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Pairwise Beats All-at-Once: Behavioral Gains from Sequential Choice Presentation

Dipankar Das

TL;DR

Digital marketplaces impose large, simultaneous choice sets that tax bounded rationality, risking context-dependent and suboptimal decisions. The authors formalize the Sequential Rationality Hypothesis (SRH) within the Random Attention Model (RAM), introducing a binary, sequential decision process that recursively compares options to preserve the utility-maximizing choice. Theoretical results show that, under monotonic attention, sequential pairwise offering can yield a higher probability of selecting the true maximizer than simultaneous offering, with key expressions $S_{\mathrm{SIM}} = \alpha_3^{3}\beta_3$ and $S_{\mathrm{SEQ}} = (\alpha_2^{2}\beta_2)^2 = \alpha_2^{4}\beta_2^{2}$ and the sufficient condition $\alpha_2^{4}\beta_2^{2} \ge \alpha_3^{3}\beta_3$. A numerical RAM illustration supports the mechanism, and the work discusses policy and platform design implications to structure choice environments that reduce cognitive costs and improve welfare, while noting the need for empirical validation. $^${}_{ }$The framework integrates cognitive realism with testable predictions, offering a path to better digital-market interfaces and regulatory guidance.$

Abstract

This paper presents the Sequential Rationality Hypothesis, which argues that consumers are better able to make utility-maximizing decisions when products appear in sequential pairwise comparisons rather than in simultaneous multi-option displays. Although this involves higher cognitive costs than the all-at-once format, the current digital market, with its diverse products listed by review ratings, pricing, and paid products, often creates inconsistent choices. The present work shows that preparing the list sequentially supports more rational choice, as the consumer tries to minimize cognitive costs and may otherwise make an irrational decision. If the decision remains the same on both offers, then that is a consistent preference. The platform uses this approach by reducing cognitive costs while still providing the list in an all-at-once format rather than sequentially. To show how sequential exposure reduces cognitive overload and prevents context-dependent errors, we develop a bounded attention model and extend the monotonic attention rule of the random attention model to theorize the sequential rational hypothesis. Using a theoretical design with common consumer goods, we test these hypotheses. This theoretical model helps policymakers in digital market laws, behavioral economics, marketing, and digital platform design consider how choice architectures may improve consumer choices and encourage rational decision-making.

Pairwise Beats All-at-Once: Behavioral Gains from Sequential Choice Presentation

TL;DR

Digital marketplaces impose large, simultaneous choice sets that tax bounded rationality, risking context-dependent and suboptimal decisions. The authors formalize the Sequential Rationality Hypothesis (SRH) within the Random Attention Model (RAM), introducing a binary, sequential decision process that recursively compares options to preserve the utility-maximizing choice. Theoretical results show that, under monotonic attention, sequential pairwise offering can yield a higher probability of selecting the true maximizer than simultaneous offering, with key expressions and and the sufficient condition . A numerical RAM illustration supports the mechanism, and the work discusses policy and platform design implications to structure choice environments that reduce cognitive costs and improve welfare, while noting the need for empirical validation. {}_{ }

Abstract

This paper presents the Sequential Rationality Hypothesis, which argues that consumers are better able to make utility-maximizing decisions when products appear in sequential pairwise comparisons rather than in simultaneous multi-option displays. Although this involves higher cognitive costs than the all-at-once format, the current digital market, with its diverse products listed by review ratings, pricing, and paid products, often creates inconsistent choices. The present work shows that preparing the list sequentially supports more rational choice, as the consumer tries to minimize cognitive costs and may otherwise make an irrational decision. If the decision remains the same on both offers, then that is a consistent preference. The platform uses this approach by reducing cognitive costs while still providing the list in an all-at-once format rather than sequentially. To show how sequential exposure reduces cognitive overload and prevents context-dependent errors, we develop a bounded attention model and extend the monotonic attention rule of the random attention model to theorize the sequential rational hypothesis. Using a theoretical design with common consumer goods, we test these hypotheses. This theoretical model helps policymakers in digital market laws, behavioral economics, marketing, and digital platform design consider how choice architectures may improve consumer choices and encourage rational decision-making.
Paper Structure (54 sections, 14 theorems, 53 equations, 2 figures, 1 table)

This paper contains 54 sections, 14 theorems, 53 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Theoretical Research
  4. Experimental Literature
  5. Bounded rationality & limited attention
  6. Limited consideration & random attention
  7. Sequential vs simultaneous evaluation
  8. Context effects that plague simultaneous menus
  9. Choice overload & assortment complexity
  10. Applied Marketing Literature Supporting Sequential Rationality Hypothesis
  11. Research Gap:
  12. Model
  13. Random Attention Theory and Sequential Rationality
  14. Attention Structure
  15. Preliminaries
  16. ...and 39 more sections

Key Result

Proposition 1

If the effective binary parameter satisfies $p_2 \ge p_3^{3/4}$, then $P_{\mathrm{SEQ}} \ge P_{\mathrm{SIM}}$. In particular, any modest uplift $p_2/p_3 \ge p_3^{-1/4}$ suffices.

Figures (2)

  • Figure 1: Sequential Binary Comparisons under the SRH Model. Note: $\mu(\{A,C\}) = 0.4$ represents the probability of choosing $A$ over $C$ in a binary setting.
  • Figure 2: Comparison of Sequential and Simultaneous Choice Models

Theorems & Definitions (23)

  • Definition 1: Choice Rule
  • Definition 2: Latent Attention Rule
  • Definition 3: Monotonic Attention
  • Definition 4: Cognitive Costs
  • Definition 5: Revised Choice Rule Under Monotone Attention
  • Remark 1
  • Proposition 1: Binary advantage threshold
  • Remark 2: Interpreting the empirical claim
  • Definition 6: Architectures and success
  • Lemma 1: Strengthened setup formulas
  • ...and 13 more