Human judgment and mathematical models
The question: «What is the right balance between using human judgment and relying on mathematical models in regulating finance and the economy?» is not correct, and shows a deep misunderstanding of not only the essence of the mathematical model, but the essence of a scientific theory at all, its connection with reality and in particular the limits of applicability of the theory or model. Between the mathematical model and human judgment is no fundamental difference. Mathematical model is nothing but a generalized and formalized human judgment. "Generalized" means that it refers not to a particular case, but to a certain type or class of cases. Using mathematical models can lead to errors such as those, that were the cause of the 2008 financial crisis, not because the mathematical models is worse than the human judgment, but because in this case, these models are applied outside of their applicability field, i.e., for cases in which circumstances do not conform, do not coincide with the type of cases for which these models were created.
Why Watson IBM computer won the champions? Because the rules of the game Jeopardy (like chess) and other circumstances of these games are unchanged and, consequently, the algorithm by which works Watson, composed especially for these rules and circumstances, there will always be applied correctly and give the correct result. But the rules of the economic game and its circumstances (as well as in the case of other problems of real life) are continuously changing. Therefore, the using of mathematical models in non trivial cases really can lead to errors.
But can we conclude from this that we should abandon the mathematical models and rely only on human judgment? After all, human judgment can also lead to errors and in any case, relating not to an individual, but many, we always have a lot of different and even opposing each other human judgments. How do we know on which of them to rely? This is especially important when it comes to macroeconomics rather than on private investment.
The solution to this problem can be only one thing: to learn to determine the limits of applicability of scientific theory, mathematical model or algorithm. This solution provides a unified method justification of scientific theories, developed by me, whose application in the economy has been the subject of my application for a grant of INET. Paradoxically, the proposal to answer the question: «What is the right balance between using human judgment and relying on mathematical models in regulating finance and the economy?», I got together with the refusal to me in getting the grant.
Modeling is a result of judgements
I would contend the issue is not of math versus judgement as it is a matter of judgement as to which observables are to be measured, the units of their measure and the scope of the model in terms of what are the boundaries. We get the answers we get by asking the questions we ask. As the old saw puts it 'to a person with a hammer, everything looks like a nail'. So to in economics, the reductionism of value to 'price' or monetary equivalent by definition focuses the actions of the players on optimizing monetary valuations of assets/income, etc. Yes, economics being a human social system to meet the needs of survival of its members, providing food, shelter, good health, etc., must ultimately conform to basic biological/ecological constraints as well as the physics of 'work' (also known as Thermodynamics). Few economists and finance people are well trained in all the relevant areas to so tend to espouse a narrow view. To the extent population grows, an economy must grow to meet increased needs. That we have added 'needs' that perhaps are less than optimal (tobacco smoking, etc.) we have perhaps some 'waste' built in. Policy makers tend to focus on a few key variables, inflation rates, monetary aggregates (including credit), production levels, employment levels, etc. some of which like Poisson bracket pairs in quantum mechanics are such that movement in one variable can cause disruption in the values of another (credit vs employment/inflation). We have been so 'growth' oriented, with most financial models discounting the future past 5-10 years no wonder we get so short sighted. The human species needs to think on a planetary scale and in terms of centuries and millenia, not just the next quarter or next election. It is the 'vision thing', we need models that reflect the long term evolution of the human directed biosphere in terms of how we provision our society/ies throughout their member's lives (working and non-working portions) with regard to universal values of dignity, want avoidance and sustainability. Let's start asking the right questions and we'll find that have the tools in our scientific/mathematical kits or can extend them as needed. Our computational tools are now sufficient to model the complexity or long-term simulations and include climatalogical and ecological impacts. One non-financial 'value' to consider as the optimized parameter is to minimize the 'footprint' of the human species on the global system. This would be the analogue of the most powerful principle of physics called the 'Principle of Least Action'. Some aboriginal societies have maintained themselves for centuries and millenia following that principle. Our 'civilized' and 'advanced' societies on the other hand seem to fall apart much more quickly and are perhaps more like algal blooms rather than long-term solutions.
