Negative responsiveness

In <a href="/facts/Social_choice_theory/ztMqy1bM">social choice</a>, the negative response, perversity, or additional support paradox is a <a href="/facts/Pathological_(mathematics)/KmKHjJ1H">pathological behavior</a> of some <a href="/facts/Electoral_system/e6zvx3Bo">voting rules</a> where a candidate loses as a result of having too much support (or wins because of increased opposition). In other words, increasing (decreasing) a candidate's <a href="/facts/Ranked_voting/z91UKPCs">ranking</a> or <a href="/facts/Rated_voting/X5basu5o">rating</a> causes that candidate to lose (win), respectively. Electoral systems that do not exhibit perversity are sometimes said to satisfy the <a href="/facts/Monotonic_function/MjQK0YL2">monotonicity</a> criterion.
Perversity is often described by <a href="/facts/Social_choice_theory/ztMqy1bM">social choice theorists</a> as an exceptionally severe kind of <a href="/facts/Pathological_(mathematics)/KmKHjJ1H">electoral pathology</a>, 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 <a href="/facts/One_man%2c_one_vote/dY1BVlMS">equal and direct suffrage</a>. Negative response is often cited as an example of a <a href="/facts/Perverse_incentive/5vDHdQTy">perverse incentive</a>, as rules with negative response can incentivize politicians to take <a href="/facts/Center_squeeze/8JRxIxP5">extreme</a> or unpopular positions in an attempt to shed excess votes.
Most <a href="/facts/Ranked_voting/z91UKPCs">ranked methods</a> (including <a href="/facts/Borda_count/0VK30c68">Borda</a> and all common <a href="/facts/Round-robin_voting/xxxA7hkA">round-robin rules</a>) satisfy positive response, as do all common <a href="/facts/Rated_voting/X5basu5o">rated voting</a> methods (including <a href="/facts/Approval_voting/XBp98Jrf">approval</a>, <a href="/facts/Highest_median_voting_rules/R1lyW42G">highest medians</a>, and <a href="/facts/Score_voting/hhpRqQny">score</a>). 
Negative responsiveness occurs in <a href="/facts/Instant-runoff_voting/td1Q35Wg">instant-runoff voting</a> (IRV), the <a href="/facts/Single_transferable_vote/LXDo1Grm">single transferable vote</a>, and the <a href="/facts/Two-round_system/2sFF4NBG">two-round system</a>. Some <a href="/facts/Quota_method/0CUwjL22">quota-based apportionment methods</a> also violate the rule, as can the <a href="/facts/Maximal_lotteries/21r1kVTa">randomized Condorcet method</a> in cases of <a href="/facts/Condorcet_cycle/PXuWT0jl">cyclic ties</a>.
The <a href="/facts/Participation_criterion/racmDXYL">participation criterion</a> is closely related, but different. While positive 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.

Negative responsiveness open-in-new

Negative responsiveness