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Non-negative responsiveness
The non-negative responsiveness or monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system satisfies non-negative responsiveness if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot). That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Voting systems that violate non-negative responsiveness can be said to exhibit the negative response, perversity, or additional support paradox.
Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology, as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win. Similar rules treat the well-being of some voters as "less than worthless". These issues have led to constitutional prohibitions on such systems as violating the right to equal and direct suffrage. Negative response is often cited as an example of a perverse incentive, as rules with negative response can incentivize politicians to take extreme or unpopular positions in an attempt to shed excess votes.
Most ranked methods (including Borda and all common round-robin rules) satisfy non-negative responsiveness, as do all common rated voting methods (including approval, highest medians, and score).
Negative responsiveness occurs in instant-runoff voting (IRV), the single transferable vote, and the two-round system. Some quota-based apportionment methods also violate the rule, as can the randomized Condorcet method in cases of cyclic ties.
The participation criterion is closely related, but different. While non-negative responsiveness deals with a voter changing their opinion (or vote), participation deals with situations where a voter choosing to cast a ballot at all has a backwards effect on the election.
Miller defined two main classes of monotonicity failure in 2012, which have been repeated in later papers:
Upward monotonicity failure: Given the use of voting method V and a ballot profile B in which candidate X is the winner, X may nevertheless lose in ballot profile B' that differs from B only in that some voters rank X higher in B' than in B
Downward monotonicity failure: Given the use of voting method V and a ballot profile B in which candidate X is a loser, X may nevertheless win in ballot profile B' that differs from B only in that some voters rank X lower in B' than in B.
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Non-negative responsiveness
The non-negative responsiveness or monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system satisfies non-negative responsiveness if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot). That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Voting systems that violate non-negative responsiveness can be said to exhibit the negative response, perversity, or additional support paradox.
Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology, as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win. Similar rules treat the well-being of some voters as "less than worthless". These issues have led to constitutional prohibitions on such systems as violating the right to equal and direct suffrage. Negative response is often cited as an example of a perverse incentive, as rules with negative response can incentivize politicians to take extreme or unpopular positions in an attempt to shed excess votes.
Most ranked methods (including Borda and all common round-robin rules) satisfy non-negative responsiveness, as do all common rated voting methods (including approval, highest medians, and score).
Negative responsiveness occurs in instant-runoff voting (IRV), the single transferable vote, and the two-round system. Some quota-based apportionment methods also violate the rule, as can the randomized Condorcet method in cases of cyclic ties.
The participation criterion is closely related, but different. While non-negative responsiveness deals with a voter changing their opinion (or vote), participation deals with situations where a voter choosing to cast a ballot at all has a backwards effect on the election.
Miller defined two main classes of monotonicity failure in 2012, which have been repeated in later papers:
Upward monotonicity failure: Given the use of voting method V and a ballot profile B in which candidate X is the winner, X may nevertheless lose in ballot profile B' that differs from B only in that some voters rank X higher in B' than in B
Downward monotonicity failure: Given the use of voting method V and a ballot profile B in which candidate X is a loser, X may nevertheless win in ballot profile B' that differs from B only in that some voters rank X lower in B' than in B.