Name | Comply? |
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Plurality | Yes [note 1] |
Two-round system | Yes |
Partisan primary | Yes |
Instant-runoff voting | Yes |
Minimax Opposition | Yes |
DSC | Yes |
Anti-plurality | Yes |
Approval | No |
Borda | No |
Dodgson | No |
Copeland | No |
Kemeny–Young | No |
Ranked Pairs | No |
Schulze | No |
Score | No |
Majority judgment | No |
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause this higher-ranked candidate to lose. [1]
For example, say a group of voters ranks Alice 2nd and Bob 6th, and Alice wins the election. In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd. Later-no-harm says that this increased support from Alice's voters should not allow Bob to win. [1]
Later-no-harm is a defining characteristic of first-preference plurality (FPP), instant-runoff voting (IRV), and descending solid coalitions (DSC), three similar systems for comparing candidates based on how many eligible voters consider each uneliminated candidate their favorite. In later-no-harm systems, the results either do not depend on lower preferences at all (as in plurality) or only depend on them if all higher preferences have been eliminated (as in IRV and DSC). [2] [3] This tends to favor candidates with strong (but narrow) support over candidates closer to the center of public opinion, which can lead to a phenomenon known as center-squeeze. [4] [5] [6] Cardinal and Condorcet methods, by contrast, tend to select candidates whose ideology is a closer match to that of the median voter. [4] [5] [6] This has led many social choice theorists to question whether the property is desirable in the first place or should instead be seen as a negative property. [6] [7] [8]
Later-no-harm is sometimes confused with resistance to a kind of strategic voting called truncation or bullet voting. [9] However, later-no-harm does not provide resistance to such strategies. For example, systems like instant runoff that pass later-no-harm but fail participation still incentivize truncation or bullet voting in some situations. [7] [10]
The plurality vote, two-round system, instant-runoff voting, and descending solid coalitions satisfy the later-no-harm criterion. First-preference plurality satisfies later-no-harm trivially, by ignoring every preference after the first. [1]
Nearly all voting methods other than first-past-the-post do not pass LNH, including score voting, highest medians, Borda count, and all Condorcet methods. The Condorcet criterion is incompatible with later-no-harm (assuming the resolvability criterion, i.e. any tie can be removed by a single voter changing their rating). [1]
Bloc voting, which allows a voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district, although the single non-transferable vote does.
Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates.
Later-No-Harm can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Harm can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.
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Assume four voters (marked bold) submit a truncated preference listing A > B = C by apportioning the possible orderings for B and C equally. Each vote is counted A > B > C, and A > C > B:
Result: A is listed last on 2 ballots; B is listed last on 3 ballots; C is listed last on 3 ballots. A is listed last on the least ballots. A wins.
Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
Result: A is listed last on 2 ballots; B is listed last on 5 ballots; C is listed last on 1 ballot. C is listed last on the least ballots. C wins. A loses.
The four voters supporting A decrease the probability of A winning by adding later preference C to their ballot, changing A from the winner to a loser. Thus, Anti-plurality doesn't satisfy the Later-no-harm criterion when truncated ballots are considered to apportion the last place vote amongst unlisted candidates equally. |
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This example shows that the Borda count violates the Later-no-harm criterion. Assume three candidates A, B and C and 5 voters with the following preferences:
Assume that all preferences are expressed on the ballots. The positions of the candidates and computation of the Borda points can be tabulated as follows:
Result: B wins with 7 Borda points.
Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots:
The positions of the candidates and computation of the Borda points can be tabulated as follows:
Result: A wins with 6 Borda points.
By hiding their later preferences about B, the three voters could change their first preference A from loser to winner. Thus, the Borda count doesn't satisfy the Later-no-harm criterion. |
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This example shows that Copeland's method violates the Later-no-harm criterion. Assume four candidates A, B, C and D with 4 potential voters and the following preferences:
Assume that all preferences are expressed on the ballots. The results would be tabulated as follows:
Result: B has two wins and no defeat, A has only one win and no defeat. Thus, B is elected Copeland winner.
Assume now, that the two voters supporting A (marked bold) would not express their later preferences on the ballots:
The results would be tabulated as follows:
Result: A has one win and no defeat, B has no win and no defeat. Thus, A is elected Copeland winner.
By hiding their later preferences, the two voters could change their first preference A from loser to winner. Thus, Copeland's method doesn't satisfy the Later-no-harm criterion. |
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This example shows that the Schulze method doesn't satisfy the Later-no-harm criterion. Assume three candidates A, B and C and 16 voters with the following preferences:
Assume that all preferences are expressed on the ballots. The pairwise preferences would be tabulated as follows:
Result: B is Condorcet winner and thus, the Schulze method will elect B. Hide later preferencesAssume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots:
The pairwise preferences would be tabulated as follows:
Now, the strongest paths have to be identified, e.g. the path A > C > B is stronger than the direct path A > B (which is nullified, since it is a loss for A).
Result: The full ranking is A > C > B. Thus, A is elected Schulze winner.
By hiding their later preferences about B and C, the three voters could change their first preference A from loser to winner. Thus, the Schulze method doesn't satisfy the Later-no-harm criterion. |
Douglas Woodall writes:
[U]nder STV the later preferences on a ballot are not even considered until the fates of all candidates of earlier preference have been decided. Thus a voter can be certain that adding extra preferences to his or her preference listing can neither help nor harm any candidate already listed. Supporters of STV usually regard this as a very important property, although it has to be said that not everyone agrees; the property has been described (by Michael Dummett, in a letter to Robert Newland) as "quite unreasonable", and (by an anonymous referee) as "unpalatable". [11]
The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate. The first round is held using simple plurality to choose the top-two candidates, and then in the second round the winner is chosen by majority vote. The two-round system is widely used in the election of legislative bodies and directly elected presidents.
In social choice theory and politics, the spoiler effect refers to a situation where the entry of a losing candidate affects the results of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
The monotonicity criterion, also called positive response or positive vote weight, is a principle of social choice theory that says that increasing a candidate's ranking or rating should not cause them to lose. Positive response rules out cases where a candidate loses an election as a result of receiving too much support from voters.
In an election, a candidate is called a Condorcet, beats-all, or majority-rule winner if a majority of voters would support them in a race against any other candidate. Such a candidate is also called an undefeated or tournament champion. Voting systems where a majority-rule winner will always win the election are said to satisfy the majority-rule principle, also known as the Condorcet criterion. Condorcet voting methods extend majority rule to elections with more than one candidate.
The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an election because they have "too much support." It says that adding voters who support A over B should not cause A to lose the election to B.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
Bullet, single-shot, or plump voting is when a voter supports only a single candidate, typically to show strong support for a single favorite.
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, ranked pairs, Kemeny–Young method, and Schulze method. Methods that fail include Bucklin voting, instant-runoff voting and Condorcet methods that fail the Condorcet loser criterion such as Minimax.
Woodall'splurality criterion is a voting system criterion for ranked voting. It is stated as follows:
Schulze STV is a draft single transferable vote (STV) ranked voting system designed to achieve proportional representation. It was invented by Markus Schulze, who developed the Schulze method for resolving ties using a Condorcet method. Schulze STV is similar to CPO-STV in that it compares possible winning candidate pairs and selects the Condorcet winner. It is not used in parliamentary elections.
Instant-runoff voting (IRV), also known as plurality with elimination or plurality loser, is a ranked-choice voting system that modifies plurality by repeatedly eliminating the last-place finisher until only one candidate is left. In the United Kingdom, it is generally called the alternative vote (AV). In the United States, IRV is often conflated with ranked-choice voting (RCV); however, this conflation is not completely standard, and social choice theorists tend to prefer more explicit terms.
The 2009 Burlington mayoral election was held in March 2009 for the city of Burlington, Vermont. This was the second mayoral election since the city's 2005 change to instant-runoff voting (IRV), after the 2006 mayoral election. In the 2009 election, incumbent Burlington mayor won reelection as a member of the Vermont Progressive Party, defeating Kurt Wright in the final round with 48% of the vote.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
The later-no-help criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
Homogeneity is a common property for voting systems. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. Specifically, if every ballot is replicated the same number of times, then the result should not change.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
Tideman's Alternative Method, also called Alternative Smith or Alternative Schwartz, is an electoral system developed by Nicolaus Tideman which selects a single winner using votes that express preferences.
The sincere favorite or no favorite-betrayal criterion is a property of some voting systems, that says voters should have no incentive to vote for someone else over their favorite. It protects voters from having to engage in a kind of strategy called lesser evil voting or decapitation.
Descending Solid Coalitions (DSC) is a ranked-choice voting system designed to preserve the advantages of instant-runoff voting while satisfying monotonicity. It was developed by voting theorist Douglas Woodall as an improvement on (and replacement for) the use of the alternative vote.
third place Candidate C is a centrist who is in fact the second choice of Candidate A's left-wing supporters and Candidate B's right-wing supporters. ... In such a situation, Candidate C would prevail over both Candidates A ... and B ... in a one-on-one runoff election. Yet, Candidate C would not prevail under IRV because he or she finished third and thus would be the first candidate eliminated
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.
However, squeezed by surrounding opponents, a centrist candidate may receive few first-place votes and be eliminated under Hare.
the 'squeeze effect' that tends to reduce Condorcet efficiency if the relative dispersion (RD) of candidates is low. This effect is particularly strong for the plurality, runoff, and Hare systems, for which the garnering of first-place votes in a large field is essential to winning