A tradeoff in making decisions

The Tradeoff in Daily Decisions

You wander around Carrefour and scan rows of wines on the shelf, how do you decide to keep walking or stop at a particular one? You have a good experience at TSE and in Toulouse, but you are curious about other programs and parts of the world, how do you decide to stay in or explore other opportunities? You are pushed with notifications by social media (looping videos in TikTok, trends in YouTube), where new recommendations and instant gratification entangle, and this time you even feel indecisive. These situations are common in our daily life, in which we face a dilemma : either one can settle down and gain the fruit of a decision, subject to time limit and other constraints; or one can think the best is yet to come and explore alternatives to find  potentially better options, though that search again cannot last long for similar constraints. 

In his autobiography (1996)1, Herbert Simon uses the metaphor of a maze to describe such a behavioral pattern. Imagine a man named Hugo lives alone in a castle. He only worries about his stomach and leads a simple life: sleeping, searching for food, eating. There are countless rooms in the castle but in each search, Hugo can only access a few rooms. In this one-way path, Hugo sometimes walks to another door if he easily finds a dining table, but, more often, hunger forces him to compromise.

Though the author did not provide any interpretation, it can be viewed this way: throughout Hugo’s life he presented a ternary behavioral pattern: being idle, seeking for food, or consuming what is at sight.  A tradeoff naturally arises: remaining at a table gets him fed but at the cost of finding something better, while going somewhere unknown could induce a risk of starvation. Some literature characterizes such a decision pattern as an exploration-exploitation tradeoff2. Many of our decisions require a fine balance between exploring different options and exploiting the explicit rewards of them. In the shopping case, we decide from refining our knowledge on wines to finally purchasing a satisfying bottle; in the school case, we transit from enjoying the current benefit of schooling to exploring greater uncertainties but potential opportunities.

External Context of Decisions

This tradeoff in decision-making seems innate to us. In fact, Hugo’s ‘boring’ life is similar to many animals’. Butterflies feed on nectar of flowers, but why do they remain at one patch before seeking another, do they possess an optimal foraging strategy? We can start the discussion on that mysterious castle, where Hugo lives. The structure of the castle shapes Hugo’s decision. Suppose there are homogeneous duplicates of Hugo, separated in the castle with random strategies. Overtime, those whose decision patterns fit best to the external setting should survive: if Hugo searches too much in empty places, he will starve to death before eating. If in some areas, distance between rooms are longer and paths are perilous, Hugo would become more satisfied with what could be found and explore less often. On the contrary, if Hugo can easily see through rooms, he will put more effort into exploring. After the selection from this castle, each Hugo represents specific decision patterns that fit best to the local region he lives in. 

Internal Choosing Organism of Decision

These decisions happen in our mind (if mind exists), and it will be incomplete to study this tradeoff without referring to the ontology of decision, our choosing organism, which has limited computational capacities. During his past searches, Hugo has developed clues that most likely led him to particularly desired foods. Whenever he senses these stimuli, he reduces his exploration effort and this works most of the time to get him food. This effort-saving strategy is a heuristic: a mental shortcut sufficient enough to reach a satisfactory result without requiring optimality or rational thinking. This approach can be viewed as an evolutionary rationality. Indeed, some economic irrationality in decision making, for instance the intransitivity  of preferences, could be possibly explained by this broader sense of rationality. In repeated choices, violation of the transitivity axiom may result from adaptation to heterogeneous environments. For instance, according to the 1/N heuristic, an investor simply allocates equally across all N funds, among which he does not represent a preference ranking. It has been shown that no rational choice model consistently outperforms this heuristic strategy, given the highly predictive uncertain stock market3.

But in the dynamic setting, innate heuristics are far from sufficient, and some can no longer be applied. Hugo also makes careful notes of new clues that might help in his future exploration, though it takes time for confirming his prediction. How do organisms deal with these new clues? If we accept the view that organisms are algorithms4, then why should our brains not function like a Bayesian machine5 that continuously incorporates information to update the statistical properties of the environment, and minimises surprises from nature? In other words, Hugo developed adaptive heuristics by updating his knowledge of the castle, to make sure his heuristics can work through time. Then the tradeoff in our choice mechanism becomes whether to trust heuristics and save the exploration effort, or invest in information acquisition to update knowledge about our surroundings and further build more adaptive heuristics. This tradeoff will depend on individual features of Hugo: even in the same context, heterogeneous duplicates of Hugo will decide in different manners. If Hugo has a small capacity of working memory, he refers more to his recognition heuristics and stops exploring once he sees something familiar. On the other hand, his exploration time increases with his working memory capacity.

Axiomatic World for Decision

Can decision-making, like some emotions, be thought as merely a result of biochemical reactions and electrical currents in our brain4? Or is there something else guiding our decision? Humans have a unique ability to see things which do not physically exist. This is not simply a counterfactual reasoning shared by some primates. If our heuristics no longer work, what should we decide? Either a person makes a decision in a completely intuitive way, or in a supposedly ‘rational’ way. The latter is highly mathematical with axiomatic paradigms for decision making, e.g. rational choice paradigm. Scientists study how people should normatively make decisions, or describe how they actually do, which is not something obvious to see, but mathematically correct6.

From the discussion above, a decision behavior happens within the external context, internal decision organisms, and the axiomatic logic world of formulas. The environment induces an interval on our behavior, in which the organism develops rational heuristics depending on the context, that work most of the time. On the other hand, as a Bayesian machine, the choosing organism keeps exploring unknowns and updating evidence of environments. In this process we represent adaptive rationality to changing surroundings. Is there also a tradeoff in the axiomatic world? One can think of the recursive argument of economizing economizing: how do we balance between deliberation cost for optimisation and further refined results? What is the link between the axiomatic world and the choosing organism? And things get even more complicated when we consider interactions: how our actions change the physical world and in return nudge our choices…

by Yuan Liu

References

1Simon, Herbert. “Mazes Without Minotaurs.” In Models of my life, (1996),  535-556,  MIT Press.

²Mehlhorn, Katja, Ben R. Newell, Peter M. Todd, Michael D. Lee, Kate Morgan, Victoria A. Braithwaite, Daniel Hausmann, Klaus Fiedler, and Cleotilde Gonzalez. “Unpacking the exploration–exploitation tradeoff: A synthesis of human and animal literatures.” Decision 2, no. 3 (2015), 191-215. doi:10.1037/dec0000033.

3DeMiguel, Victor, Lorenzo Garlappi, and Raman Uppal. “Optimal Versus Naive Diversification: How Inefficient is the 1/NPortfolio Strategy?” Review of Financial Studies 22, no. 5 (2009), 1915-1953. doi:10.1093/rfs/hhm075.

4Harari, Yuval N. Homo Deus: A Brief History of Tomorrow. New York: Random House, 2016.

5Gershman, Samuel J. “What does the free energy principle tell us about the brain?” 2019.

6Herfeld, Catherine. “Rational choice as a toolbox for the economist: an interview with Itzhak Gilboa.” Erasmus Journal for Philosophy and Economics 7, no. 2 (2014), 116. doi:10.23941/ejpe.v7i2.176.

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