Meredith M. Paker

Economic History

Notes & updates

Socially-determined choice sets

Some thoughts on how we evaluate the choices of individuals that I prepared for a class. I'm eager to hear any thoughts or reactions!

The standard economic model takes an individual’s preferences as given and stable -- the foundations of a complete and transitive preference ordering that permits agents to maximize a utility function that corresponds to their well-being. By using a more nuanced philosophical model of preferences from Hausman (2012), we can disentangle the effects of imperfect information, cognitive biases, and non-self-interest on final choices. I argue below that these factors fail to explain all irrational or counterintuitive economic choices, and that instead, societal constraints determine choice sets in addition to influencing the choice among alternatives of a given set. The implication of modelling socially-constrained choice sets is that it becomes impossible to immediately distinguish counterintuitive choices due to irrationality from those due to agents facing different initial choice sets.

The assumptions that preferences are given, stable, complete, and transitive are typically harmless mathematical assumptions rather than substantial statements about human nature (Bradley (2009), p. 224; see Cartwright (1999)). However, these limited economic models become problematic when one aspires to deal directly with the causes and motives of events and actions, which may require more complex models that come closer to the real decision-making processes of humans. Deeper models of choice in economics ensure that we accurately evaluate the motivations and rationality of agents.

Standard choice models

In typical economic models of choice, an agent faces a set X of n choices x_i, i in {1,...n}, with complete and transitive preferences over all x_i. Preferences are directly associated with the agent’s well-being (Varian (1992) p. 94; Mas-Colell, Whinston, and Green (1995), p. 6). The agent is then assumed implicitly or explicitly to maximize a utility function subject to constraints through a choice determination axiom. Varian states,“Our basic hypothesis is that a rational consumer will always choose a most preferred bundle from the set of affordable alternatives” where an affordable alternative is one that satisfies a consumer’s budget constraint (Varian (1992), p. 98). Thus agents choose x_i to maximize a utility function subject to the prices and income environment.
In his seminal book on preferences in economics, Hausman argues that preferences are total subjective comparative evaluations, and that final choices depend on preferences among the objects of choice, beliefs about what is available for choice, and facts about what can be chosen (Hausman (2012)). His decision-making model is a useful addition to the standard economic model because it decomposes the relationship between preferences and choices and because it illuminates important channels of influence.

Figure 1: The standard model of choice from Hausman (2012), edited for clarity

In this model, preferences among alternatives in the choice set are determined by subjective beliefs about and preferences for the characteristics of those alternatives. These traits can be static properties of an alternative or consequences of selecting that alternative. For example, a preference for a blue shirt rather than a red shirt may stem from an agent’s belief that a blue shirt brings out the color of their eyes, and their preference for this consequence. In Figure 1, beliefs about the properties and consequences of alternatives affect the pref- erences among them through (b), and preferences about these properties and consequences affect preferences among the alternatives through (a).

However, this total comparative preference ranking does not constitute the final choice from the choice set. Both the agent’s subjective beliefs about which alternatives are available to them and the literal feasibility of selecting these alternatives factor into the final choice from the choice set. For example, an agent may select a red shirt if they believe that no blue shirt is available. Similarly, they may select a red shirt if the available blue shirt is outside their price range (and thus not feasible due to their budget constraint). In Figure 1, beliefs about the availability of alternatives affect the final choice through (e) and the constraints making certain alternatives infeasible affect the final choice through (f).

Importantly, constraints that affect an alternative’s feasibility can influence the agent’s subjective beliefs about which alternatives are available to them though (g), but are not required to. Thus in the simple shirt example, the high price of blue shirts can constrain the agent’s choice in two subtly different ways. If the agent wishes to buy a blue shirt and discovers at the register that they do not have enough funds, the constraint directly affects their choice through channel (f). However, if the price of blue shirts causes the agent to believe that they cannot afford blue shirts through channel (g), the agent might not even go looking for a blue shirt at all, affecting the final choice of shirt then through (e). Thus constraints can affect final choices directly or through the agent’s beliefs.

Hausman suggests that individual agents’ preferences and choices reliably indicate their well-being when “people are competent evaluators (and free of rational flaws), they are self- interested, and they have accurate relevant information” (Hausman (2016), p. 29). Thus we can divide failures of the model into decision-making flaws, non-self-interested choices, and imperfect information leading to counterintuitive choices. These categories can help policymakers understand what has gone wrong when the standard philosophical decision-making model fails and an agent makes a counterintuitive and seemingly irrational choice.
Consider, however, a slightly more complex example. Hoxby and Avery find that a majority of high-achieving low-income students in the United States do not apply to any selective university, despite having the grades necessary for them to be good candidates and despite having access to financial aid that would cover most of the cost (Hoxby and Avery (2013)). This choice is remarkable given the high returns to a college degree in the US. Their analysis finds that this choice is not driven by an information deficit or by a mis-evaluation of the value of a college education or of their probability of success in college. Should we then believe that all of these students are making non-self-interested choices, failing to maximize their future earnings? While this is certainly the case for some students, it is possible that more is at work. Hoxby and Avery find among their results that, ceteris paribus, a student’s neighborhood has a large effect on whether they apply to college. This suggests that social factors might affect an individual’s choices without affecting their actual preferences or their decision-making process.

Socially-determined choice sets

In this section, I broaden the scope of the basic model to include the determination of the choice set an agent faces. In the previous model, constraints affect the way that agents select among options in a given choice set. The expanded model allows constraints to affect the literal choice set an agent faces. This illuminates problems such as those just described while also revealing important ambiguities in what we can know about a person’s preferences given their choices.
The fundamental component of this new model is a path-dependent (David (2007)) social process that determines which choice set an agent faces. This should be conceived of as some complex system of constraints that affects the world that the agent interacts with. In a sense, this determining process can be seen as giving different agents different initial conditions based on their personal histories and experiences. An agent’s different positions in life can affect which choice set they see, separate of what they know or do not know about feasible alternatives for them.
To return to the previous example, there is a subtle difference between a student not knowing that college is an option for them and not even considering college in the first place. It is possible that some of the students in the Hoxby and Avery study never made a real choice not to go to college, or a choice to value something above college. If college was not a feature of their universe, and not something their neighbors or their families had ever had experience with, then the option may never have been seriously entertained. This difference is important because interventions that increase information about college (like campaigns informing students how much financial aid they would get, admission predictor tools, better counselors, etc.) would be ineffective for students who are not applying to college due to these external social constraints. Misguided interventions could even be harmful by treating these students as irrational for not selecting their best option, when really the students are facing entirely different choice sets than the one projected on them.
So, consider simultaneously two cases. In the first case, an agent chooses among a set A of n choices x_i, i in {1, ...n}. Assume the agent has complete and transitive preferences, as above, and then assign the subscript i on each element of A such that x_i is preferred to x_{i+1} and that x_i is preferred to x_j for all j >= i.
Given this ordering of elements, now consider a second case where the agent chooses among a set B which contains all elements of A except x_1, the highest ranked. Thus we have A = {x_1, x_2,...x_n} and B = {x_i | x_i in A, i != 1}. Let C_i be one if the agent makes choice x_i and zero otherwise. Then define F_i to be one if the choice x_i is feasible to the agent and zero otherwise, independent of what the agent believes and independent of whether the option is reflected in the agent’s choice set. This expands the scope of the model from the conventional model, which only considers the alternatives that are immediately feasible to the agent.

Given this framework, we have eight possible outcomes as indicated in Figure 2.

Figure 2: Possible outcomes given different choice sets

This model presents two separate initial choice sets and examines their possible outcomes given the feasibility of the highest-ranked alternative and the choice of the agent. As defined above, choice set A is an unrestricted choice set, while choice set B does not include the highest-ranked alternative due to some external social constraints.

An outcome is economically optimal if the philosophical choice model presented with no errors would lead to that selection. The economically optimal outcomes in the model (distinguished with bold edges) are outcomes (1), (4), (6), and (8). I consider an outcome to be “optimal for the agent” if the agent ends up with their highest-ranked alternative, which is in both cases x_1. This relies on the previously discussed assumption that the given preference ranking aligns with the agent’s well-being. Thus the only outcome that is optimal for the agent is (1).

In the ideal outcome of the chart, (1), if a person faces an unrestricted choice set with their highest-ranked option feasible to them, they choose and achieve that option. This is obviously rational by the economic theory presented above. It is also optimal for the agent’s well-being because they end up with their highest-ranked alternative. In all of the following suboptimal outcomes, a policymaker aims to help the agent achieve (1).

(2) is a seemingly irrational choice. The agent facing an unrestricted choice set with their highest-ranked option available to them instead chooses a lower-ranked option. This is not an optimal outcome for the person because they do not achieve their highest-ranked alternative. Ending up at (2) could reflect a number of different errors discussed above. The agent could have ranked their preferences poorly, could have a false view of what is available to them, or could have made a counterpreferential choice intentionally. In all cases, the agent has made an obvious mistake and ended up at a suboptimal outcome, which can be directly analyzed and addressed by a policy-maker.

In (3), the agent faces an unrestricted choice set but their highest-ranked option is not available to them. Regardless, they still attempt to select this highest-ranked option. This leads to a type F error, where they fail to obtain their highest ranked option and end up at a suboptimal outcome. With expanded or adjusted information, the agent could instead pick a lower-ranked option outright, as in (4), but this is still suboptimal.

Though (4) is economically rational -- an agent picks the best option feasible for them -- it is by assumption non-optimal for the agent. In this case, a policymaker would aim to make the highest-ranked option feasible (i.e. make F_1 = 1), likely through legal or institutional changes.

Outcomes (5)-(8) are distinct because the agent is choosing from choice set B, which omits the highest-ranked option. Thus x_1 is never chosen, regardless of whether it is feasible, and (5) and (7) never occur by definition. The feasibility of an option is defined objectively, so an option could not be in an agent’s choice set but still be feasible for them if, say, they could afford it or if it was legally permitted. (6) is such a case; the highest-ranked alternative is feasible for the agent but cannot be chosen because it is not represented in the choice set. A policymaker then would attempt to address the broader constraints on the agent’s choice set in hopes that the agent could end up at outcome (1).

In (8), which is economically rational, the agent picks the best available option. However, this is not optimal for the agent since it is not their highest-ranked option. A policymaker would need to simultaneously make the best option feasible for the agent while addressing the larger constraints restricting their choice set.

Implications of the model

This model highlights cases where the basic economic model does not match what is optimal for the agent. By taking constraints that make some alternatives infeasible as given, economic models can falsely view (3), (4), and (8) as optimal. Additionally, in (2), if an agent elects not to pick their highest-ranking option, then preferences have been modeled too narrowly.

The standard model of choice also fails to capture the subtle difference between (6) and (2). If we observe an agent who fails to select their highest-ranking option, even though that option is feasible, we might offer explanations stemming from (2). The agent could have ranked their preferences poorly due to a cognitive bias, they could have imperfect information, or they could be making a non-self-interested choice intentionally. However, the alternative explanation offered by (6) is that an agent could be facing an entirely different choice set than the one an observer might assume they have. Unlike in (2), this explanation could depend entirely on society-level error, which has implications for policy responses and political attitudes. Without further information, it is impossible to immediately tell whether observed counterintuitive choices are due to the irrationality of agents (as in (2)) or due to the agents facing different choice sets than an observer might ascribe them (as in (6)).

A third error highlighted by this model is mistaking (4) for (2). In (4), the highest- ranking option is not chosen because it is not feasible for an agent. If these constraints are largely legal or institutional, it would be easy for one to mistakenly assume that the highest-ranked option was available to an agent when it in fact was not.

In conclusion, I've considered here the standard philosophical model of decision-making where the choice of an alternative is determined by preferences among the alternatives and beliefs about the feasibility of the alternatives, all subject to direct constraints on the alternatives. This standard model can fail due to cognitive biases, imperfect information, or non-self-interested choices. I then propose an adjusted model that takes societal constraints as determining choice sets rather than exclusively influencing the feasibility of alternatives in a given choice set. I note  how the initial choice set influences an agent’s final outcomes but also can influence perceptions of their decision-making, which suggests that counterintuitive choices should not be overtinterpreted due to the ambiguity introduced when one allows socially-determined choice sets in the model.


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What do you think? Feel free to comment below with your ideas, suggestions, or corrections. A full PDF of this work is available on my research page as "Adjusting the Economic Model of Decision-Making to Permit Socially-Determined Choice Sets" (2016)