Sornette’s Quantum Decision Theory

Mathematics

Yukalo, VI & Sornette, D Mathematical Structure of Quantum Decision Theory 2010

Sornette claims that:

… the axioms of QDT correctly embody at a coarse-grained level the effective thought processes underlying decision making of real humans.

He displays a model in which:

… the probability of prospects with larger uncertainty and/or perceived potential harm will be suppressed, while that of less uncertain and/or harmful prospects will be enhanced.

He notes that

…the thought processes, involved in the definition and analysis of alternative prospects and scenarios, do not necessarily separate them according to the recipes of standard probability theory.

The standard theory considers atomic decisions where the consequences are considered in terms of a utility function. No examples are provided, but the theory would seem to fit computer chess, where it is often infeasible to consider the utility of a single move. Instead, one tries to look far enough ahead until any uncertainty is ‘resolved’, i.e. until one can see how to apply one’s (partial) utility function. If one has two pieces can be move to create a challenge it is often the case that moving them in either order will give you the same position, but an opponent will react differently, and so – as in quantum mechanics – order matters: moves do not commute. But – in a certain sense – ‘sequencing distributes over choice’. QDT concerns such decision considerations.

In QDT the ‘objective’ probability is adjusted according to the relative attractiveness of the actions, the “uncertainty about mode of action”. Actions are more attractive when they are assessed as:
(a) leading to more certain gain,
(b) leading to more uncertain loss,
(c) being active under certainty,
(d) being passive under uncertainty.

Together they relate to the ‘attitude to risk’. For example, investors may shift from equities to gilts when the equity yields are more uncertain, and may avoid ‘locking in’ investments when they are uncertain about their needs. It is shown how this adjustment for differences in attractiveness explains many conventional ‘paradoxes’. Sornette adds a specific, quantum, formulation.

Informatics

Processing Information in Quantum Decision Theory (2010) has much of the same material as above, but also proposes that QDT might be used in a quantum computer. It explicitly describes uncertainty as an emotional reaction, and notes that:

It has been reported [by psychologists] that, if people, when confronting uncertainty paralyzing them against acting, are presented with a detailed explanation of the possible outcomes, they then may change their mind and decide to act, thus reducing the disjunction effect. … This line of reasoning suggests that it should be possible to decrease the aversion to uncertainty by other means … .

This seems to paint uncertainty aversion as a ‘bad thing’, so that QDT is a model of bad decision-making, to be improved by masking the uncertainty.

Comments

The standard (rational) approach assumes that one’s utility function somehow encodes all of the available information, so that it is not worth looking ahead at the impact of one’s actions, beyond valuing the immediate outcomes. Sornette can be interpreted as showing that humans act as if it were beneficial to look ahead, but he does not challenge the view that this is pointless, at best. But chess players who look ahead tend to do better. Is this because of the limited rationality of the human brain? Or because there is often an actual benefit in looking ahead?

Laplace noted that the standard probability theory only applies to ‘the current situation’. Thus, for example, in 2005-8 an investment strategy based on statistics was only valid for as long as the boom lasted. Such an investor would be ‘driving while looking in the rear-view mirror’, not a good idea. Keynes suggests some alternative ways of considering uncertainty, which lead to different, perhaps better, approaches. Perhaps we should deduce from Sornette that humans act as if they are unsure about the stability of the current situation?

An alternative interpretation of the above reports by psychologists is that instead of trying to ‘help’ people to overcome their uncertainty aversion, we should try to help people to look ahead: we should try to remove the cause of uncertainty rather than try to mask it.

I also have some quibbles with QDT as a practical predictive model. The ‘prospects’ and ‘scenarios’ are considered to be independent of, and non-responsive to, the acts of the decision-maker. There is no sense of innovation and counter-innovation or of co-evolution. And I could hardly think of a real decision situation in which actions are distributive. For example, it seems to me that when humans play chess their ‘total’ observable moves (e.g., including where they look) are rarely distributive. Similarly, the actions of a large investor can affect markets, so QDT would seem confined to the activity of small investors, in which case one would still wish to model Keynes’ ‘animal spirits’, affecting the perceived attractiveness. But QDT is nonetheless informative, at least for medium-term decision-making.

QDT rightly emphasizes non-commutativity of actions but hardly seems realistic and gives a psychological rather than an effectiveness explanation for the impact of uncertainty. It may be that we need to distinguish between two types of activity: those that have an enduring significance, and those that don’t, as in anticipating crises. Human-decision-making may have been shaped by the need to make decisions that matter, whereas Sornette’s model seems to me to be of decisions that don’t very much.

Dave Marsay

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