Mutual majority criterion: Difference between revisions
Show that DAC also fails independence of mutual majority-dominated alternatives; link the counterexample to the more general Left, Center, Right scenario.
(Show that DAC also fails independence of mutual majority-dominated alternatives; link the counterexample to the more general Left, Center, Right scenario.) |
|||
Line 91:
=== Independence of mutual majority-dominated alternatives ===
Similar to [[Independence of Smith-dominated Alternatives]], a "independence of mutual majority-dominated alternatives" criterion could be envisioned.
Both [[instant-runoff voting]] and [[Descending Acquiescing Coalitions]] fail this criterion, as can be shown by [[Left, Center, Right]] scenarios when y+z also constitutes a majority.
For instance:
{{ballots|
4: L>C>R
3: R>C>L
2: C>L>R}}
The smallest mutual majority set is {L, C}, and C beats L pairwise, so in any election where those two candidates are the only one in the running, C wins. However, [[IRV]] first eliminates C and then L beats R. [[DAC]] first excludes R from the set of viable candidates (because the {L, C} coalition is the largest). Then L has the greatest first preference count of the two and thus wins.
=== Finding the mutual majority set ===
| |||