Monday 7 August 2017

Antifragility and justice

Towards the end of last week I noticed a flotsam on my Twitter feed coming from a storm involving NN Taleb and the prominent British classisist Prof Beard. The origins were in a BBC schools animation that depicted a Roman soldier as dark skinned. This elicited a response on Infowars that the BBC was re-writing history. I was interested in this because that week my family had driven down to the Vindolanda and Roman Army Museums on Hadrian’s Wall and I had been struck that a significant portion of the garrison at Vindolanda came from Hama in Syria, a region familiar today as being a source of refugees into Europe. Taleb was attacking Beard for being part of the conspiracy. Since the evidence for Syrians at Vindolanda comes from written records discovered in the 1970s, I cannot believe the ‘left’ are that competent at formulating such a clever consipiracy.

[PS there are links between Financial Mathematics and the mathematics of population genetics: Alison Etheridge is prominent in both fields.   My gut instinct was the apparent lack of non-Caucasian genes in the current British population was not evidence of their having been non-Caucasian Romans in Britain.  @mpigliucci explains this and highlights how Taleb is a victim of his own biases.]

I was also interested because Taleb was involved. Along with many academic mathematicians working on finance I do not have a strong affinity with Black Swan or Fooled by Randomness. The reason why is as follows. Taleb, along with other ‘public’ financial mathematicians like Elie Ayache and Doyne Farmer, were part of a cohort of applied mathematicians, engineers and physicists who entered finance in the 1970s and 1980s, were successful, became rich and have used that wealth to direct public perceptions of financial mathematics. At the time, option pricing was accomplished by solving partial differential equations and these ‘quants’ had expertise rooted in dynamical – deterministic – systems (note that Taleb’s mathematical PhD in Management Science was awarded in 1998, not before he went into Finance with an MBA). There is a sense amongst most actuaries and financial mathematicians, trained in probability theory, that Taleb’s books resonate with this audience because the books highlight the significance of randomness, something these people were not really educated in. As one senior British actuary said to me: “What does Taleb think actuarial science has been concerned with for 300 years if not Black Swans and not being Fooled by Randomness”. This frustration reflects decades of ‘quants’ in banks regarding actuaries as being ponderous dinosaurs.
A profile of Taleb by Malcolm Gladwell (who shares Taleb’s skill for simplification) suggested that Taleb’s ideas are founded on his experiences of the Lebanese civil war and surviving cancer. While Taleb dismisses this I wonder if there is some truth in the theory. Taleb is concerned with how people face up to uncertainty and how they respond, discussed most recently in Antifragile. I share this concern but have been dissatisfied with Taleb's arguments, in particular I feel that Taleb believes, like many of his colleagues, that there are individuals peculiarly able to make judgements under uncertainty. This was part of the motivation for writing Ethics in Quantitative Finance.
My reasoning is based in mathematics, which is subtly different to Taleb's which just uses mathematical symbolism. Consider a closed system of 100 agents, each initially endowed with $45. Now, at each time step each agent randomly gives another agent $1. What do you think the distribution of money should be? The immediate thought might be the distribution would remain uniform, with a little noise. However, this not the case, as presented in a nice simulation. Some people will end up with lots of money, others will be bankrupted. The rich can become rich simply through luck, not skill. This should not perturb the likes of NN Taleb or Robert Mercer, since the model does not consider how genius might skew the distribution, extending the right tail at the expense of the middle. It is more challenging to the 'left' who might seek to implement policies that make the wealth distribution more uniform, since such policies might be considered to be equivalent to pushing water up hill.
Moving on, there are some points that were made with respect to my last post about maths in economics that are important in understanding my approach. One comment was that
The more fatal weakness of this line of argument seems to me the starting assumptions: mathematics involves "identifying how we see relations between objects." That seems right, but left undefined here is the term "objects." What exactly is an object?

In mathematics, an object is something we can quantify. Now comes the problem: in economics, what we need to identify is the relation between emotions (greed, fear of loss, investor euphoria, etc.) and behavior (buying, selling, tolerance for risk, and so forth).

Alas, this requires that we mathematize emotions. To my knowledge, no one has succeeded in doing this in some 8,000 years of recorded history.
I take a less pessimistic view. Plato split the soul into three parts. The epithymetikon (‘from the heart’) was the part of the soul concerned with carnal desires, sometimes represented as a black horse. Alongside this was the thymoeides (‘spirit’) and represented energy and the motivation to act, this was sometimes represented as a white horse. The third component was the logistikon (‘reason’, from logos the Greek for ‘what is said’) or nous (‘mind’) that distinguishes right from wrong, which Plato associated with the Athenian temperament. The logistikon was sometimes represented as a charioteer controlling the other parts of the soul, making sure that the spirit would not become dominated by carnal desires, which would be wrong. Through the medieval period these ideas became refined into one of balancing passions and interests. This did not involve quantification, which is only a small part of mathematics, but by identifying a balance point, which involves measurement. Adam Smith's great contribution, according to Albert Hirschman, was in enabling the quantification of passions and interests through money, precipitating capitalism tied up with utility maximisation. My argument in EQF is that part of the long story of financial mathematics is concerned with this balancing of passions and interests and this was considered to be a question of Justice. This predates Smith's quantification of passions and interests,. When mathematics was dominated by geometry, this was considered in terms of proportions, but with monetisation came arithmetic.
Justice, according to Socrates and taken up by Plato and Aristotle and their heirs, is the quality that a complex, functionally differentiated system (a society) needs to enable it to work well. On this basis a society is Just when it enables individuals, who all have different capacities and capabilities, in the society to do their best by allowing them to do what they are best at. This relates to comments relating to the use of mathematics in economics raises, that people are different and so cannot be reduced to a mathematical representation (e.g. "The rigidity of mathematics makes it difficult to fully capture the richness and complexity of human behaviour "). This is true, however I highlight how financial mathematics is founded on reciprocity which is a component of Justice, and this is the fundamental invariant not just in finance, social systems in general but across any functionally differentiated system. The mathematics of the Fundamental Theorem of Asset Pricing is not involved in quantification but is concerned with ensuring Justice.
On the basis of this definition of Justice the universe is Just, since it works well as a complex, functionally differentiated system. It is concerned with different things being in the correct balance and is different from the idea that justice is based on everything being the same, which might be characterised as a 'left-wing' approach.
Now we can return to Taleb's account of "Antifragility" that starts with
Antifragility is ... behind everything that has changed with time: evolution, culture, ideas, revolutions, political systems, technological innovation, cultural and economic success, corporate survival, good recipes (say, chicken soup or steak tartare with a drop of cognac), the rise of cities, cultures, legal systems, equatorial forests, bacterial resistance … even our own existence as a species on this planet. And antifragility determines the boundary between what is living and organic (or complex), say, the human body, and what is inert, say, a physical object like the stapler on your desk.
This excerpt immediately raises the question: what is the difference between antifragility and Socrates' conception of Justice. Critically I have removed part of the text, which actually begins
Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.
Suggesting the antifragile is about improvement, but I don't think this establishes any clear water with the ancient philosophers. Furthermore the argument that the best antidote to fragility is "skin in the game" is not so different from the Enlightenment attitude, espoused from Locke to Kant, that only property owners could participate in democratic politics. The issue here, and dominated British politics for much of the nineteenth century, was that this excluded the majority from participating in democracy. Taleb's conclusion refers to the Golden Rule "Do to others what you want them to do to you".
These observations suggest that Taleb's argument in Antifragile is close to mine in EQF. The difference is I focus on how the idea of Justice is embedded in financial mathematics, why this is so and what it implies. My conclusion is that in oredr to be able to manage radically (Knightian/non-ergodic, etc.) uncertainty a broad range of opinions need to be solicited and considered and so markets are discursive arenas and must address truth, truthfulness and rightness. Taleb suggests the essence of his book is "Everything gains or loses from volatility. Fragility is what loses from volatility and uncertainty." This seems a little trite to me, echoing the actuary: "What has civilisation been worried about for 4,000 years?" The problem, as I see it , in Taleb's book is that he leaves himself open criticisms captured in a paper by Andrea Terzi (in what I would class as a 'left-wing' journal). The point Terzi makes is
Taleb admits that the system cannot be made foolproof to BSE [Black Swan events] but believes it can be made more resistant through some form of economic and social Darwinism. His prescriptions include consenting that what is fragile breaks early and never gets too big to endanger the system should a BSE appear; letting economic players who make errors be punished for their failures; not precluding recessions from mopping up the system from the unfit to survival; and not indulging in debt.
Taleb seems to have slipped into pseudo-Nietzschean philosophy that distinguishes man and superman. He seems to identify with the supermen and denigrates most scholars as 'imbeciles'. This view has been supported in the evidence of responses supporting Taleb's attack on Beard from, what look to me like, neo-Nazis. My concern is that I feel the problems of finance, that Taleb purports to solve, are about an obsession with identifying 'geniuses' at the expense of deliberation and doubt. 
 I am not allowing comments on this article as I anticipate they will be dominated alt-right abuse.