Monotonicity: Difference between revisions
Content added Content deleted
(Add weak and strong possible monotonicity criterion to multi-winner section (speculative?)) |
(→Woodall: linking to Douglas Woodall) |
||
| Line 104: | Line 104: | ||
=== Woodall === |
=== Woodall === |
||
{{seealso|Douglas Woodall}} |
|||
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: |
[[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: |
||
* l ([[Mono-raise criterion|'''MONO-RAISE''']]) x is raised on some ballots without changing the orders of the other candidates; |
* l ([[Mono-raise criterion|'''MONO-RAISE''']]) x is raised on some ballots without changing the orders of the other candidates; |
||
| Line 115: | Line 116: | ||
* l (MONO-ADD-PLUMP): A candidate {{math|''x''}} should not be harmed if further ballots are added that have {{math|''x''}} top with no second choice. |
* l (MONO-ADD-PLUMP): A candidate {{math|''x''}} should not be harmed if further ballots are added that have {{math|''x''}} top with no second choice. |
||
* l ([[Mono-add-top criterion|'''MONO-ADD-TOP''']]) further ballots are added that have x top (and are otherwise arbitrary); |
* l ([[Mono-add-top criterion|'''MONO-ADD-TOP''']]) further ballots are added that have x top (and are otherwise arbitrary); |
||
* l (MONO-REMOVE-BOTTOM) some ballots are removed, all of which have x bottom, below all other candidates. |
* l (MONO-REMOVE-BOTTOM) some ballots are removed, all of which have x bottom, below all other candidates. |
||
=== Multi-winner monotonicity === |
=== Multi-winner monotonicity === |
||