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Pessimism Traps and Algorithmic Interventions

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

TL;DR

This work reframes pessimism traps as information cascades within a Bayesian sequential-decision framework, showing that even rational agents can converge on suboptimal actions due to public history. It develops a time-varying subsidy (nudging) mechanism that not only breaks incorrect cascades but can sustain the correct cascade after subsidies end, with rigorous random-walk analyses and proofs of intervention efficacy. The authors extend the model to $k$ groups, where the government can deploy a distribution over subsidies without knowing each group’s optimal action, and they demonstrate that all groups can be guided to their respective correct cascades with high probability. Empirical simulations corroborate the theory, revealing that early, signal-revealing subsidies improve outcomes and are budget-feasible, offering a potentially scalable policy tool for mitigating pessimism traps in marginalized communities.

Abstract

In this paper, we relate the philosophical literature on pessimism traps to information cascades, a formal model derived from the economics and mathematics literature. A pessimism trap is a social pattern in which individuals in a community, in situations of uncertainty, begin to copy the sub-optimal actions of others, despite their individual beliefs. This maps nicely onto the concept of an information cascade, which involves a sequence of agents making a decision between two alternatives, with a private signal of the superior alternative and a public history of others' actions. Key results from the economics literature show that information cascades occur with probability one in many contexts, and depending on the strength of the signal, populations can fall into the incorrect cascade very easily and quickly. Once formed, in the absence of external perturbation, a cascade cannot be broken -- therefore, we derive an intervention that can be used to nudge a population from an incorrect to a correct cascade and, importantly, maintain the cascade once the subsidy is discontinued. We study this both theoretically and empirically.

Pessimism Traps and Algorithmic Interventions

TL;DR

This work reframes pessimism traps as information cascades within a Bayesian sequential-decision framework, showing that even rational agents can converge on suboptimal actions due to public history. It develops a time-varying subsidy (nudging) mechanism that not only breaks incorrect cascades but can sustain the correct cascade after subsidies end, with rigorous random-walk analyses and proofs of intervention efficacy. The authors extend the model to groups, where the government can deploy a distribution over subsidies without knowing each group’s optimal action, and they demonstrate that all groups can be guided to their respective correct cascades with high probability. Empirical simulations corroborate the theory, revealing that early, signal-revealing subsidies improve outcomes and are budget-feasible, offering a potentially scalable policy tool for mitigating pessimism traps in marginalized communities.

Abstract

In this paper, we relate the philosophical literature on pessimism traps to information cascades, a formal model derived from the economics and mathematics literature. A pessimism trap is a social pattern in which individuals in a community, in situations of uncertainty, begin to copy the sub-optimal actions of others, despite their individual beliefs. This maps nicely onto the concept of an information cascade, which involves a sequence of agents making a decision between two alternatives, with a private signal of the superior alternative and a public history of others' actions. Key results from the economics literature show that information cascades occur with probability one in many contexts, and depending on the strength of the signal, populations can fall into the incorrect cascade very easily and quickly. Once formed, in the absence of external perturbation, a cascade cannot be broken -- therefore, we derive an intervention that can be used to nudge a population from an incorrect to a correct cascade and, importantly, maintain the cascade once the subsidy is discontinued. We study this both theoretically and empirically.
Paper Structure (30 sections, 11 theorems, 5 equations, 7 figures, 1 algorithm)

This paper contains 30 sections, 11 theorems, 5 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Preliminaries and Basic Model
  5. Single Sequence Model
  6. On Our Modeling Choices
  7. Time-Varying Subsidy
  8. Extension to multiple groups
  9. Formally Defining The Setting
  10. Main Result
  11. Experiments
  12. Data Generation and Procedure
  13. Results
  14. Impact of Financial Supplement on Correct Cascades
  15. Average Subsidy Progression
  16. ...and 15 more sections

Key Result

Theorem 1

The subsidy scheme used in Algorithm 1 causes all agents to act according to their signals until the population falls into the correct cascade. The subsidy value is $r_t = R \left( \frac{\gamma_t -1 }{1 + \frac{1- p}{p} \gamma_t}\right)\,,$ where $\gamma_t = \left( \frac{1-p}{p} \right)^{2|A|-t} \fr

Figures (7)

  • Figure 1: Impact of Financial Supplement on Finding Correct Cascade with Supplement, 100 agents.
  • Figure 2: Probability of Finding Correct Cascade without Supplement
  • Figure 3: Average Subsidy Progression for 100 Agents
  • Figure 4: Proportion Correct Cascades for 10 Agents
  • Figure 5: Proportion Correct Cascades for 1000 Agents
  • ...and 2 more figures

Theorems & Definitions (21)

  • Definition 1: Information Cascade
  • Remark 1
  • Definition 2: Pessimism Trap
  • Remark 2
  • Definition 3
  • Theorem 1
  • Theorem 2
  • Definition 4
  • Definition 5
  • Theorem 3
  • ...and 11 more