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Quantum-like Modelling and Complex Adaptive Systems: Policy Implications

By Prof Dr. Sudip Patra

Over the last decade, there has been a steep rise of interest in the so-called quantum-like paradigm in decision science, with applications in social science, for example in economics, finance, and political science. Quantum-like modelling is based on mathematical and conceptual features which are also prevalent in quantum science (quantum mechanics and quantum field theory). However, this similarity is not suggestive of it being a genuine quantum physics based analysis of human behaviour, let alone social systems. Mainly cognitive scientists (9781107012820_frontmatter.pdf (cambridge.org)) have performed voluminous data analysis based on such quantum-like models, to suggest that human cognition or choice-making in particular contexts, such as uncertainty, actually can be better described by such models as compared to extant or still used neoclassical decision models. 

For example, we may take the example of two different random walk models: Markov random walk model, and quantum-like random walk model. While both these models are used for predicting choice making by decision makers under different interesting contexts —sequential choice-making, or joint choice making for instance— the underlying assumptions and mathematical frameworks are very different.

Markov models are based on the assumption that decision-makers themselves always have full knowledge about their preference states, it is the modeller who doesn’t have full knowledge of such preferences and thus must work with ‘subjective’ probability distributions over such preferences. Such models are based on so-called axioms of classical probability theory (Kolmogorov axioms).

Quantum random walks are also stochastic(which would mean truly random), but hold that decision makers themselves have inherent uncertainties about some preference states. For example, if the decisions are about feelings or are made under an uncertain information atmosphere. Such inherent uncertainties are not well described in the Markovian framework, hence a quantum-like framework is warranted. Here preference states are represented as ‘super-positions’ of preferences or beliefs, with a different kind of mathematical modelling than the ‘set’ theory used in the last kind of models. Often such mathematics is termed Hilbert space modelling.

Now, recently, cognitive scientists (https://psyarxiv.com/frq96/) have found that it might be more productive to have a hybrid of Markov and quantum-like modelling, where both epistemic / ignorance probabilities as well as inherent or objective uncertainties can be accommodated. 

Complex adaptive systems could possibly  be suitable platforms for such hybrid decision models. This is because  complex adaptive systems by definition refer to interaction between a myriad of agents, who have completely different types of knowledge. For example, consider an economy where we have millions of real-time decision-makers, as well as regulators and policymakers who would influence such decision making. Now for regulators, it is vital to have inputs from agents about their preferences, where there obviously would be ‘ignorance’ about full information regarding such preferences. Hence, epistemic uncertainty. Again in many contexts, decision makers themselves would be uncertain about their own preference states: deeper/ ontic uncertainty(which means uncertainty is an objective property of this physical universe). Hence, when such actors interact with each other there would be a need to develop a framework comprising both such uncertainties. Hybrid models suggested might be a better framework, as they could inform policymakers better compared to stand-alone Markov or quantum-like models.

Further discussion: what is uncertainty?

There is very dense literature on what uncertainty is, or at a more basic level, what probability is. Generally, we may divide the various subtle debates under two broad headings: subjectivists and objectivists. It is well known that Lord Keynes and Cambridge University Prodigy, F Ramsey debated the very issue with its applications in economics or social science in general. While the former was advocating probabilities as the subjective degree of beliefs or credence about future possible events, the latter was leaning towards accepting probabilities as features of the physical universe itself. There is no doubt that subjectivist schools, later hugely successful Bayesians, dominated social science and certainly policy research. Some commentators would hold that expectations based on subjective probabilities are the crux of the economy, which further motivates any policy design.

Currently, we have a new ‘behavioural science’ domain of policymaking which derives a lot of design ideas from behavioural economics where Bayesian thinking on probabilistic models is  commonplace.

However, since the last decade or so(Quantum cognition: a new theoretical approach to psychology – PubMed (nih.gov)) it has been demonstrated through the use of a huge amount of choice data that there are contexts in which decision makers themselves are uncertain about their preference states. This can’t be fully aligned with the subjective probability framework. The former framework is about an ignorant observer of a coin toss, hence for maximum ignorance, they would assign 0.5 probability to both head and tail. However a fully knowledgeable agent (such as  a powerful computer: quantum computer?) might be able to track the coin all through and knows all through what is the state, and hence does not need such a subjective assignment. But inherent uncertainty would mean that whatever may be the degree of information about an event, the event itself is truly stochastic until a final measurement is made and one of the potential values obtained. 

Quantum Physics is riddled with the interpretation of probability, for example, the standard orthodox framework holds that objective probability is true, or nature herself is probabilistic. However, there are other interpretations: QBism (Quantum Bayesianism, which treats probabilities as subjective beliefs rather than objective property of the world)or multiple worlds where subjective probabilities can be fundamental.From a social science and complex adaptive systems perspective, we may note that both ideas/frameworks are needed for a comprehensive theory. Hybrid models are effective from such a perspective. It is also the case that subjective and objective views may be reconciled, as philosophers have proposed (David Lewis (Stanford Encyclopaedia of Philosophy)) A principal principle view is that if one rational agent knows about the objective probability of an event, such as the coin toss, it is rational to coincide their subjective degree of beliefs accordingly.

Prof Dr. Sudip Patra is Executive Deputy Director, CEASP, Jindal School of Government and Public Policy.

Image credits – livescience.com

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