electowiki

Monotonicity: Difference between revisions

Page Discussion

Monotonicity (view source)

Revision as of 09:44, 26 March 2022

232 bytes added ,  2 years ago
Add WDS nonmonotonicity probability figure for IRV
VisualWikitext
(Add: monotonicity isn't participation, and no DPC methods have been proven monotone. Do some cleanup. Remove part with citation needed from 2011.)
(Add WDS nonmonotonicity probability figure for IRV)
Line 72:
Crispin Allard argued, based on a mathematical model that the probability of monotonicity failure actually changing the result of an election for any given [[single-member district|constituency]] would be 1 in 4000;<ref>[http://www.mcdougall.org.uk/VM/ISSUE5/P1.HTM Estimating the Probability of Monotonicity Failure in a UK General Election]</ref> however, Lepelley ''et al.''<ref name="Mathematical Social Sciences 1996 pp. 133–146">{{cite journal | last=Lepelley | first=Dominique | last2=Chantreuil | first2=Frédéric | last3=Berg | first3=Sven | title=The likelihood of monotonicity paradoxes in run-off elections | journal=Mathematical Social Sciences | volume=31 | issue=3 | date=1996-06-01 | issn=0165-4896 | doi=10.1016/0165-4896(95)00804-7 | pages=133–146 | url=https://www.sciencedirect.com/science/article/pii/0165489695008047 | access-date=2020-02-03}}</ref> found a probability of {{nowrap|397/6912 {{=}} 5.74%}} for 3-candidate elections.
 
AnotherWarren probabilitySmith model,argued that in the "[[impartial culture"]] model, yieldsIRV aboutfails 15monotonicity with 14.5% probability in three-candidate elections.<ref>{{cite web | last = Smith | first = Warren D. | url=https://rangevoting.org/Monotone.html | title=Monotonicity and Instant Runoff Voting | website = rangevoting.org}}</ref> In elections with more than 3 candidates, these probabilities tend to increase eventually toward 100% (in some models this limit has been proven, in others it is only conjectured). Nicholas Miller also disputed Allard's conclusion and provided a different mathematical model.<ref name="Annual Meeting of the Public Choice Society 2002">{{cite web | title=Monotonicity failure under STV and related voting systems | url=https://userpages.umbc.edu/~nmiller/RESEARCH/MONOTONICITY.pdf | access-date=2020-02-03 |date=2002-03-22}}</ref>
 
==Real-life monotonicity violations==
Kristomun
1,196

edits

Retrieved from "https://electowiki.org/wiki/Special:MobileDiff/15270"