Mathematical models: a state of exception

Prof. Andrea Saltelli presents his book “The Politics of Modelling” in Oxford 

“We do everything with mathematical models”, says UPF-BSM Professor and Academic Counsellor Andrea Saltelli, an expert on uncertainty and sensitivity analysis, amongst other fields. From economic forecasts, to prediction of Covid evolution, from business analytics to algorithms used by banks, platforms or social media, a huge number of elements that surround our daily life is based on numbers and mathematical models.  

In fact, the Covid pandemic, with all its statistics of infected people and curves flattened, increased dramatically the visibility of mathematical modelling. But this visibility was also accompanied by a great level of controversy, whether it was for possible deficiencies of the models, or just due to simple disagreements about the policies.  

The book “The Politics of Modelling: Numbers Between Science and Policy” is indeed a result of covid pandemic, says Saltelli, co-editor of the volume with Monica di Fiore, a Researcher from the Institute for Cognitive Sciences and Technologies in Rome. The book was recently launched at a crowded event that took place at Oxford Martin School with the participation of some of its contributors, that came from different schools and universities: Wendy Espeland, Professor of Sociology at Northwestern University; Jerome Ravetz, Professor of Philosophy in Oxford; Marta Kuc-Czarnecka, Professor in Gdańsk University of Technology; Andrew Stirling, Professor at the University of Sussex; Arnald Puy, Associate Professor at the University of Birmingham; and of course, Professor Saltelli representing UPF-BSM.   

Five rules to ensure models serve society 

“In June 2020, a group of 22 scholars led by myself wrote a manifesto on the journal Nature about the use of mathematical models during covid. The title was ‘Five ways to ensure that models serve society’, because we felt models weren’t always well-used during covid pandemic, and our aim was to try to reverse that”, explains Professor Saltelli. Some of the scholars decided to continue the research, and after a long process of reviewing, the book, which is the tangible consequence of the manifesto, was finally published by Oxford in August 2023.  

“The Politics of Modelling” follows the structure of the manifesto and expands its 5 main rules, which are: 

1. Mind the framing: match purpose and context 

2. Mind the hubris: complexity can be the enemy of relevance 

3. Mind the assumptions: quantify uncertainty and assess sensitivity 

4. Mind the consequences: quantification in economic and public policy 

5. Mind the unknowns: exploring the politics of ignorance in mathematical models 

Mathematical models will only work if these previous five conditions work, warns Andrea Saltelli. Indeed, the leitmotiv of the book, he adds, is “the concept of reciprocal domestication between models and society, which in simple words means that, although we have powerful models that can do many things, maybe society doesn’t understand them completely. In fact, general audiences probably don’t know the conditionalities that make mathematical models work”.  

Professor Saltelli also believes mathematical models live in what he calls a state of exception: in general, people tend to consider mathematics an exact science, but this is not always true, because in some specific cases, they are not as exact and precise as they are supposed to be. “They are fragile in some ways. This is one of the things we try to explain in the book”. 

Therefore, to combat this state of exception, one should start discussing the reproducibility of models, foster complexity of interpretation rather than complexity of construction, and encourage forms of activism following the French statactivists, who foster with their work the reciprocal domestication between statistics and society – something similar should be possible for mathematical models. 

Finally, another interesting concept contained in the book is the one of visible and invisible numbers: visible numbers are the ones everyone can see, like public statistics or economic forecasts that appear on the news; invisible numbers, on the other side, are the ones that we cannot see but are contained in the mathematical models we all use every day, for instance a social media algorithm. Sometimes these algorithms take important decisions, like establishing what news to show us first, or even, if it’s a bank algorithm, conceding a credit or not, in what some people call the algorithm governance. 

All in all, the goal of the book is to help unravel the meanings and implications of models in the real world, for readers that may include decision makers, policy analysts, journalists, scholars or even modelers, and of course to improve the use of models and to enrich them with perspectives from many disciplines. “Because the richer the model is, the more reliable for policy-making it will be”, concludes Andrea Saltelli.