Negative responsiveness

In social choice, the negative response,^[1]^[2] perversity,^[3] or additional support paradox^[4] is a pathological behavior of some voting rules 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 ranking or rating causes that candidate to lose (win), respectively.^[4] Electoral systems that do not exhibit perversity are sometimes said to satisfy the monotonicity criterion.^[5]

Perversity is often described by social choice theorists as an exceptionally severe kind of electoral pathology,^[6] as such rules can have "backwards" responses to voters' opinions, where popularity causes defeat while unpopularity leads to a win.^[7] Similar rules treat the well-being of some voters as "less than worthless".^[8] These issues have led to constitutional prohibitions on such systems as violating the right to equal and direct suffrage.^[9]^[10] 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.^[11]

Most ranked methods (including Borda and all common round-robin rules) satisfy positive response,^[5] as do all common rated voting methods (including approval, highest medians, and score).^{[note 1]}

Negative responsiveness occurs in instant-runoff voting (IRV),^[12] the single transferable vote,^[3] and the two-round system.^[11] Some quota-based apportionment methods also violate the rule,^[13] as can the randomized Condorcet method in cases of cyclic ties.

The participation criterion 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.^[13]

^ May, Kenneth O. (1952). "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision". Econometrica. 20 (4): 680–684. doi:10.2307/1907651. ISSN 0012-9682. JSTOR 1907651.
^ Pukelsheim, Friedrich (2014). Proportional representation: apportionment methods and their applications. Internet Archive. Cham; New York : Springer. ISBN 978-3-319-03855-1.
^ ^a ^b Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN 0092-5853. JSTOR 2110496.
^ ^a ^b Felsenthal, Dan S. (April 2010). "Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected". GBR. pp. 1–52.
^ ^a ^b D R Woodall, "Monotonicity and Single-Seat Election Rules", Voting matters, Issue 6, 1996
^ Felsenthal, Dan S.; Tideman, Nicolaus (2014-01-01). "Interacting double monotonicity failure with direction of impact under five voting methods". Mathematical Social Sciences. 67: 57–66. doi:10.1016/j.mathsocsci.2013.08.001. ISSN 0165-4896. It is generally agreed among social choice theorists that a voting method that is susceptible to any type of monotonicity failure suffers from a particularly serious defect.
^ Arrow, Kenneth J. (2017-12-13). Social Choice and Individual Values. doi:10.12987/9780300186987. ISBN 978-0-300-18698-7. Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.
^ Arrow, Kenneth J. (2017-12-13). Social Choice and Individual Values. p. 25. doi:10.12987/9780300186987. ISBN 978-0-300-18698-7. Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.
^ Pukelsheim, Friedrich (2014). Proportional representation : apportionment methods and their applications. Internet Archive. Cham; New York : Springer. ISBN 978-3-319-03855-1.
^ dpa (2013-02-22). "Bundestag beschließt neues Wahlrecht". Die Zeit (in German). ISSN 0044-2070. Retrieved 2024-05-02.
^ ^a ^b Cite error: The named reference :4 was invoked but never defined (see the help page).
^ Ornstein, Joseph T.; Norman, Robert Z. (2014-10-01). "Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections". Public Choice. 161 (1–2): 1–9. doi:10.1007/s11127-013-0118-2. ISSN 0048-5829. S2CID 30833409.
^ ^a ^b Dančišin, Vladimír (2017-01-01). "No-show paradox in Slovak party-list proportional system". Human Affairs. 27 (1): 15–21. doi:10.1515/humaff-2017-0002. ISSN 1337-401X.

Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).

[1] May, Kenneth O. (1952). "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision". Econometrica. 20 (4): 680–684. doi:10.2307/1907651. ISSN 0012-9682. JSTOR 1907651.

[:4222-2] Pukelsheim, Friedrich (2014). Proportional representation: apportionment methods and their applications. Internet Archive. Cham; New York : Springer. ISBN 978-3-319-03855-1.

[jstor.org-3] Doron, Gideon; Kronick, Richard (1977). "Single Transferrable Vote: An Example of a Perverse Social Choice Function". American Journal of Political Science. 21 (2): 303–311. doi:10.2307/2110496. ISSN 0092-5853. JSTOR 2110496.

[:0-4] Felsenthal, Dan S. (April 2010). "Review of paradoxes afflicting various voting procedures where one out of m candidates (m ≥ 2) must be elected". GBR. pp. 1–52.

[Woodall-Monotonicity222-5] D R Woodall, "Monotonicity and Single-Seat Election Rules", Voting matters, Issue 6, 1996

[Felsenthal-severe-6] Felsenthal, Dan S.; Tideman, Nicolaus (2014-01-01). "Interacting double monotonicity failure with direction of impact under five voting methods". Mathematical Social Sciences. 67: 57–66. doi:10.1016/j.mathsocsci.2013.08.001. ISSN 0165-4896. It is generally agreed among social choice theorists that a voting method that is susceptible to any type of monotonicity failure suffers from a particularly serious defect.

[:1-7] Arrow, Kenneth J. (2017-12-13). Social Choice and Individual Values. doi:10.12987/9780300186987. ISBN 978-0-300-18698-7. Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.

[Arrow-8] Arrow, Kenneth J. (2017-12-13). Social Choice and Individual Values. p. 25. doi:10.12987/9780300186987. ISBN 978-0-300-18698-7. Since we are trying to describe social welfare and not some sort of illfare, we must assume that the social welfare function is such that the social ordering responds positively to alterations in individual values, or at least not negatively. Hence, if one alternative social state rises or remains still in the ordering of every individual without any other change in those orderings, we expect that it rises, or at least does not fall, in the social ordering.

[:42322-9] Pukelsheim, Friedrich (2014). Proportional representation : apportionment methods and their applications. Internet Archive. Cham; New York : Springer. ISBN 978-3-319-03855-1.

[:0322-10] (2013-02-22). "Bundestag beschließt neues Wahlrecht". Die Zeit (in German). ISSN 0044-2070. Retrieved 2024-05-02.

[:4-11] Cite error: The named reference :4 was invoked but never defined (see the help page).

[Ornstein-13] Ornstein, Joseph T.; Norman, Robert Z. (2014-10-01). "Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections". Public Choice. 161 (1–2): 1–9. doi:10.1007/s11127-013-0118-2. ISSN 0048-5829. S2CID 30833409.

[:5-14] Dančišin, Vladimír (2017-01-01). "No-show paradox in Slovak party-list proportional system". Human Affairs. 27 (1): 15–21. doi:10.1515/humaff-2017-0002. ISSN 1337-401X.

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