Editorial Feature

Novel Approach to Medical Judgment and Decisions Based on Quantum Probability Theory

Clinical research has become a significant and crucial component of medical science’s transition from basic to clinical research. Patients can benefit from sound decision-making, accurate diagnosis, and treatment. Quantum probability is particularly well suited to dealing with the ambiguous and contextual situations that can emerge during medical decision-making. Quantum models to this effect are explored in the journal Quantum Reports.

Study: Application of Quantum Cognition to Judgments for Medical Decisions. Image Credit: Anatolii Stoiko/Shutterstock.com

Effective medical practice necessitates good decision-making. Physicians must determine the correct diagnosis as well as the most effective treatment plan. The goal of this article is to show how research on the psychology of judgment and decision-making can help with the task of making medical decisions.

More specifically, the researchers reveal a new approach to judgment and decision-making based on quantum probability theory, which could shed new light on seemingly irrational judgments and point to ways to correct these errors.

Several cognitive errors that affect human judgment and decision-making have been identified by decision scientists over the last 50 years, and most of these decision errors were also proven by medical practitioners.

Some of these errors could have a big impact on therapeutic radiation oncology decisions. Depending on their age and training, radiation oncologists vary greatly in their aggressiveness and risk assessments for tissue damage outside of the target areas.


When deciding on a treatment, it is important to think about the chances of various outcomes created by the treatment plan. Unpacking an event into mutually exhaustive and exclusive parts is the process of breaking down a general treatment outcome into more specific options. The term “order dependence” refers to a situation in which the probability of two events is determined by the order in which they are considered.

The empirical finding that individuals judge the probability of a conjunction to be higher than the probability of a single event is known as conjunction errors.

Conjunction errors are also observed in physician judgments. Radiation oncologists frequently face the challenge of evaluating the timing of events. Conjunction errors are not constrained to medical situations; they can also occur in situations involving intuitive physics that are relevant to medical physics.

What causes these erroneous probability judgments? People (including physicians) use a judgmental heuristic known as the “representativeness” heuristic instead of using standard probability theory. People judge the likelihood of an event based on the match between a model (supplied by the background story) and an outcome, according to representativeness (an event that is being judged).

The representativeness heuristic can be formalized by a probability on the basis of quantum theory, which may be of interest to medical physicists. The conjunction fallacy is explained in quantum probability in the following simple but rigorous way.

The background information or story, as per quantum theory, creates a belief state, which would be a unit length vector in the vector space. In a vector space, an event like a “heart attack” is represented as a subspace. A projector is assigned to each subspace. Another event, like “over fifty,” is represented by a different subspace with a different projector.

The probability of the event “heart attack” is calculated by the squared length of the projection of the state on the subspace for “heart attack.” The probability of the events “over fifty and then heart attack” is then computed.

According to research, order effects do exist with these probability judgments. Another crucial prediction is that the conjunction’s judged probability can only be higher than the probability of one of the single events.

When the conjunction outpaces both single events, it is said to be a double conjunction error. Even though double conjunction errors are uncommon in empirical studies, they have indeed been discovered in some cases; therefore this prediction presents a challenge to quantum theory’s current formulation.

The empirical finding that individuals evaluate the probability of a disjunction to be below the probability of a single event found in the disjunction is known as disjunction errors.

The disjunction error can be explained using the same quantum model that has been used to explain the conjunction error.

As previously stated, the quantum cognition model should predict that the order in which events are evaluated matters in conjunction and disjunction errors. In fact, order effects in medical decisions have been found.

The order in which events are evaluated is also a crucial component in radiation therapy decisions. When treating a mediastinum tumor, for example, a radiation oncologist must consider the risk of damage to the spinal cord, heart, and lungs. Focusing on one risk, such as lung cancer, alters the context for evaluating another, such as heart disease.

Of course, there have been previous attempts to account for order effects using traditional models. However, the proposed quantum model when tested and compared to a popular anchor-adjustment model, performed better.

When a bigger category event is broken down into smaller events, the union equals the larger event - this is referred to as an unpacking effect.

For radiation oncologists, the unpacking of events is also a problem. The same principles apply to the quantum model for unpacking effects as they do to the classical model.

When an irrelevant cue is assessed before a medical judgment, an anchoring judgment error occurs, which pulls the medical judgment toward the irrelevant cue’s evaluation. Radiation therapy decisions may also be influenced by anchoring effects.

The projection postulate from quantum theory is used in a quantum cognition account of anchoring effects. Following a measurement, the system’s new state is created by projecting the earlier state onto the subspace portraying the observed event and then normalizing the projection.


Quantum cognition is a new theory of decision-making and judgment based on quantum axioms rather than conventional probability theory. It loosens the axioms of commutativity and distributivity that are constructed into traditional probability in some ways. It offers a systematic account of many common probability judgment errors found in medical decision-making by relaxing these axioms.

The scope of this article is limited to analyzing the application of quantum probability theory in medical judgments. Evidence-based medicine is still the best way to practice medicine today. The article asserts that quantum decision-making at all levels of human cognition is a step toward precision medicine.

Journal Reference:

Yi, S., Lu, M., Busemeyer, J. (2022) Application of Quantum Cognition to Judgments for Medical Decisions. Quantum Reports, 4(2), pp. 193–200. Available Online: https://www.mdpi.com/2624-960X/4/2/13/htm.

References and Further Reading

  1. Tversky, A & Kahneman, D (1983) Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, pp. 293–315. doi/10.1037/0033-295X.90.4.293.
  2. Crupi, V., et al. (2018) Double conjunction fallacies in physicians’ probability judgment. Medical Decision Making, 8, pp. 756–760. doi.org/10.1177%2F0272989X18786358.
  3. Rao, G (2009) Probability error in diagnosis: The conjunction fallacy among beginning medical students. Family medicine, 41, pp. 262–265.
  4. Ludwin-Peery, E., et al. (2020) Broken physics: A conjunction-fallacy effect in intuitive physical reasoning. Psychological Science, 31, pp. 1602–1611. doi.org/10.1177%2F0956797620957610.
  5. Busemeyer, J. R., et al. (2011) A quantum theoretical explanation for probability judgment errors. Psychological Review, 118, pp. 193–218. doi.apa.org/doi/10.1037/a0022542.
  6. Hughes, R. I. G (1989) The Structure and Interpretation of Quantum Mechanics; Harvard University Press: Cambridge, MA, USA.
  7. Khrennikov, A Y & Haven, E (2009) Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts. Journal of Mathematical Psychology, 53, pp. 378–388. doi.org/10.1016/j.jmp.2009.01.007.
  8. Yearsley, J M & Trueblood, J T (2018) A quantum theory account of order effects and conjunction fallacies in political judgments. Psychonomic Bulletin & Review, 25, pp. 1517–1525. doi.org/10.3758/s13423-017-1371-z.
  9. Aerts, D (2009) Quantum structure in cognition. Journal of Mathematical Psychology, 53, pp. 314–348. doi.org/10.1016/j.jmp.2009.04.005.
  10. Yates, J F & Carlson, B W (1986) Conjunction errors: Evidence for multiple judgment  procedures, including “signed summation”. Organizational Behavior and Human Decision Processes, 37, pp. 230–253. doi.org/10.1016/0749-5978(86)90053-1.
  11. Bar-Hillel, M & Neter, E (1993) How alike is it versus how likely is it: A disjunction fallacy in probability judgments. Journal of Personality and Social Psychology, 85, pp. 1119–1131. doi.apa.org/doi/10.1037/0022-3514.65.6.1119.
  12. Bergus, G. R., et al. (1998) Clinical diagnosis and order of information. Medical Decision Making, 18, pp. 412–417. doi.org/10.1177%2F0272989X9801800409.
  13. Hogarth, R M & Einhorn, H J (1992) Order effects in belief updating: The belief adjustment modeling. Cognitive Psychology, 24, pp. 1–55. doi.org/10.1016/0010-0285(92)90002-J.
  14. Trueblood, J T & Busemeyer, J R (2011) A quantum probability account of order effects in inference. Cognitive science, 35, pp. 1518–1552. doi.org/10.1111/j.1551-6709.2011.01197.x.
  15. Redelmeier, D. A., et al. (1995) Probability judgment in medicine: Discounting unspecified possibilities. Medical Decision Making, 15, pp. 227–230. doi.org/10.1177%2F0272989X9501500305.
  16. Brewer, N. T., et al. (2007) The influence of irrelevant anchors on the judgments and choices of doctors and patients. Medical Decision Making, 27, pp. 203–211. doi.org/10.1177%2F0272989X06298595.
  17. White, L. C., et al. (2014) Sometimes it does hurt to ask: The constructive role of articulating impressions. Cognition, 133, pp. 48–64. doi.org/10.1016/j.cognition.2014.05.015.
  18. Nilsson, H (2008) Exploring the conjunction fallacy within a category learning framework. Journal of Behavioral Decision Making, 21, pp. 471–490. doi.org/10.1002/bdm.615.
  19. Sloman, S., et al. (2003) Frequency illusions and other fallacies. Organizational Behavior and Human Decision Processes, 91, pp. 296–309. doi.org/10.1016/S0749-5978(03)00021-9.
  20. Pothos, E M & Busemeyer, J R (2022) Quantum Cognition. Annual Review of Psychology, 73, pp. 749–778. doi.org/10.1146/annurev-psych-033020-123501.
Skyla Baily

Written by

Skyla Baily

Skyla graduated from the University of Manchester with a BSocSc Hons in Social Anthropology. During her studies, Skyla worked as a research assistant, collaborating with a team of academics, and won a social engagement prize for her dissertation. With prior experience in writing and editing, Skyla joined the editorial team at AZoNetwork in the year after her graduation. Outside of work, Skyla’s interests include snowboarding, in which she used to compete internationally, and spending time discovering the bars, restaurants and activities Manchester has to offer!


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