The Mathematical Threshold of Ballot Exhaustion in Ranked-Choice Voting

In the final tabulation round of the August 2022 special election for Alaska's single US House seat, 11,222 ballots were no longer in the count. The voters who cast them had participated in the election, but because they did not rank the candidates who advanced to the final pairing, their ballots became "exhausted." Representative Mary Peltola secured the seat with 91,266 votes against Sarah Palin's 86,026. The combined total of those active ballots—177,292—was the denominator used to calculate Peltola's 51.5 percent majority.

Ranked-choice voting (RCV) is designed to ensure that a winning candidate secures a majority of the vote, eliminating the plurality outcomes common in first-past-the-post systems. However, the mathematical definition of that majority depends entirely on the denominator. As candidates are eliminated from the bottom up, voters who only ranked eliminated candidates drop out of the active pool. The majority threshold is not 50 percent plus one of all ballots cast, but 50 percent plus one of the ballots that survive to the final round.[2]

This structural mechanic, known as ballot exhaustion, alters the threshold required to win. An analysis of three major RCV implementations reveals that the final round denominator consistently shrinks by between 4.6 percent and 14.7 percent compared to initial turnout. The reduction occurs primarily because voters either choose not to rank all available slots, or because the ballot design limits the number of candidates they can rank.[2]

During the 2018 midterm elections, Maine became the first state to use RCV for a federal congressional race. In the Second Congressional District, incumbent Bruce Poliquin led the first round with 134,184 votes to Jared Golden's 132,013, with two independent candidates capturing the remainder. Because no candidate cleared 50 percent, the independents were eliminated.

By the final round, 8,253 ballots had exhausted. Golden won the seat with 142,440 votes to Poliquin's 138,931. Golden's total represented 50.6 percent of the 281,371 active ballots in the final round, but only 49.1 percent of the 289,624 total ballots cast in the race. The Maine Department of the Secretary of State's official guidance explicitly notes this mechanic: "If you choose to vote for only one candidate, and that candidate is eliminated, your ballot will not factor into subsequent rounds."

The rate of exhaustion scales with the size of the candidate field and the complexity of the ballot. In the June 2021 New York City Democratic mayoral primary, 13 candidates appeared on the ballot, and voters were permitted to rank up to five. Eric Adams led the first round with 289,403 votes, representing 30.7 percent of the 942,066 total ballots cast.

It took eight rounds of elimination to reduce the field to the final two candidates, Adams and Kathryn Garcia. By the eighth round, 138,378 ballots had exhausted—14.7 percent of the initial turnout. Adams won with 404,513 votes to Garcia's 397,316. While Adams secured 50.4 percent of the final-round active ballots, his winning total represented 42.9 percent of the voters who initially showed up to the polls.

Exhaustion occurs for two distinct reasons: voluntary truncation and involuntary truncation. Voluntary truncation happens when a voter actively chooses to "bullet vote"—selecting only their preferred candidate and leaving the rest blank—or stops ranking after their second or third choice. If all of their ranked choices are eliminated, they have effectively abstained from the remaining contest.[2]

Involuntary truncation occurs when a voter ranks the maximum number of candidates allowed by the ballot design, but all of those candidates are still eliminated. In the New York City primary, a voter who faithfully ranked five candidates could still see their ballot exhaust if none of those five made it to the final two. The Congressional Research Service notes in its 2023 evaluation that "jurisdictions must balance the physical limitations of ballot design with the mathematical risk of involuntary ballot exhaustion."[1]

Proponents of ranked-choice systems argue that voluntary exhaustion is a feature of voter agency, not a flaw in the system. If a voter genuinely has no preference between the final two candidates, an exhausted ballot accurately records their refusal to choose. In a traditional runoff election held weeks later, this same dynamic manifests as a drop in voter turnout. RCV simply processes that drop-off instantly.[2]

Critics point out that the system relies on voters fully understanding the consequences of truncation. A voter who bullet-votes for a fringe candidate under the mistaken belief that ranking others will harm their favorite has inadvertently disenfranchised themselves from the deciding round. This dynamic places a heavy burden on election administrators to conduct comprehensive voter education campaigns before implementation.[2]

Some jurisdictions outside the United States solve the exhaustion problem by mandating full preferences. In Australia's federal elections, which use a compulsory preferential voting system, a ballot is only valid if the voter numbers every single box. This eliminates ballot exhaustion entirely, ensuring the final denominator matches the initial turnout. However, it increases the rate of "informal" or spoiled ballots, as voters who make a numbering error or refuse to rank a candidate they despise have their entire ballot discarded.[2]

The mathematical reality of the shrinking denominator forces a shift in campaign strategy. In a plurality system, campaigns focus on turning out their base and suppressing the opponent's base. In an RCV system, a campaign must aggressively court the second- and third-choice preferences of rival factions to ensure those ballots flow to them rather than exhausting.[2]

The debate over ranked-choice voting often centers on its ability to eliminate the "spoiler effect" of third-party candidates. Yet the mechanics of tabulation show that the system does not magically produce a candidate supported by an absolute majority of the electorate. It produces a candidate supported by a majority of the voters who expressed a preference among the final options, relying on the quiet subtraction of those who did not.[2]