Theorizing risk attitudes and rationality using agent based modeling

This poster presents results from applying agent-based modeling to an exploration of risk attitudes and rational decision making in the
context of group interaction. We are also interested in the place of agent-based modeling and computational philosophy within the
computational humanities. Computational philosophy has not typically been included in Digital Humanities; computational work has
been done using philosophy texts as a source for analysis (Kinney 2022; Malaterre et al. 2021; Fletcher et al. 2021; Zahorec et al.
2022), but there are few examples of philosophical arguments being made based on computation (Zahorec et al. 2022). Modeling is
largely accepted as a computational humanist method (McCarty 2004; So 2022), but typically models are based on data rather than
designed simulations as a method analogous to a thought experiment (Mayo-Wilson / Zollman 2021). Agent-based modeling is not as
common in computational humanities, but we are interested in its potential; for instance, see work modeling correspondence networks
to better understand lost information and biases in correspondence data sets (Buarque / Vogl 2023), or work simulating past human
societies (Romanowska et al. 2021).

Our project explores Lara Buchak’s theory of risk-weighted rational decision making by extending it to the context of group
populations and interactions. Buchak has proposed risk-weighted expected utility maximization, which incorporates individual risk
attitudes into the standard expected utility (EU) calculation based on utility and probability of outcomes (Buchak 2017). This theory
provides an explanation for differences of behavior seen in human populations, while still allowing those different choices to be
rational. Buchak’s theory has previously only been applied to individual decision making; our work uses agent-based modeling to
develop and analyze simulations which incorporate a variety of risk attitudes (risk avoidance and risk seeking) into game theoretic
interactions.

This project is a collaboration between a philosopher and a research software engineer; we have worked together to develop
simulations that implement agents with risk attitudes making risky choices. This presentation focuses on results from an
implementation of a hawk/dove game with multiple risk attitudes and risk attitude adjustment. In the hawk/dove game cooperation, or
playing dove, is better for the population, but acting aggressively, or playing hawk, is better for an individual if they are in a
neighborhood of doves. To set up the game, we place agents on a grid and have them play against each of their neighbors, and
accumulate payoffs based on the success of their plays.

We define risk attitudes 0 through 9, where that number corresponds to the minimum number of neighbors playing dove for an agent
to play hawk. An agent with risk attitude 0 is most risk seeking and always plays hawk; an agent with risk attitude 1 will play hawk if at
least one neighbor plays dove; an agent with risk attitude 9 always takes the safe choice and plays dove; an agent with risk attitude 4
or 5 is risk neutral (breaking ties in different ways), which corresponds to expected utility. In this simulation we randomly set agent
initial risk attitudes, and then every ten rounds agents compare their payoffs with their neighbors and adopt the most successful risk
attitude in their neighborhood. The simulation is coded to stop once risk attitude adjustments stabilize.

We define 13 different population states based on primary and second majority of risk averse, risk inclined, or risk moderate, and
analysis of over 1 million runs indicate that while it’s more likely to stabilize with the population having become majority risk inclined,
that is not the only outcome; we also see cases where the population stabilizes as risk neutral, risk avoidant, and many cases with no
clear majority. This diversity of stable populations provides support for the argument that no one risk attitude is uniquely
rational, but rather that risk attitudes are conventional. This matches what we observe in the real world: that different populations have
different risk attitudes.

Our simulations include numerous parameters to vary grid size; adjustment frequency, strategy, and wealth comparison;
neighborhood sizes for observing previous choice, playing against, and comparing payoffs for adjusting risk attitudes; and different
distributions for initializing risk attitudes. Analysis of parameters and adjusted risk attitudes shows that the strongest correlations are
the initial distribution of risk attitudes, which tend to be preserved.

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This poster was accepted and presented at the DH2024 conference in Washington, D.C.