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Designing Algorithmic Recommendations to Achieve Human-AI Complementarity

Bryce McLaughlin, Jann Spiess

TL;DR

This article forms an algorithmic-design problem that leverages the potential-outcomes framework from causal inference to model the effect of recommendations on a human decision-maker's binary treatment choice and introduces a monotonicity assumption that leads to an intuitive classification of human responses to the algorithm.

Abstract

Algorithms frequently assist, rather than replace, human decision-makers. However, the design and analysis of algorithms often focus on predicting outcomes and do not explicitly model their effect on human decisions. This discrepancy between the design and role of algorithmic assistants becomes particularly concerning in light of empirical evidence that suggests that algorithmic assistants again and again fail to improve human decisions. In this article, we formalize the design of recommendation algorithms that assist human decision-makers without making restrictive ex-ante assumptions about how recommendations affect decisions. We formulate an algorithmic-design problem that leverages the potential-outcomes framework from causal inference to model the effect of recommendations on a human decision-maker's binary treatment choice. Within this model, we introduce a monotonicity assumption that leads to an intuitive classification of human responses to the algorithm. Under this assumption, we can express the human's response to algorithmic recommendations in terms of their compliance with the algorithm and the active decision they would take if the algorithm sends no recommendation. We showcase the utility of our framework using an online experiment that simulates a hiring task. We argue that our approach can make sense of the relative performance of different recommendation algorithms in the experiment and can help design solutions that realize human-AI complementarity. Finally, we leverage our approach to derive minimax optimal recommendation algorithms that can be implemented with machine learning using limited training data.

Designing Algorithmic Recommendations to Achieve Human-AI Complementarity

TL;DR

This article forms an algorithmic-design problem that leverages the potential-outcomes framework from causal inference to model the effect of recommendations on a human decision-maker's binary treatment choice and introduces a monotonicity assumption that leads to an intuitive classification of human responses to the algorithm.

Abstract

Algorithms frequently assist, rather than replace, human decision-makers. However, the design and analysis of algorithms often focus on predicting outcomes and do not explicitly model their effect on human decisions. This discrepancy between the design and role of algorithmic assistants becomes particularly concerning in light of empirical evidence that suggests that algorithmic assistants again and again fail to improve human decisions. In this article, we formalize the design of recommendation algorithms that assist human decision-makers without making restrictive ex-ante assumptions about how recommendations affect decisions. We formulate an algorithmic-design problem that leverages the potential-outcomes framework from causal inference to model the effect of recommendations on a human decision-maker's binary treatment choice. Within this model, we introduce a monotonicity assumption that leads to an intuitive classification of human responses to the algorithm. Under this assumption, we can express the human's response to algorithmic recommendations in terms of their compliance with the algorithm and the active decision they would take if the algorithm sends no recommendation. We showcase the utility of our framework using an online experiment that simulates a hiring task. We argue that our approach can make sense of the relative performance of different recommendation algorithms in the experiment and can help design solutions that realize human-AI complementarity. Finally, we leverage our approach to derive minimax optimal recommendation algorithms that can be implemented with machine learning using limited training data.
Paper Structure (21 sections, 3 theorems, 33 equations, 10 figures, 6 tables)

This paper contains 21 sections, 3 theorems, 33 equations, 10 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Hiring as a Binary Treatment Choice Problem
  4. Algorithm Design as a Principal--Agent Problem
  5. Making Sense of Recommendations with Potential Outcomes
  6. Recommendations Induce Potential Outcomes
  7. Objective of Recommendation Algorithms
  8. Monotonic Responses and Compliance-Aware Recommendations
  9. Complementary Recommendations in an Experiment
  10. Experimental Setup
  11. Treatments
  12. Data and Main Results
  13. Additional Analysis and Robustness Checks
  14. Training Recommendation Algorithms on Decision Data
  15. Challenges in Learning Recommendation Algorithms from Training Data
  16. ...and 6 more sections

Key Result

Proposition 1

Under ms-asm:Mon, the potential outcome triplet $(D_U(\text{\normalfont\color{red}N};f^{\textnormal{rec}}),D_U({{\color{gray}\varnothing}};f^{\textnormal{rec}}),D_U(\text{\normalfont\color{blue} H};f^{\textnormal{rec}}))$ can be fully expressed by the active decision $D^{\varnothing}_U(f^{\textnorma

Figures (10)

  • Figure 1: This diagram illustrates how the elements of our model are related to each other. The algorithm's information $X$ determines the recommendation $R$ through the algorithm $f^{\textnormal{rec}}$. This recommendation in turn impacts the agent's (manager's) decisions $D$ in a way that depends on $f^{\textnormal{rec}}$. The agent's decision is also impacted by their information $U$. Both the algorithm's information $X$ and the agent's information $U$ can be predictive of the outcome (ability) $Y$. This outcome, combined with the agent's decision, determines the loss $\ell(Y,D)$. The dashed line between $X$ and $U$ indicates that they may contain common information. The shading of $U$ illustrates the challenge that, from the perspective of the principal (firm), the private information of the agent (manager) may never be directly observed.
  • Figure 2: This diagram expands \ref{['ms-fig:diagram']} by adding potential decisions $D_U(\cdot;f^{\textnormal{rec}})$ explicitly, which determine decisions by $D=D_U(R;f^{\textnormal{rec}})$. The line between the recommendation algorithm and potential decisions points to the challenge that the latter may be affected by the overall design of the algorithm beyond the instance-specific recommendation.
  • Figure 3: Representation of a given set of candidate recommendation algorithms $\mathcal{F}$ that could be implemented in terms of the triage effect TE and the response effect RE. The optimal triage $f^{\textnormal{tri}*}$ minimizes the triage effect over $\mathcal{F}$, while the optimal recommendation rule $f^{\textnormal{rec}*}$ minimizes the sum $TE+RE$. The optimal decision rule $f^{\textnormal{dec}*}$ need not lie on the Pareto frontier that minimizes these two losses, highlighted in red.
  • Figure 4: Summary of how the information available to the subject (the applicant's role) and the information of the algorithm (the applicant's personality type) relate to the applicant's ability (bad or good). This information is shown to all participants in the experiment and is easily accessible throughout their decision-making process.
  • Figure 5: Sample hiring decision from the Predictive treatment.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Proposition 1: Simplified potential outcomes
  • Theorem 1
  • Proposition 2: Triage as learning from mistakes
  • proof : Proof of \ref{['ms-prop:simpPO']}
  • proof : Proof of \ref{['ms-thm:LFM']}
  • proof : Proof of \ref{['ms-prop:trilfm']}