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  • Writer's pictureEvelyn Chen

Making Decisions using Utility Functions

This article introduces utility functions in decision-making by comparing its rationale and process to another decision-making method, expected monetary value (EMV), emphasising utility functions’ strengths in this process. Critical discussion for using utility functions in decision-making focuses on the utility functions’ weaknesses, most of which arise when cognitive biases violate the behavioural assumptions underpinning the utility function theory. Examples from my own experiences will reinforce the arguments throughout the essay. Whilst this article discusses the strengths of using utility functions to make decisions, this article also seeks to highlight how cognitive biases cause the utility functions’ weaknesses.


If the probabilities of certain outcomes happening can be assessed, people can find the EMV of their decisions. According to Table 1, I should choose to study Journalism because its EMV is higher than Comparative Literature.


Table 1: Applying the EMV to my personal decision-making scenario

Because an expected value can be regarded as an average outcome if a process is repeated in the long-run, the EMV assumes that the decision is made repeatedly over a long period. However, this assumption will not always hold: for example, in this scenario, I will decide which Master’s specialism I choose only once in my life so it will not be a repeated decision.


Another limitation of the EMV method is that it ignores all other factors apart from money one uses to make decisions. Whilst choosing which subject I will study at university, I also consider factors such as my level of enjoyment of the subject, the different methods in which exams and lessons are administered and how good the subject’s teachers on the course are. For example, although Journalism’s expected monetary value is higher than Comparative Literature’s expected monetary value, I may choose to study Comparative Literature instead. This is because my enjoyment of Comparative Literature is greater and I prefer the teaching methods on the Comparative Literature course compared to the Journalism course’s teaching method.


The EMV method also fails to take into account the decision maker’s attitude to risk. For example, if my parents were able to financially support me after my graduation, I might be more willing to choose Comparative Literature, the subject with the lower probability of employment, because I do not need to financially support myself immediately after graduation. As a result, my risk attitude towards this decision is risk-seeking. Consequently, the decision-maker’s risk attitude would affect the outcome of the decision, something that the expected monetary value method ignores.


Finally, the EMV method assumes that money’s value to the decision-maker is linear when this is not a realistic assumption. For example, an increase in graduate starting salary from £20,000 to £30,000 may be regarded by the decision-maker as more preferable than an increase from £70,000 to £80,000; yet the EMV criterion assumes that both increases are equally desirable.


The decision-making method that overcomes the EMV method’s aforementioned limitations is the application of the utility function to decision-making. According to Von-Neuman and Morgenstern (1944), there are five assumptions on people’s preferences that underlie the expected utility function, including


  1. Completeness: People can rank decisions’ outcomes based on personal preference.

  2. Monotonicity: A gamble with a preferred outcome that has a higher probability of happening will be preferred to a gamble which assigns a lower probability to a preferred outcome.

  3. Independence: If a decision-maker is indifferent between two possible outcomes, then they will be indifferent between two lotteries that offer them with equal probabilities.

My personal decision-making scenario is that I have to decide between studying 2 Masters's specialisms after I earn my Bachelor’s degree: Comparative Literature and Journalism. In this scenario, the utility of each specialism is determined by the following factors:


  1. The average starting graduate salary for that subject is

  2. My personal enjoyment of the subject

  3. The difficulty and frequency of assessments for each course

  4. The quality of the teaching on each course

My level of risk-tolerance is low because my parents do not have the financial means to support me after graduation, which means I would live in destitution if I am unemployed after earning my Masters. Living in destitution is a financial situation I am keen to avoid.


Table 2: Applying the utility function to my decision-making scenario

Comparative Literature’s expected utility exceeds Journalism’s expected utility; thus, I will apply for Comparative Literature upon completion of my Bachelors.


Nevertheless, unlike my personal scenario, some decisions can have more than two options, each with a great deal of different decision-relevant factors and limited information on probabilities. In those situations, applying the expected utility method is not feasible.


Another limitation of using expected utility functions in decision-making is that utilities are subject to rapid change: the expected utility function method relies on the decision-maker’s preferences and attitudes, factors which easily change under different scenarios. In my personal decision-making scenario, Comparative Literature may have a higher utility than Journalism because at that moment, I enjoy studying Comparative Literature more; next week, I may come to despise Comparative Literature, leading to a fall in Comparative Literature’s utility.


More significantly, the expected utility function has limited predictive accuracy in the real world. This is because the assumptions of human behaviour which underlie utility functions in decision-making do not always hold in certain scenarios.


One example of this is the Allais Paradox. The Allais Paradox violates Von-Neuman and Morgenstern’s behavioural assumption of ‘Independence’. The Allais Paradox arises when comparing participants' choices in two different experiments, each of which consists of a choice between two gambles.


Table 3: The payoffs for each gamble in experiment 1 and 2

According to the expected utility function, people should choose Gamble B in experiment 1 and choose Gamble D in experiment 2. Indeed, both experiments involve 50 percent reductions in probability (from 100 percent to 50 percent, and from 10 percent to 5 percent). Yet, in a variety of different scenarios, ranging from the global telecommunication industry, Dutch populace and UK hospital patients (Debbah, M. et al, 2019, Huck, S. et al,2012, Oliver, A.,2003), people have chosen responses contrary to what the expected utility function predicts.


Kahneman and Tversky (1981) explained that the Allais Paradox happened due to the cognitive bias of ‘loss aversion’. Loss aversion is when people find it more preferable to avoid losses than acquire gains. Linked to loss aversion is prospect theory (Kahneman and Tversky, 1979), which states that preferences of individuals vary on the same decisions due to the different ways in which those choices are presented.


The Ellsberg Paradox is another paradox that shows how the expected utility function has limited predictive power in the real world (Ellsberg, D.,1961). The Ellsberg paradox is a thought experiment involving two urns, each containing 100 balls. The first urn contains exactly 50 black balls and 50 red balls, while the second contains 100 black and red balls in an unknown ratio. If asked to bet money on a colour being drawn from one urn or the other, people would tend to choose the known bet in the first urn and avoid the ambiguity of not knowing the winning odds in the second urn. This behaviour violated the expected utility’s completeness and monotonicity axioms because of the ambiguity aversion bias: people prefer what they already know to the unknown (Halevy, Y, 2007, Schmeidler, D. 1989). One real-life example is that people avoid certain medical treatments when the risks are less known (Berger et al, 2013).


To conclude, whilst applying the expected utility function to decision-making seems more convenient than using the EMV, the expected utility function’s assumptions of human behaviour are often violated due to the decision-makers’ cognitive biases. Nonetheless, using the expected utility method in my personal decision-making scenario is appropriate because there are no behavioural assumptions that are violated, there are only two options, each with a similar and a limited number of decision-relevant factors, and all probabilities are accounted for. Therefore, the expected utility function can only be applied to similar scenarios to mine. Behavioural decision theory studies heuristics and their resulting cognitive biases. In decisions where the utility functions cannot be applied, people should use behavioural decision theory to produce more realistic outcomes.

 

Bibliography


  • Ezran, P., Haddad, Y. & Debbah, M. (2019) Allais’ paradox and resource allocation in telecommunication networks. Telecommunication Syst 70, 337–348. https://doi.org/10.1007/s11235-018-0484-7

  • Huck, S., Müller, W. (2012) Allais for all: Revisiting the paradox in a large representative sample. J Risk Uncertain 44, 261–293. https://doi.org/10.1007/s11166-012-9142-8

  • Oliver, A. (2003) A quantitative and qualitative test of the Allais paradox using health outcomes. Journal of Economic Psychology. 24. 35-48. 10.1016/S0167-4870(02)00153-8.

  • Tversky, A and Kahneman, D. (1981) The framing of decisions and the psychology of choice Science, 211 (4481), pp. 453-458

  • Halevy, Y. (2007). Ellsberg Revisited: An Experimental Study. Econometrica, 75(2), 503-536. Retrieved May 20, 2021, from http://www.jstor.org/stable/4501998

  • Schmeidler, D. (1989). Subjective Probability and Expected Utility without Additivity. Econometrica, 57(3), 571-587. doi:10.2307/1911053

  • Berger, L., Bleichrodt, H., & Eeckhoudt, L. (2013). Treatment decisions under ambiguity. Journal of Health Economics, 32, 559-569.

  • Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), 263-291. doi:10.2307/1914185

  • Von Neumann, J., Morgenstern, O., & Rubinstein, A. (1944). Theory of Games and Economic Behaviour. Princeton; Oxford: Princeton University Press. Retrieved May 21, 2021, from http://www.jstor.org/stable/j.ctt1r2gkx

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