Candidate Moderation under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Study

While theoretical models suggest Condorcet voting methods produce more moderate winners than Instant Runoff Voting, this study demonstrates that incorporating realistic voter behaviors, such as partial ballots, significantly diminishes the moderating advantage of Condorcet methods.

The Gist

Imagine you are organizing a huge party to pick a new leader for your neighborhood. You have a big problem: the neighborhood is very divided. Half the people love spicy food, and the other half only eat bland food. You want to pick a leader who can get along with everyone, not just one side.

This paper is about testing two different ways to vote to see which one is better at finding that "middle-ground" leader.

The Two Contenders

1. The "Instant Runoff" (IRV): This is like a game of musical chairs. Everyone votes for their favorite. If no one gets a majority, the person with the fewest votes is kicked out. Their supporters' votes are then passed to their second choice. This keeps happening until someone wins. This is the system currently used in places like Maine and Alaska.
2. The "Condorcet" Method: This is like a giant round-robin tournament. You pit every candidate against every other candidate one-on-one. If Candidate A beats Candidate B, and Candidate A beats Candidate C, then Candidate A is the winner. The idea is that this method finds the person who is the "best compromise" for the most people.

The Previous Study (The "Perfect World" Theory)

A few years ago, some researchers (Atkinson, Foley, and Ganz) ran computer simulations to see which method worked better. They built a "Perfect World" model with three strict rules:

• Perfect Knowledge: Every voter knows exactly where every candidate stands on the political spectrum.
• Perfect Participation: Every single voter shows up to vote.
• Perfect Ballots: Every voter ranks every single candidate from first to last.

Their Result: In this perfect world, the Condorcet method was a superhero. It consistently picked leaders who were right in the middle (moderate), while the Instant Runoff method often picked leaders who were more extreme (on the edges). They concluded that if you want to stop polarization, you should use Condorcet.

The New Study (The "Real World" Reality Check)

The authors of this new paper (McCune et al.) said, "Wait a minute. Real life isn't a perfect world."

In real elections, people are messy:

• They don't know everything: Voters might be confused about where a candidate actually stands.
• They don't show up: Some people skip the election entirely.
• They don't rank everyone: This is the big one. In real ranked-choice elections, many people only vote for their one favorite candidate and leave the rest blank. This is called a "bullet vote" or a truncated ballot. It's like ordering a pizza and only saying "I want pepperoni" without telling the chef what you'd accept if they ran out of pepperoni.

The researchers built new computer simulations that included these messy, real-world behaviors. They used data from the Cooperative Election Survey (a massive poll of American voters) to make their models realistic.

The Big Surprise

When they added the "messy" factors (especially people only ranking one candidate), the results changed completely.

• The Gap Disappeared: The huge advantage the Condorcet method had in the "Perfect World" vanished. In the "Real World" simulations, Condorcet and Instant Runoff picked leaders who were about equally moderate.
• The "Middle" Got Harder to Reach: In fact, under realistic conditions, it became harder for a truly moderate candidate to win using the Condorcet method.
• New Heroes Emerged: The study found that other voting methods, like Bucklin and Borda (which are different ways of counting points), actually did a better job of picking moderate leaders than Condorcet did when real-world messiness was included.

The Analogy: The Pizza Party

Think of it like this:

In the Perfect World, everyone at the party fills out a detailed survey saying exactly how much they like every topping. The Condorcet method looks at all these surveys and finds the topping (leader) that everyone agrees is "okay." It works great.

In the Real World, most people just shout, "I want Pepperoni!" and walk away. They don't care about the other toppings.

• When the Condorcet method tries to calculate the "best compromise" based on these incomplete shouts, it gets confused. It might pick a candidate who is actually quite polarizing because the data is missing.
• The Instant Runoff method just keeps eliminating the least popular shouts until someone has enough support. It ends up with a result that is surprisingly similar to the Condorcet method.

The Takeaway

The main point of this paper is: Don't trust models that assume people are robots.

The previous study suggested that Condorcet voting is the magic bullet for fixing political polarization. This new study says, "Not so fast." Once you account for the fact that real people are lazy, confused, or only vote for their favorite, Condorcet isn't nearly as special as we thought. It doesn't guarantee a moderate winner anymore, and other methods might actually work just as well (or better).

The Bottom Line: If you are a city planner or a politician trying to decide which voting system to use, don't just look at the fancy math from the "Perfect World." Look at how real people actually behave, because that changes the outcome completely.

Technical Summary

Here is a detailed technical summary of the paper "Candidate Moderation Under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Survey" by McCune et al.

1. Problem Statement

The paper addresses a debate in political science and social choice theory regarding which voting methods best mitigate political polarization by electing "moderate" candidates (those ideologically close to the median voter).

• Context: Recent literature, specifically Atkinson, Foley, and Ganz (2024) [1], utilized one-dimensional spatial models based on Cooperative Election Survey (CES) data to argue that Condorcet methods (which elect the candidate who wins all head-to-head matchups) are significantly superior to Instant Runoff Voting (IRV) in electing moderate candidates.
• The Gap: The prior work relied on "theoretically ideal" assumptions: voters possess perfect information about candidate positions, all voters cast complete preference rankings (no truncation), and all eligible voters participate.
• Research Question: Do the conclusions of Atkinson et al. hold when realistic voter behaviors—specifically ballot truncation (voters ranking only some candidates), abstention, and voter uncertainty—are incorporated into the simulation models?

2. Methodology

The authors extend the framework of Atkinson et al. by constructing new simulation models using CES data that introduce realistic constraints.

A. Data and Voter Distribution

• Source: Cooperative Election Survey (CES) data.
• Spatial Model: A one-dimensional ideological spectrum from $-0.5$ (Extreme Left) to $0.5$ (Extreme Right).
• Distribution Types:
  • Trimodal: Based on self-identification (Very Liberal to Very Conservative), resulting in three clusters (Liberal, Middle, Conservative).
  • Bimodal: Derived from the trimodal data by shifting "Middle of the Road" voters to their partisan leanings, creating a highly polarized distribution.
• Candidate Selection: Uses the "citizen-candidate" model where $k \in \{3, 4\}$ candidates are randomly selected from the voter pool. Voter preferences are determined by Euclidean distance to candidates.

B. The Six Simulation Models

The authors define six models to test the robustness of previous findings, treating specific behaviors as binary switches:

1. Theoretical Ideal: Complete ballots, full turnout, perfect information (replicates [1]).
2. Ideological Truncation: Voters cast truncated ballots (bullet votes) if candidates are ideologically distant (distance $> 0.37$ for 3 candidates, $> 0.26$ for 4).
3. Random Truncation: Voters cast truncated ballots based on fixed probabilities derived from real-world IRV data (e.g., 35% chance of a bullet vote).
4. Abstention: Voters only participate if a candidate is within a specific ideological distance (simulating turnout rates of 60–70%).
5. Noise: Voters perceive candidate positions with random error (up to $\pm 0.14$), simulating uncertainty.
6. Most Realistic: Combines Ideological Truncation, Abstention, and Noise.

C. Voting Methods Analyzed

The study compares five methods:

• Plurality: First-past-the-post (baseline).
• IRV: Eliminate lowest first-place votes, transfer until majority.
• Condorcet (Minimax): Elects the candidate with the "smallest worst" head-to-head loss.
• Bucklin: Rounds of counting first and second choices until a majority is reached.
• Borda: Points assigned based on rank position (pessimistic model for truncated ballots).

D. Metrics

The primary metric is the average distance from the median voter to the elected winner. A smaller distance indicates a more "moderate" outcome. The authors calculate the relative difference between IRV and Condorcet distances to quantify the "moderating advantage."

3. Key Contributions

1. Integration of Realistic Truncation: The paper is among the first to systematically incorporate truncated ballots (a common real-world phenomenon) into spatial models of ranked-choice voting.
2. Refutation of Theoretical Superiority: It demonstrates that the significant moderating advantage of Condorcet methods over IRV, found in idealized models, largely disappears when realistic voter behaviors are modeled.
3. Identification of Superior Alternatives: The study identifies that under realistic conditions, Bucklin and Borda methods often outperform both Condorcet and IRV in electing candidates closest to the median voter.
4. Strategic Implications: It highlights how candidate strategies (e.g., encouraging bullet voting) might shift under Condorcet rules, potentially undermining the theoretical benefits.

4. Key Results

A. The Disappearance of the Condorcet Advantage

• Theoretical Ideal: Confirms Atkinson et al.; Condorcet winners are significantly closer to the median voter than IRV winners (e.g., in bimodal 4-candidate elections, IRV winners were ~40% more extreme).
• Realistic Models: When Ideological Truncation or the Most Realistic model is applied, the gap between IRV and Condorcet collapses.
  • In the Most Realistic model (bimodal, 4 candidates), the relative difference drops from 40.6% (Ideal) to 2.8%.
  • In some scenarios, IRV winners are actually closer to the median voter than Condorcet winners.
• Driver of Change: Ballot truncation is identified as the primary factor reducing the moderating advantage of Condorcet methods. Random truncation and noise have less impact.

B. Performance of Other Methods

• Under realistic models, Bucklin and Borda frequently select winners closer to the median voter than Condorcet or IRV.
• In bimodal 4-candidate elections under the Most Realistic model:
  • Bucklin was the most moderating method in 29 out of 50 states.
  • Borda was the most moderating in 21 states.
  • Condorcet was the most moderating in 0 states.
  • IRV was the most moderating in only 1 state (Vermont).

C. Variability by State and Distribution

• The degree to which the "Condorcet advantage" disappears varies by state characteristics (mean and variance of the voter distribution).
• States with high variance (polarized) and low mean (centrally located) show the largest collapse in the IRV/Condorcet gap when truncation is introduced.
• The effect is generally stronger in 4-candidate elections than in 3-candidate elections.

5. Significance and Implications

• Challenge to Reform Advocacy: The paper suggests that arguments for adopting Condorcet methods specifically to combat polarization (based on theoretical models) may be overstated. In real-world settings with partial ballots, Condorcet methods do not offer a distinct moderating advantage over IRV.
• Normative Concerns:
  • Legitimacy: Condorcet winners often have the fewest first-place votes, which could lead to public perception of illegitimacy ("the candidate with the fewest votes won").
  • Strategic Behavior: The authors argue that if Condorcet methods were adopted, candidates might strategically encourage their supporters to cast bullet votes to disrupt the Condorcet cycle or prevent a centrist candidate from winning, potentially leading to more truncation rather than less.
• Methodological Warning: The study serves as a cautionary tale for social choice research, emphasizing that purely theoretical models with idealized assumptions (complete information, full rankings) may fail to predict real-world electoral outcomes.

Conclusion

The authors conclude that while Condorcet methods are theoretically robust, their practical ability to elect moderate candidates is significantly diminished by realistic voter behaviors, particularly ballot truncation. Consequently, Condorcet methods may not be the optimal tool for reducing polarization, and other methods like Bucklin or Borda might be more effective in actual elections. The paper calls for further empirical study of Condorcet methods in jurisdictions that might adopt them.