlighted here.
The volume is fairly accessible to the academic audience—particularly after reading the first chapter—and the appendix to Chapter 1 is especially helpful in demonstrating how these methods can be put into practice by providing indicative code that demonstrates how easy it is to run simulations of such probabilistic models in the relatively simple R software package. However, I do believe that the editors could still have done more to make probabilistic modelling even more accessible through this volume, especially to the more philologically-minded historian. Perhaps this could have been done with a few more pages detailing in more basic terms exactly how to put these methods into operation—including sending the reader to an elementary introduction to R so that they might better understand the code provided—in an educational appendix to the volume as a whole. This could also have been the place to make the key further reading (currently hiding in the footnotes to Chapter 1) clearer than it currently is, which would have helped to better handhold historians without much mathematical or technical training on how to apply these methods going forward. This volume makes a clarion call for others to follow in its wake, but doesn’t quite lower the drawbridge enough to let everyone in.
A point of caution regards one particular element of the mathematical models in the volume: there is both an overuse and an abuse of the triangle probability distribution in a number of chapters, with the ‘maximum’ value often being set at the highest level estimated for a variable in the scholarship, without acknowledgement of the fact that this effectively (and sometimes incorrectly) sets the likelihood of that value being taken to zero. I appreciate that this is done to reduce the assumptions and simplify calculation, but a beta, alpha, or skewed normal distribution would usually provide a much more accurate presentation of the possible range of values, setting this ‘maximum’ as the 95th or 99th percentile, and the usual ‘minimum’ as the 5th or 1st percentile.
Despite these minor issues, the volume as a whole is to be commended, and I recommend it both to historians of the ancient Mediterranean—for whom the conclusions of each chapter hold salience, even without engaging closely with the methods applied—as well as to economic and social historians from other areas, for whom the tools and approaches will certainly have potential applications in their own research. I found myself scoping out which questions concerning Late Antique and Early Islamic Egypt could benefit from an application of such approaches, and discovered numerous research horizons opening up.
The editors make a compelling and clear argument (directly and through their contributors) that probabilistic methods deserve further use, and are more accessible than one may initially think: I can’t help but find myself agreeing.
Authors and Titles
- “Probabilistic Modelling in Ancient History”, Daniel Jew and Myles Lavan
Part I: Uncertainty
- “Assessing the Scale of Property Confiscation in the Ancient Greek World”, Emily Mackil
- “Senators and Senatorial Wealth at Pompeii: Reconstructing the Local Wealth Distribution”, Bart Danon
- “The Roman Coinage under the Antonines Revisited: An Economy of Silver, Not Gold”, Gilles Bransbourg
Part II: Variability and Missing Data
- “Children and Their Impact on Family Finances in Roman Egypt”, Paul V. Kelly
- “The Financial Sustainability of Grain Funds: A Model-Based Approach Using Monte Carlo Simulation”, Nicolas Solonakis, Anicet Touré and Mohamed Elhouderi
- “New Approaches to the Urban Population and Urbanization Rate of the Roman Empire, AD 1 to 200”, J. W. Hanson
“Afterword”, Bart Danon, Daniel Jew and Myles Lavan