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A Theoretical Model for Grit in Pursuing Ambitious Ends

Avrim Blum, Emily Diana, Kavya Ravichandran, Alexander Williams Tolbert

TL;DR

The paper studies how grit influences decision-making between a stable, immediate reward and a striving, delayed payoff under uncertainty by modeling a two-armed improving bandit. It analyzes two notions of rationality—competitive ratio and Bayesian uncertainty—to derive how gritty traits (optimism and discomfort tolerance) shape strategy, switch points, and rewards, including the impact of financial safety nets. Key results identify switching points such as $s = T - \sqrt{\frac{2T}{\tilde{\alpha}}}$ for optimism and $\alpha_\gamma = \frac{\gamma+1}{2}$ for comfort, and show that safety nets can extend exploration without sacrificing baseline reward, aligning with observed benefits of grants. The Bayesian extension demonstrates that uncertainty tolerance broadens the exploration window but can incur diminishing returns, offering a mechanistic account of grit and informing policy discussions on interventions to support ambitious pursuit.

Abstract

Ambition and risk-taking have been heralded as important ways for marginalized communities to get out of cycles of poverty. As a result, educational messaging often encourages individuals to strengthen their personal resolve and develop characteristics such as discipline and grit to succeed in ambitious ends. However, recent work in philosophy and sociology highlights that this messaging often does more harm than good for students in these situations. We study similar questions using a different epistemic approach and in simple theoretical models -- we provide a quantitative model of decision-making between stable and risky choices in the improving multi-armed bandits framework. We use this model to first study how individuals' "strategies" are affected by their level of grittiness and how this affects their accrued rewards. Then, we study the impact of various interventions, such as increasing grit or providing a financial safety net. Our investigation of rational decision making involves two different formal models of rationality, the competitive ratio between the accrued reward and the optimal reward and Bayesian quantification of uncertainty.

A Theoretical Model for Grit in Pursuing Ambitious Ends

TL;DR

The paper studies how grit influences decision-making between a stable, immediate reward and a striving, delayed payoff under uncertainty by modeling a two-armed improving bandit. It analyzes two notions of rationality—competitive ratio and Bayesian uncertainty—to derive how gritty traits (optimism and discomfort tolerance) shape strategy, switch points, and rewards, including the impact of financial safety nets. Key results identify switching points such as for optimism and for comfort, and show that safety nets can extend exploration without sacrificing baseline reward, aligning with observed benefits of grants. The Bayesian extension demonstrates that uncertainty tolerance broadens the exploration window but can incur diminishing returns, offering a mechanistic account of grit and informing policy discussions on interventions to support ambitious pursuit.

Abstract

Ambition and risk-taking have been heralded as important ways for marginalized communities to get out of cycles of poverty. As a result, educational messaging often encourages individuals to strengthen their personal resolve and develop characteristics such as discipline and grit to succeed in ambitious ends. However, recent work in philosophy and sociology highlights that this messaging often does more harm than good for students in these situations. We study similar questions using a different epistemic approach and in simple theoretical models -- we provide a quantitative model of decision-making between stable and risky choices in the improving multi-armed bandits framework. We use this model to first study how individuals' "strategies" are affected by their level of grittiness and how this affects their accrued rewards. Then, we study the impact of various interventions, such as increasing grit or providing a financial safety net. Our investigation of rational decision making involves two different formal models of rationality, the competitive ratio between the accrued reward and the optimal reward and Bayesian quantification of uncertainty.

Paper Structure

This paper contains 32 sections, 6 theorems, 20 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Our Approach To Studying Grit
  3. Our Contributions
  4. Related Work
  5. Key Features of Grit According to Morton and Paul
  6. Formal Setting: Improving Multi-Armed Bandits
  7. Rationality in Terms of Competitive Ratio
  8. Rationality in This Model
  9. Modelling Grit: Optimism
  10. Results
  11. Modelling Grit: Discomfort Tolerance
  12. Financial Support
  13. No safety net
  14. Free reimbursement
  15. Which wins? Trust fund or grit?
  16. ...and 17 more sections

Key Result

Lemma 3.2

Any strategy that interweaves plays of $f_1$ and $f_2$ can be converted into a strategy that plays only $f_2$ followed by only $f_1$ that achieves at least as much reward.

Figures (2)

  • Figure 1: Switch point as a function of standard deviation $\sigma$ for prior of $\mathcal{N}(25, \sigma^2).$
  • Figure 2: This table shows the reward the agents described in Section \ref{['subsec:optimism']} receive if $\theta\,,$ the true threshold beyond which $f_2$ pays off, lies in different regions. The columns are increasing in grit from left to right. We can see that if $\theta$ is larger, more grit can actually result in less reward, since the agent switches back to the stable arm and accrues less reward there.

Theorems & Definitions (19)

  • Definition 2.1
  • Definition 3.1
  • Lemma 3.2
  • proof
  • Definition 3.3
  • Lemma 3.4
  • Proposition 3.5
  • proof
  • Definition 3.6
  • Definition 3.7
  • ...and 9 more