In social choice theory and politics, the spoiler effect or refers to a situation where a losing candidate affects the results of an election simply by participating, assuming voter opinions don't change.[1][2] If a major candidate is perceived to have lost an election because of a minor candidate, the minor candidate is called a spoiler candidate and the major candidate is said to have been spoiled. Often times the term spoiler will be applied to candidates or situations which do not meet the full definition, typically in real-world scenarios where the introduction of a new candidate can cause voters to change their opinions, either through their campaign or merely by existing. If a voting system is not affected by spoilers under this definition, it satisfies the independence of irrelevant alternatives criterion.[3]
Arrow's impossibility theorem demonstrates that all rank-based voting systems are vulnerable to the spoiler effect. However, the frequency and severity of spoiler effects depends substantially on the voting method. Plurality is highly sensitive to spoilers while instant-runoff is less so, with both typically exhibiting this phenomenon through center-squeeze or vote splitting.[4][5] Majority-rule methods are only rarely affected by spoilers, which are limited to rare situations called cyclic ties.[6][7][8] Rated voting systems are not subject to Arrow's theorem, and many such systems are spoilerproof, so long as the defining assumption about voter opinions remains valid.[3][9][10]
Spoiler effects also occur in some methods of proportional representation, such as the single transferable vote and the largest remainders method of party-list representation. Here, a new party entering an election can cause seats to shift from one unrelated party to another, even if the new party wins no seats; this is known as the new states paradox.
In decision theory, independence of irrelevant alternatives is a fundamental principle of rationality, that says the choice between two outcomes, A or B, should not depend on an unrealized outcome, C. A famous joke by Sidney Morgenbesser illustrates this principle:
A man is deciding whether to order apple or blueberry pie before settling on apple. The waitress informs him that cherry pie is also an option, to which the man replies "in that case, I'll have the blueberry."
Amongst a long list of sometimes-conflicting voting criteria, activists and some social choice theorists have argued that voting methods should be spoiler-independent. While the concept in-and-of-itself is not controversial, strict mathematical satisfaction can be in direct conflict with other properties that are also considered valuable. The mathematician and political economist Marquis de Condorcet studied the spoiler effect as early as 1780s.[11]
Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by strategic nomination. Some systems are particularly infamous for their ease of manipulation, such as the Borda count, which lets 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,"[12][13] and eventually led to its abandonment by the French Academy of Sciences.[13]
Vote-splitting systems like choose-one and instant-runoff voting have the opposite problem: because running many similar candidates at once can make it difficult for any one of them to win the election, these systems tend to concentrate power in the hands of parties and political machines. The parties signal to the voters they should focus their support on a particular candidate. In many cases, this leads plurality voting systems to behave like a de facto two-round system, where the top-two candidates are nominated by party primaries.[citation needed]
In some situations, a spoiler can extract concessions from other candidates by threatening to remain in the race unless they are bought off, typically with a promise of a high-ranking political position.[citation needed]
Different electoral systems have different levels of vulnerability to spoilers. As a rule of thumb, spoilers are extremely common with plurality voting, common in plurality-runoff methods, rare with paired counting (Condorcet), and impossible with rated voting.[note 1]
Plurality-runoff methods like the two-round system[14] and instant-runoff voting[9] still suffer from vote-splitting in each round though they reduce the effect. As a result, they do not eliminate the spoiler effect. The elimination of weak spoilers in earlier rounds somewhat reduces their effects on the results compared to single-round plurality voting, but spoiled elections remain common, moreso than in other systems.[10]
Modern tournament voting eliminates vote splitting effects completely, because every one-on-one matchup is evaluated independently.[14] If there is a Condorcet winner, Condorcet methods are completely invulnerable to spoilers; in practice, somewhere between 90% and 99% of real-world elections have a Condorcet winner.[15][16] Some systems like ranked pairs have even stronger spoilerproofing guarantees that are applicable to most situations without a Condorcet winner.
Cardinal voting methods can be fully immune to spoiler effects.[9][10]
Vote splitting most easily occurs in plurality voting.[17][better source needed] In the United States vote splitting most commonly occurs in primary elections. The purpose of primary elections is to eliminate vote splitting among candidates in the same party before the general election. If primary elections or party nominations are not used to identify a single candidate from each party, the party that has more candidates is more likely to lose because of vote splitting among the candidates from the same party. In a two-party system, party primaries effectively turn plurality voting into a two-round system.
Vote splitting is the most common cause of spoiler effects in the commonly-used plurality vote and two-round runoff systems. 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.[18] 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.[18][19]
Spoilers also occur in the two-round system and instant-runoff voting at a substantially higher rate than for modern pairwise-counting or rated voting methods, though slightly less often than in plurality.[20][21] As a result, instant-runoff voting still tends towards two-party rule.[9]
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 Montroll would have won a one-on-one election with Kiss).[22] In Alaska's first-ever IRV election, Nick Begich was defeated in the first round by spoiler candidate Sarah Palin.[23]
Spoiler effects rarely occur when using tournament solutions, because each candidate's total in a paired comparison does not involve any other candidates. Instead, methods can separately compare every pair of candidates and check who would win in a one-on-one election.[24] This pairwise comparison means that spoilers can only occur in the rare situation[15][16] known as a Condorcet cycle.[24]
For each pair of candidates, there is a count for how many voters prefer the first candidate (in the pair) to the second candidate, and how many voters have the opposite preference. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which causes vote splitting in other methods.
Rated voting methods ask voters to assign each candidate a score on a scale (usually from 0 to 10), instead of listing them from first to last. The best-known of these methods is score voting, which elects the candidate with the highest total number of points. Because voters rate candidates independently, changing one candidate's score does not affect those of other candidates, which is what allows rated methods to evade Arrow's theorem.
While true spoilers are not possible under score voting, voters who behave strategically in response to candidates can create pseudo-spoiler effects (which can be distinguished from true spoilers in that they are caused by voter behavior, rather than the voting system itself).
Several weaker forms of independence of irrelevant alternatives (IIA) have been proposed as a way to compare ranked voting methods. Usually these procedures try to insulate the process from weak spoilers, ensuring that only a handful of candidates can change the outcome.
Local independence from irrelevant alternatives (LIIA) is a weaker kind of independence that requires both of the following conditions:[25]
For every electoral method, it is possible to construct an order-of-finish that ranks candidates in terms of strength. This can be done by first finding the winner, then repeatedly deleting them and finding a new winner. This process is repeated to find which candidates rank 3rd, 4th, etc. As a result, LIIA can also be thought of as indicating independence from the weakest alternative, i.e. the alternative who would not win unless every other candidate dropped out.
Despite being a very weak form of spoiler-resistance (requiring that only the last-place finisher is unable to affect the outcome), LIIA is satisfied by only a few voting methods. These include Kemeny-Young and ranked pairs, but not Schulze or instant-runoff voting. Rated methods such as approval voting, range voting, and majority judgment also pass.
Besides its interpretation in terms of majoritarianism, the Condorcet criterion can be interpreted as a kind of spoiler-resistance. In general, Condorcet methods are highly resistant to spoiler effects. Intuitively, this is because the only way to dislodge a beats-all champion is by beating them, so spoilers can only exist when there is no beats-all champion (which is rare). This property, of stability for Condorcet winners, is a major advantage of Condorcet methods.
Smith-independence is another kind of spoiler-resistance for Condorcet methods. This criterion says that a candidate should not affect the results of an election, unless they have a "reasonable claim" to the title of Condorcet winner (fall in the Smith set). Smith candidates are ones who can defeat every other candidate either directly or indirectly (e.g. if A can defeat B, who in turn defeats C).
Independence of clones is the most commonly-fulfilled spoiler-resistance criterion, and says that "cloning" a candidate—adding a new candidate identical to an existing one—should not affect the results. Two candidates are considered identical if they are ranked side-by-side on every ballot; in other words, if there is no other candidate ranked in between them. The criterion is satisfied by ranked-choice runoff voting, all systems that satisfy independence of irrelevant alternatives (including cardinal systems), and most tournament solutions.
This criterion is very weak, as adding a substantially similar (but not quite identical) candidate to a race can still substantially affect the results, causing vote splitting. For example, the center squeeze pathology that affects RCV means that several similar (but not identical) candidates competing in the same race will tend to hurt each others' chances of winning.
In a Borda count, 5 voters rank 5 alternatives [A, B, C, D, E].
3 voters rank [A>B>C>D>E]. 1 voter ranks [C>D>E>B>A]. 1 voter ranks [E>C>D>B>A].
Borda count (a=0, b=1): C=13, A=12, B=11, D=8, E=6. C wins.
Now, the voter who ranks [C>D>E>B>A] instead ranks [C>B>E>D>A]; and the voter who ranks [E>C>D>B>A] instead ranks [E>C>B>D>A]. They change their preferences only over the pairs [B, D], [B, E] and [D, E].
The new Borda count: B=14, C=13, A=12, E=6, D=5. B wins.
The social choice has changed the ranking of [B, A] and [B, C]. The changes in the social choice ranking are dependent on irrelevant changes in the preference profile. In particular, B now wins instead of C, even though no voter changed their preference over [B, C].
A single example is enough to show that every Condorcet method must fail independence of irrelevant alternatives. Say that 3 candidates are in a Condorcet cycle. Label them Rock, Paper, and Scissors. In a one-on-one race, Rock loses to Paper, Paper to Scissors, etc. Without loss of generality, say that Rock wins the election with a certain method. Then, Scissors is a spoiler candidate for Paper: if Scissors were to drop out, Paper would win the only one-on-one race (Paper defeats Rock). The same reasoning applies regardless of the winner.
This example also shows why Condorcet elections are rarely (if ever) spoiled: spoilers can only happen if there is no Condorcet winner. Condorcet cycles are rare in large elections,[15][16] and the median voter theorem shows cycles are impossible whenever candidates are arrayed on a left-right spectrum.
Plurality voting is a degenerate form of ranked-choice voting, where the top-rated candidate receives a single point while all others receive none. The following example shows a plurality voting system with 7 voters ranking 3 alternatives (A, B, C).
In an election, initially only A and B run: B wins with 4 votes to A's 3, but the entry of C into the race makes A the new winner.
The relative positions of A and B are reversed by the introduction of C, an "irrelevant" alternative.
A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does not do away with the spoiler problem entirely, although it ... makes it less likely
IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. ... Approval voting thus appears to solve the problem of vote splitting simply and elegantly. ... Range voting solves the problems of spoilers and vote splitting
plurality-rule voting is seriously vulnerable to vote-splitting ... runoff voting ... as French history shows, it too is highly subject to vote-splitting. ... [Condorcet] majority rule avoids such vote-splitting debacles because it allows voters to rank the candidates and candidates are compared pairwise
You likely have opinions about all those candidates. And yet, you only get a say about one.
Those votes that are cast for minor party candidates are perceived as taking away pivotal votes from major party candidates. ... This phenomenon is known as the 'spoiler effect'.
a spoiler effect occurs when entry by a third-party candidate causes party A to defeat party B even though Party B would have won in a two-candidate race.
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does not do away with the spoiler problem entirely, although it ... makes it less likely
IRV is excellent for preventing classic spoilers-minor candidates who tip the election from one major candidate to another. It is not so good when the 'spoiler' has a real chance of winning
There is a Condorcet ranking according to distance from the center, but Condorcet winner M, the most central candidate, was squeezed between the two others, got the smallest primary support, and was eliminated.