Definitions for monotonicity criterion
mono·tonic·i·ty cri·te·ri·on

WikipediaRate this definition:0.0 / 0 votes

1. Monotonicity criterion

   The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic 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. Douglas R. Woodall called the criterion mono-raise. Raising a candidate x on some ballots while changing the orders of other candidates does not constitute a failure of monotonicity. E.g., harming candidate x by changing some ballots from z > x > y to x > y > z isn't a violation of the monotonicity criterion. The monotonicity criterion renders the intuition that there should be neither need to worry about harming a candidate by (nothing else than) up-ranking nor it should be possible to support a candidate by (nothing else than) counter-intuitively down-ranking. There are several variations of that criterion; e.g., what Douglas R. Woodall called mono-add-plump: A candidate x should not be harmed if further ballots are added that have x top with no second choice. Agreement with such rather special properties is the best any ranked voting system may fulfill: The Gibbard–Satterthwaite theorem shows, that any meaningful ranked voting system is susceptible to some kind of tactical voting, and Arrow's impossibility theorem shows that individual rankings can't be meaningfully translated into a community-wide ranking where the order of candidates x and y is always independent of irrelevant alternatives z. Noncompliance with the monotonicity criterion doesn't tell anything about the likelihood of monotonicity violations, failing in one of a million possible elections would be as well a violation as missing the criterion in any possible election. Of the single-winner ranked voting systems, Borda, Schulze, ranked pairs, maximize affirmed majorities, descending solid coalitions, and descending acquiescing coalitions are monotonic, while Coombs' method, runoff voting, and instant-runoff voting (IRV) are not. Most variants of the single transferable vote (STV) proportional representations are not monotonic, especially all that are currently in use for public elections (which simplify to IRV when there is only one winner). All plurality voting systems are monotonic if the ballots are treated as rankings where using more than two ranks is forbidden. In this setting first past the post and approval voting as well as the multiple-winner systems single non-transferable vote, plurality-at-large voting (multiple non-transferable vote, bloc voting) and cumulative voting are monotonic. Party-list proportional representation using D'Hondt, Sainte-Laguë or the largest remainder method is monotonic in the same sense. In elections via the single-winner methods range voting and majority judgment nobody can help a candidate by reducing or removing support for them. The definition of the monotonicity criterion with regard to these methods is disputed. Some voting theorists argue that this means these methods pass the monotonicity criterion; others say that, as these are not ranked voting systems, they are out of the monotonicity criterion's scope.

How to pronounce monotonicity criterion?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say monotonicity criterion in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of monotonicity criterion in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of monotonicity criterion in Pythagorean Numerology is: 4

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Monotonicity_Criterion