Monotonicity: Difference between revisions
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Reformat list of Woodall's monotonicity criteria to better match the formatting in his paper
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[[Douglas Woodall]] defined several variations or types of monotonicity.<ref name="Woodall-Monotonicity" /> In Woodall's definitions, a candidate x should not be harmed if:
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=== Multi-winner monotonicity ===
Monotonicity would be more aptly named ''endorsement monotonicity'' since it is the preservation of monotonicity relative to endorsement. Since it is the most important form of monotonicity is bears the simple naming. There are however two other important forms of monotonicity for multi-winner voting systems, [[Population monotonicity]] and [[House monotonicity criterion |House monotonicity]].
Multi-winner monotonicity could also be considered in a weaker and stronger sense: the weak form is satisfied whenever, if A is one of the winners, ranking A higher does not kick A out of the winning set; whereas the stronger form is satisfied whenever, if A is one of the winners, ranking A higher does not kick ''anyone'' out of the winning set. In a single winner election, these criteria are the same, but the stronger form is harder to satisfy for multi-winner.
==Footnotes==
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