The later-no-help criterion is a
voting system
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections ma ...
criterion formulated by
Douglas Woodall
Douglas Robert Woodall (born November 1943 in Stoke-on-Trent) is a British mathematician and psephologist. He studied mathematics at the University of Cambridge, and earned his Ph.D. at the University of Nottingham in 1969, his thesis being " ...
. 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
Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, ...
strategy called
mischief voting, which can deny victory to a sincere
Condorcet winner
An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
.
Complying methods
Two-round system
The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resul ...
,
Single transferable vote
Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate p ...
(including traditional forms of
Instant Runoff Voting
Instant-runoff voting (IRV) is a type of ranked preferential voting method. It uses a majority voting rule in single-winner elections where there are more than two candidates. It is commonly referred to as ranked-choice voting (RCV) in the Un ...
and
Contingent vote
The contingent vote is an electoral system used to elect a single representative in which a candidate requires a majority of votes to win. It is a variation of instant-runoff voting (IRV). Under the contingent vote, the voter ranks the cand ...
),
Approval voting
Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate.
Description
Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
,
Borda count
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the ...
,
Range voting
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added (or averaged), and the candidate with the highest total is elected. It has been described by various ...
,
Bucklin voting
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking o ...
, and
Majority Judgment
Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating.
Unlike other vo ...
satisfy the later-no-help criterion.
When a voter is allowed to choose only one preferred candidate, as in
plurality voting
Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per ...
, later-no-help can either be considered satisfied (as the voter's later preferences can not help their chosen candidate) or not applicable.
Noncomplying methods
All
Minimax Condorcet
In voting systems, the Minimax Condorcet method (often referred to as "the Minimax method") is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is sometim ...
methods (including the pairwise opposition variant),
Ranked Pairs
Ranked pairs (sometimes abbreviated "RP") or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create ...
,
Schulze method
The Schulze method () is an electoral system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners. The Schulze method is also known a ...
,
Kemeny-Young method,
Copeland's method
Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history:
* Ramon Llull described the system in 1299, so it is sometimes referred to as "Llull's method"
* The ...
,
Nanson's method
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 (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the C ...
, and Descending Solid Coalitions, a variant of Woodall's
Descending Acquiescing Coalitions, do not satisfy later-no-help. The
Condorcet criterion
An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
is incompatible with later-no-help.
Checking Compliance
Checking for failures of the Later-no-help criterion requires ascertaining the probability of a voter's preferred candidate being elected before and after adding a later preference to the ballot, to determine any increase in probability. Later-no-help presumes that later preferences are added to the ballot sequentially, so that candidates already listed are preferred to a candidate added later.
Examples
Anti-plurality
Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates.
Later-No-Help 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-Help 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.
Truncated Ballot Profile
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 3 ballots; B is listed last on 2 ballots; C is listed last on 6 ballots. B is listed last on the least ballots. B wins. A loses.
Adding Later Preferences
Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
Result: A is listed last on 3 ballots; B is listed last on 4 ballots; C is listed last on 4 ballots. A is listed last on the least ballots. A wins.
Conclusion
The four voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Anti-plurality fails the Later-no-help criterion when truncated ballots are considered to apportion the last place vote amongst unlisted candidates equally.
Coombs' method
Coombs' method repeatedly eliminates the candidate listed last on most ballots, until a winner is reached. If at any time a candidate wins an absolute majority of first place votes among candidates not eliminated, that candidate is elected.
Later-No-Help can be considered not applicable to Coombs if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Coombs if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.
Truncated Ballot Profile
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 4 ballots; B is listed last on 4 ballots; C is listed last on 6 ballots. C is listed last on the most ballots. C is eliminated, and B defeats A pairwise 8 to 6. B wins. A loses.
Adding Later Preferences
Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
Result: A is listed last on 4 ballots; B is listed last on 6 ballots; C is listed last on 4 ballots. B is listed last on the most ballots. B is eliminated, and A defeats C pairwise 8 to 6. A wins.
Conclusion
The four voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Coombs' method fails the Later-no-help criterion when truncated ballots are considered to apportion the last place vote amongst unlisted candidates equally.
Copeland
This example shows that Copeland's method violates the Later-no-help criterion. Assume four candidates A, B, C and D with 7 voters:
Truncated preferences
Assume that the two voters supporting A (marked bold) do not express later preferences on the ballots:
The results would be tabulated as follows:
Result: Both A and B have two pairwise wins and one pairwise tie, so A and B are tied for the Copeland winner. Depending on the tie resolution method used, A can lose.
Express later preferences
Now assume the two voters supporting A (marked bold) express later preferences on their ballot.
The results would be tabulated as follows:
Result: B now has two pairwise defeats. A still has two pairwise wins, one tie, and no defeats. Thus, A is elected Copeland winner.
Conclusion
By expressing later preferences, the two voters supporting A promote their first preference A from a tie to becoming the outright winner (increasing the probability that A wins). Thus, Copeland's method fails the Later-no-help criterion.
Dodgson's method
Dodgson's' method elects a Condorcet winner if there is one, and otherwise elects the candidate who can become the Condorcet winner after the fewest ordinal preference swaps on voters' ballots.
Later-No-Help can be considered not applicable to Dodgson if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Dodgson if the method is assumed to apportion possible rankings among unlisted candidates equally, as shown in the example below.
Truncated Ballot Profile
Assume ten 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: B is the Condorcet winner and the Dodgson winner. A loses.
Adding Later Preferences
Now assume that the ten voters supporting A (marked bold) add later preference C, as follows:
Result: There is no Condorcet winner. A is the Dodgson winner, because A becomes the Condorcet Winner with only two ordinal preference swaps (changing B > A to A > B). A wins.
Conclusion
The ten voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Dodgson's method fails the Later-no-help criterion when truncated ballots are considered to apportion the possible rankings amongst unlisted candidates equally.
Ranked pairs
For example, in an election conducted using the
Condorcet
Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...
compliant method
Ranked pairs
Ranked pairs (sometimes abbreviated "RP") or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create ...
the following votes are cast:
A is preferred to C by 70 votes to 30 votes. (Locked)
B is preferred to A by 42 votes to 28 votes. (Locked)
B is preferred to C by 42 votes to 30 votes. (Locked)
B is the
Condorcet winner
An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
and therefore the
Ranked pairs
Ranked pairs (sometimes abbreviated "RP") or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create ...
winner.
Suppose the 28 A voters specify second choice C (they are ''burying'' B).
The votes are now:
A is preferred to C by 70 votes to 30 votes. (Locked)
C is preferred to B by 58 votes to 42 votes. (Locked)
B is preferred to A by 42 votes to 28 votes. (Cycle)
There is no
Condorcet winner
An electoral system satisfies the Condorcet winner criterion () if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidatesthat is, a ...
and A is the
Ranked pairs
Ranked pairs (sometimes abbreviated "RP") or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create ...
winner.
By giving a second preference to candidate C the 28 A voters have caused their first choice to win. Note that, should the C voters decide to ''bury'' A in response, B will beat A by 72, restoring B to victory.
Similar examples can be constructed for any Condorcet-compliant method, as the Condorcet and later-no-help criteria are incompatible.
Commentary
Woodall writes about Later-no-help, "... under STV
ingle transferable votethe 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
Harm is a moral and legal concept.
Bernard Gert construes harm as any of the following:
* pain
* death
* disability
*mortality
* loss of abil ity or freedom
* loss of pleasure.
Joel Feinberg gives an account of harm as setbacks to intere ...
any candidate already listed. Supporters of STV usually regard this as a very important property, although not everyone agrees; the property has been described (by
Michael Dummett
Sir Michael Anthony Eardley Dummett (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He wa ...
, in a letter to Robert Newland) as 'quite unreasonable', and (by an anonymous referee) as 'unpalatable.'"
[ Woodall, Douglas, Properties of Preferential Election Rules]
Voting matters - Issue 3, December 1994
/ref>
See also
*Later-no-harm criterion
The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. Woodall defined the criterion as " ding a later preference to a ballot should not harm any candidate already listed." For example, a ranked voting method in w ...
References
Further reading
* Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002
Brown v. Smallwood, 1915
{{voting systems
Electoral system criteria