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Optimal Strategies in Ranked Choice Voting

Sanyukta Deshpande, Nikhil Garg, Sheldon Jacobson

TL;DR

This paper addresses the complexity of optimal strategies in Ranked Choice Voting (RCV) and Single Transferable Vote (STV) by formulating a structure-based framework that separates social choice orders from per-round sequences. It develops polynomial-time reductions and an allocation-based algorithm to compute minimal vote-addition strategies that realize target outcomes, and demonstrates substantial practical gains via reductions on real data from the 2024 US Republican Primary. Theoretical results characterize when strategic voting or vote additions are beneficial, both under perfect and imperfect information, with coalition effects arising primarily under uncertainty. A case study shows that while predators of spoilers can be effective in theory, such strategies are fragile under polling noise, underscoring the nuanced, context-dependent nature of manipulation in multistage transfer voting. Overall, the work provides a tractable, principled approach to analyzing and forecasting RCV/STV dynamics and informs media and campaign strategy under uncertainty.

Abstract

Ranked Choice Voting (RCV) and Single Transferable Voting (STV) are widely valued; but are complex to understand due to intricate per-round vote transfers. Questions like determining how far a candidate is from winning or identifying effective election strategies are computationally challenging as minor changes in voter rankings can lead to significant ripple effects - for example, lending support to a losing candidate can prevent their votes from transferring to a more competitive opponent. We study optimal strategies - persuading voters to change their ballots or adding new voters - both algorithmically and theoretically. Algorithmically, we develop efficient methods to reduce election instances while maintaining optimization accuracy, effectively circumventing the computational complexity barrier. Theoretically, we analyze the effectiveness of strategies under both perfect and imperfect polling information. Our algorithmic approach applies to the ranked-choice polling data on the US 2024 Republican Primary, finding, for example, that several candidates would have been optimally served by boosting another candidate instead of themselves.

Optimal Strategies in Ranked Choice Voting

TL;DR

This paper addresses the complexity of optimal strategies in Ranked Choice Voting (RCV) and Single Transferable Vote (STV) by formulating a structure-based framework that separates social choice orders from per-round sequences. It develops polynomial-time reductions and an allocation-based algorithm to compute minimal vote-addition strategies that realize target outcomes, and demonstrates substantial practical gains via reductions on real data from the 2024 US Republican Primary. Theoretical results characterize when strategic voting or vote additions are beneficial, both under perfect and imperfect information, with coalition effects arising primarily under uncertainty. A case study shows that while predators of spoilers can be effective in theory, such strategies are fragile under polling noise, underscoring the nuanced, context-dependent nature of manipulation in multistage transfer voting. Overall, the work provides a tractable, principled approach to analyzing and forecasting RCV/STV dynamics and informs media and campaign strategy under uncertainty.

Abstract

Ranked Choice Voting (RCV) and Single Transferable Voting (STV) are widely valued; but are complex to understand due to intricate per-round vote transfers. Questions like determining how far a candidate is from winning or identifying effective election strategies are computationally challenging as minor changes in voter rankings can lead to significant ripple effects - for example, lending support to a losing candidate can prevent their votes from transferring to a more competitive opponent. We study optimal strategies - persuading voters to change their ballots or adding new voters - both algorithmically and theoretically. Algorithmically, we develop efficient methods to reduce election instances while maintaining optimization accuracy, effectively circumventing the computational complexity barrier. Theoretically, we analyze the effectiveness of strategies under both perfect and imperfect polling information. Our algorithmic approach applies to the ranked-choice polling data on the US 2024 Republican Primary, finding, for example, that several candidates would have been optimally served by boosting another candidate instead of themselves.
Paper Structure (41 sections, 16 theorems, 20 tables, 7 algorithms)

This paper contains 41 sections, 16 theorems, 20 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Related literature
  3. Model
  4. Notation and Framework
  5. Structural properties of the social choice function
  6. Algorithmic Framework
  7. Optimizing to reach an outcome structure
  8. Efficiently navigating the search space
  9. Reduction of the candidates set
  10. Reducing the space of sequences
  11. 2024 US Republican Primaries Case Study
  12. Data and Methods
  13. Results
  14. Strategies under perfect information
  15. Strategies to win the election
  16. ...and 26 more sections

Key Result

Proposition 2.1

With suitable tie-breaking, each voter data $\mathcal{B}$ corresponds to a single structure (a pair of an order and a sequence). For each structure, a set of non-linear constraints involving variables $V^i_{a, b,\dots, j}$ defines a distinct region in the voter ballot space where the election outcom

Theorems & Definitions (36)

  • Example 2.1
  • Proposition 2.1
  • Theorem 3.1
  • proof : Proof Sketch
  • Theorem 3.2
  • proof : Proof Sketch
  • Proposition 3.3
  • proof : Proof Sketch
  • Proposition 3.3
  • proof : Proof Sketch
  • ...and 26 more