The Condorcet Paradox: Why Instant-Runoff Voting Can Eliminate the Most Popular Candidate

Instant-runoff voting guarantees that a third-party candidate will never spoil an election for a major contender, but it cannot guarantee that the most broadly popular candidate actually wins. The system's mathematical elimination rules routinely discard consensus candidates who would defeat every other rival in a direct head-to-head matchup.[4]

This structural vulnerability is known as a Condorcet failure. It occurs because instant-runoff systems eliminate candidates based strictly on their first-choice support, ignoring how many voters ranked them second or third until it is too late.

When a polarizing race features a strong liberal, a strong conservative, and a moderate, the moderate often finishes third in initial preferences. Under instant-runoff rules, that moderate is eliminated immediately, even if majorities from both opposing camps would have preferred them over the opposing extreme.[2]

The mechanism forces a choice between two different definitions of democratic consent. Jurisdictions must decide whether an election should reward the candidate with the most passionate base, or the candidate who is most acceptable to the broadest cross-section of the electorate.[4]

"Ranked choice voting does exactly what it promises by eliminating the spoiler effect, but it does not promise to elect the Condorcet winner," notes the Center for Election Science. "It measures core support first, and consensus second."

Solving the Spoiler Effect

Municipalities and states adopt instant-runoff ballots primarily to fix the plurality voting trap. In a traditional election, two ideologically similar candidates split the majority vote, allowing a candidate opposed by most of the electorate to win with a narrow plurality.[3]

Instant-runoff ballots solve this by allowing voters to rank their preferences. If no candidate secures an outright majority of first-choice votes, the candidate with the fewest top-tier votes is eliminated from the tally.[3]

The ballots cast for that eliminated candidate are not discarded. Instead, election officials transfer those votes to each voter's second choice, recalculating the totals until one candidate crosses the 50 percent threshold.[3]

This transfer mechanism means a voter can safely rank a fringe candidate first without inadvertently helping their least favorite candidate win. If the fringe candidate fails to gain traction, the voter's ballot simply flows to a more viable backup option.[3]

FairVote, a leading advocacy group for the system, argues this fundamentally changes campaign incentives. "Candidates must compete for second-choice votes from their opponents' supporters, which discourages negative campaigning and rewards broad coalition building," the organization states in its operational guidelines.[3]

The First-Round Squeeze

The system's vulnerability lies entirely in how it decides who to eliminate. Because the algorithm only looks at the top active ranking on each ballot, it is blind to the depth of a candidate's secondary support during the initial rounds.[2]

A consensus candidate might be the second choice of 80 percent of the electorate. However, if they are the first choice of only 15 percent of voters, they will likely finish at the bottom of the initial tally and face immediate elimination.

Once a candidate is eliminated, their name is permanently removed from the mathematical simulation. It does not matter if the remaining voters would have overwhelmingly preferred them in the final round; the system has already erased them from the board.[4]

This dynamic routinely punishes centrist candidates in highly polarized environments. Voters on the left rank the liberal first and the centrist second, while voters on the right rank the conservative first and the centrist second.[2]

The centrist becomes the only candidate capable of uniting the electorate, yet they receive the fewest first-choice votes. The instant-runoff algorithm eliminates the unifying figure first, leaving the electorate to choose between the two polarizing extremes.

The Alaska Anomaly

The August 2022 special election for Alaska's at-large congressional district provided a flawless real-world demonstration of this mathematical quirk. The race featured Democrat Mary Peltola and two Republicans, Sarah Palin and Nick Begich.[1]

In the first round of voting, Peltola secured 40 percent of the first-choice ballots, Palin took 31 percent, and Begich finished last with 28.5 percent. Following the instant-runoff rules, state election officials eliminated Begich.[1]

When Begich's ballots were redistributed to their second choices, Peltola defeated Palin in the final round by a margin of 51.5 percent to 48.5 percent. The system functioned exactly as designed, preventing the two Republicans from spoiling the race for each other.[1]

However, a subsequent analysis of the cast vote record revealed a stark mathematical paradox. If the election had been conducted as a series of one-on-one matchups, Begich would have defeated both of his opponents by comfortable margins.[2]

In a hypothetical head-to-head race against Peltola, Begich commanded 87,887 votes to her 79,444, because Palin's conservative supporters overwhelmingly preferred him. Against Palin, Begich won 100,210 to 63,555, drawing heavy support from Peltola's Democratic base.[1]

Begich was the only candidate who held a majority against every other challenger. Yet because his support was broad rather than deep, the instant-runoff system eliminated the most popular overall candidate in the very first round.[4]

The Condorcet Standard

Election theorists evaluate voting systems against a benchmark called the Condorcet criterion, named for the 18th-century French mathematician Nicolas de Condorcet. The principle states that if a candidate exists who can beat every other candidate in isolated two-way races, that candidate must win the election.

Plurality voting routinely fails the Condorcet test because of vote splitting. Instant-runoff voting also fails the test, albeit less frequently, because of the first-round elimination squeeze that discards consensus candidates before their broad support can be tallied.[2]

Alternative systems, such as approval voting or Condorcet-compliant matrix voting, are designed to pass this specific mathematical test. Under approval voting, citizens simply check a box for every candidate they find acceptable, naturally elevating the most broadly palatable option.

"When you force voters to rank candidates, you are asking them to prioritize passion over consensus," notes a 2024 review in Electoral Studies. "The Condorcet winner is often everyone's second choice, and instant-runoff rules are uniquely hostile to second choices."[2]

Despite this mathematical flaw, instant-runoff voting remains the most widely adopted alternative to traditional plurality elections in the United States, largely because it is easier to explain to the public than matrix-based pairwise counting.[4]

Mathematical Impossibilities

The failure to guarantee a Condorcet winner is not necessarily a fatal flaw, but rather a reflection of systemic trade-offs. In 1951, economist Kenneth Arrow proved mathematically that no ranked voting system can perfectly satisfy all criteria for fairness simultaneously.[5]

Arrow's Impossibility Theorem demonstrates that fixing one vulnerability in a voting system inevitably creates another. A system that guarantees the Condorcet winner might fail the monotonicity criterion, meaning a candidate could theoretically lose because they received too many first-place votes.[5]

Lawmakers adopting instant-runoff ballots are making a deliberate policy choice. They are prioritizing the elimination of the spoiler effect and the requirement for a final-round majority over the guarantee of electing a theoretical consensus winner.[4]

For most elections, this trade-off remains entirely theoretical. The candidate with the most first-choice votes is usually also the Condorcet winner, meaning the instant-runoff algorithm and the pairwise matrix produce the exact same outcome.[2]

But in highly fractured, polarized electorates, the math diverges. As more jurisdictions adopt ranked ballots to manage crowded fields, the elimination of broadly popular centrists will transition from a mathematical edge case into a routine political reality.[4]