Section: Overall Objectives

Overall Objectives

Applications of mathematics in social sciences (economy, sociology, law,...) are increasing at a fast pace. In a growing number of areas, decisions are being made in an actuarial way rather than in a clinical one, as has been the norm for decades or even centuries. This means that actions are based on the outputs of (mathematical) models instead on the informed judgement of experts. This occurs daily in financial economics (for instance for option pricing, portfolio management and risk assessment), and is also on the verge of becoming routine in certain domains of law and certain countries (most notably the USA, where examples include evidence-based sentencing and the setting of certain fines).

Such a paradigm shift certainly has several benefits, but it may also be harmful at least because it rigidifies the system. What we mean by this is that, when most actors in a given field use the same model, with possibly minor variants, massive unanticipated effects will occur:

1. if the model is either wrong, or wrongly specified or used beyond its nominal conditions, the fact that everyone makes the same erroneous decisions may lead either to system-wide crises (this has happened several times in finance in recent years) or to profound uncontrolled modifications of reality (this has also occurred in finance but also in law). This second case, leading to “silent revolutions”, is maybe more problematic;

2. even when the model is approximately correct or used in normal conditions, hard and fast, uniform answers will reduce diversity in an often damaging way.

Both situations above are related to the concept of performativity introduced by social scientists. More precisely, item 1 leads to what we call convergent or divergent performativity, while item 2 leads systematically to convergent performativity.

How can one eliminate or at least reduce the negative impacts of the generalizing use of actuarial approaches in social sciences ? Clearly, the trend seems unstoppable and even if it were, this would probably not be desirable: quantitative, mathematically well-founded methods are likely to permit great progress in many domains. There is for instance a strong need for good models that would help judges fix financial amounts in various areas including spousal support and fines in cases of violation of intellectual property. The aim of Anja is to propose ways to minimize the drawbacks of model-based approaches using essentially the following devices:

1. be aware of the performative effect of models: by taking into account the impact of actuarially-based actions on reality when setting-up a model, this impact will be endogenised and, thus, to some extent, controlled. In other words, whenever possible, we study the feedback between reality and the proposed model.

2. insist that the output of models be systematically probabilistic: instead of a hard answer, always propose a range of answers with associated probability distribution. This should greatly reduce the rigidification of the system by allowing to re-introduce a part of expertise, thus preserving some diversity, and in turn minimise the occurrence of crises or unwanted modifications of reality. From a theoretical point of view, this amounts to using tools introduced in the now well-developed area of uncertainty propagation. The basic idea is that uncertainties on the various parameters are propagated at all stages of the modelling process, so that, at each step, computations are made on probability densities rather than numbers. This approach raises various difficulties when the models are non-linear, as will typically be the case in our applications.

Although our long term aim is to provide a general frame enabling to fulfil the above objectives, our first studies will focus on a limited number of well identified situations in economy and law described in Sections 4.1 and 4.2.

Our program clearly requires strong interdisciplinary collaborations. Anja is actively involved in on-going work with financial economists and lawyers.