# Spoiler effect

In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof.
The frequency and severity of spoiler effects depends substantially on the voting method. Instant-runoff or ranked-choice voting (RCV), the two-round system (TRS), and especially first-past-the-post (FPP) without winnowing or primary elections are highly sensitive to spoilers (though RCV and TRS less so in some circumstances), and all three rules are affected by center-squeeze and vote splitting. Majority-rule (or Condorcet) methods are only rarely affected by spoilers, which are limited to rare situations called cyclic ties. Rated voting systems are not subject to Arrow's theorem. Whether such methods are spoilerproof depends on the nature of the rating scales the voters use to express their opinions.
Spoiler effects can also occur in some methods of proportional representation, such as the single transferable vote (STV or RCV-PR) and the largest remainders method of party-list representation, where it is called a new party paradox. A new party entering an election causes some seats to shift from one unrelated party to another, even if the new party wins no seats. This kind of spoiler effect is avoided by divisor methods and proportional approval.$^{:Thm.8.3}$

## Motivation

In decision theory, independence of irrelevant alternatives is a fundamental principle of rational choice which says that a decision between two outcomes, A or B, should not depend on the quality of a third, unrelated outcome C. A famous joke by Sidney Morgenbesser illustrates this principle:
   A man is deciding whether to order apple, blueberry, or cherry pie before settling on apple. The waitress informs him that the cherry pie is very good and a favorite of most customers. The man replies "in that case, I'll have the blueberry."
Politicians and social choice theorists have long argued for the unfairness of spoiler effects. The mathematician and political economist Nicolas de Condorcet was the first to study the spoiler effect, in the 1780s.

### Manipulation by politicians

Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by strategic nomination. Such systems may produce an incentive to entry, increasing a candidate's chances of winning if similar candidates join the race, or an incentive to exit, reducing the candidate's chances of winning.
Some systems are particularly infamous for their ease of manipulation, such as the Borda count, which exhibits a particularly severe entry incentive, letting any party "clone their way to victory" by running a large number of candidates. This famously forced de Borda to concede that "my system is meant only for honest men," and eventually led to its abandonment by the French Academy of Sciences.
Other systems exhibit an exit incentive. The vote splitting effect in plurality voting demonstrates this method's strong exit incentive: if multiple candidates with similar views run in an election, their supporters' votes will be diluted, which may cause a unified opposition candidate to win despite having less support. This effect encourages groups of similar candidates to form an organization to make sure they don't step on each other's toes.

## By electoral system

Susceptibility to spoilers :
| Electoral system | Spoiler effect |
| Plurality voting | High |
| Runoffs or RCV | Medium |
| Condorcet methods | Low |
| Score or Medians | Depends |
Different electoral systems have different levels of vulnerability to spoilers. In general, spoilers are common with plurality voting, somewhat common in plurality-runoff methods, rare with majoritarian methods, and with a varying level of spoiler vulnerability with most rated voting methods.

### First-preference plurality

In cases where there are many similar candidates, spoiler effects occur most often in first-preference plurality (FPP). For example, in the United States, vote splitting is common in primaries, where many similar candidates run against each other. The purpose of a primary election is to eliminate vote splitting among candidates from the same party in the general election by running only one candidate. In a two-party system, party primaries effectively turn FPP into a two-round system.
Vote splitting is the most common cause of spoiler effects in FPP. In these systems, the presence of many ideologically-similar candidates causes their vote total to be split between them, placing these candidates at a disadvantage. This is most visible in elections where a minor candidate draws votes away from a major candidate with similar politics, thereby causing a strong opponent of both to win.

### Runoff systems

Plurality-runoff methods like the two-round system and RCV still experience vote-splitting in each round. This produces a kind of spoiler effect called a center squeeze. Compared to plurality without primaries, the elimination of weak candidates in earlier rounds reduces their effect on the final results; however, spoiled elections remain common compared to other systems. As a result, instant-runoff voting still tends towards two-party rule through the process known as Duverger's law. A notable example of this can be seen in Alaska's 2024 race, where party elites pressured candidate Nancy Dahlstrom into dropping out to avoid a repeat of the spoiled 2022 election.

### Tournament (Condorcet) voting

Spoiler effects rarely occur when using tournament solutions, where candidates are compared in one-on-one matchups to determine relative preference. For each pair of candidates, there is a count for how many voters prefer the first candidate in the pair to the second candidate. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which is usually the cause for spoilers in other methods. This pairwise comparison means that spoilers can only occur when there is a Condorcet cycle, where there is no single candidate preferred to all others.
Theoretical models suggest that somewhere between 90% and 99% of real-world elections have a Condorcet winner, and the first Condorcet cycle in a ranked American election was found in 2021. Some systems like the Schulze method and ranked pairs have stronger spoiler resistance guarantees that limit which candidates can spoil an election without a Condorcet winner.$^{:228–229}$

### Rated voting

Rated voting methods ask voters to assign each candidate a score on a scale (e.g. rating them from 0 to 10), instead of listing them from first to last. Highest median and score (highest mean) voting are the two most prominent examples of rated voting rules. Whenever voters rate candidates independently, the rating given to one candidate does not affect the ratings given to the other candidates. Any new candidate cannot change the winner of the race without becoming the winner themselves, which would disqualify them from the definition of a spoiler. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.
The outcome of rated voting depends on the scale used by the voter or assumed by the mechanism. If the voters use relative scales, i.e. scales that depend on what candidates are running, then the outcome can change if candidates who don't win drop out. Empirical results from panel data suggest that judgments are at least in part relative. Thus, rated methods, as used in practice, may exhibit a spoiler effect caused by the interaction between the voters and the system, even if the system itself passes IIA given an absolute scale.

### Proportional representation

Spoiler effects can also occur in some methods of proportional representation, such as the single transferable vote (STV or RCV-PR) and the largest remainders method of party-list representation, where it is called a new party paradox. A new party entering an election causes some seats to shift from one unrelated party to another, even if the new party wins no seats. This kind of spoiler effect is avoided by divisor methods and proportional approval.$^{:Thm.8.3}$

## Spoiler campaign
### United States

A spoiler campaign in the United States is often one that cannot realistically win but can still determine the outcome by pulling support from a more competitive candidate. The two major parties in the United States, the Republican Party and Democratic Party, have regularly won 98% of all state and federal seats. The US presidential elections most consistently cited as having been spoiled by third-party candidates are 1844 and 2000. The 2016 election is more disputed as to whether it contained spoiler candidates or not. For the 2024 presidential election, Republican lawyers and operatives have fought to keep right-leaning third-parties like the Constitution Party off swing state ballots while working to get Cornel West on battleground ballots. Democrats have helped some right-leaning third-parties gain ballot access while challenging ballot access of left-leaning third-parties like the Green Party. According to the Associated Press, the GOP effort to prop up possible spoiler candidates in 2024 appears more far-reaching than the Democratic effort. Barry Burden argues that they have almost no chance of winning the 2024 election but are often motivated by particular issues.
Third party candidates are always controversial because almost anyone could play spoiler. This is especially true in close elections where the chances of a spoiler effect increase. Strategic voting, especially prevalent during high stakes elections with high political polarization, often leads to a third-party that underperforms its poll numbers with voters wanting to make sure their least favorite candidate is not in power. Third-party campaigns are more likely to result in the candidate a third party voter least wants in the White House. Third-party candidates prefer to focus on their platform than on their impact on the frontrunners.

### Notable unintentional spoilers

An unintentional spoiler is one that has a realistic chance of winning but falls short and affects the outcome of the election. Some third-party candidates express ambivalence about which major party they prefer and their possible role as spoiler or deny the possibility.

#### 2009 Burlington mayoral election

In Burlington, Vermont's second IRV election, spoiler Kurt Wright knocked out Democrat Andy Montroll in the second round, leading to the election of Bob Kiss, despite the election results showing most voters preferred Montroll to Kiss. The results of every possible one-on-one election can be completed as follows:
| Andy Montroll (D) | 6262 (Montroll) – 591 (Simpson) | 4570 (Montroll) – 2997 (Smith) | 4597 (Montroll) – 3664 (Wright) | 4064 (Montroll) – 3476 (Kiss) | 4/4 Wins |
| Bob Kiss (P) | 5514 (Kiss) – 844 (Simpson) | 3944 (Kiss) – 3576 (Smith) | 4313 (Kiss) – 4061 (Wright) | 3/4 Wins | IRV winner |
| Kurt Wright (R) | 5270 (Wright) – 1310 (Simpson) | 3971 (Wright) – 3793 (Smith) | 2/4 Wins | Spoiler for Montroll | Spoiler for Montroll |
| Dan Smith (I) | 5570 (Smith) – 721 (Simpson) | 1/4 Wins | | | |
| James Simpson (G) | 0/4 Wins | | | | |
This leads to an overall preference ranking of:
* Montroll – defeats all candidates below, including Kiss (4,064 to 3,476)
* Kiss – defeats all candidates below, including Wright (4,313 to 4,061)
* Wright – defeats all candidates below, including Smith (3,971 to 3,793)
* Smith – defeats Simpson (5,570 to 721) and the write-in candidates
Montroll was therefore preferred over Kiss by 54% of voters, over Wright by 56%, and over Smith by 60%. Had Wright not run, Montroll would have won instead of Kiss.
Because all ballots were fully released, it is possible to reconstruct the winners under other voting methods. While Wright would have won under plurality, Kiss won under IRV, and would have won under a two-round vote or a traditional nonpartisan blanket primary. Montroll, being the majority-preferred candidate, would have won if the ballots were counted using ranked pairs (or any other Condorcet method).

#### 2022 Alaska's at-large congressional district special election

In Alaska's first-ever IRV election, Nick Begich was eliminated in the first round to advance Mary Peltola and Sarah Palin. However, the pairwise comparison shows that Begich was the Condorcet winner while Palin was both the Condorcet loser and a spoiler:
Pairwise comparison matrix by vote totals :
| | Begich | Peltola | Palin |
| Begich | - | 88,126 | 101,438 |
| Peltola | 79,486 | - | 91,375 |
| Palin | 63,666 | 86,197 | - |
Pairwise as a percentage :
| Winner | | Loser | Winner | Loser |
| Begich | vs. | Peltola | 52.6% | vs. 47.4% |
| Begich | vs. | Palin | 61.4% | vs. 38.6% |
| Peltola | vs. | Palin | 51.5% | vs. 48.5% |
In the wake of the election, a poll found 54% of Alaskans, including a third of Peltola voters, supported a repeal of RCV. Observers noted such pathologies would have occurred under Alaska's previous primary system as well, leading several to suggest Alaska adopt any one of several alternatives without this behavior.