Independence of irrelevant alternatives: Difference between revisions
Content added Content deleted
imported>Km-elmet (Added some other less strict versions.) |
imported>Km-elmet m (grammar) |
||
| Line 7: | Line 7: | ||
Therefore, less strict properties have been proposed: |
Therefore, less strict properties have been proposed: |
||
:- '''Independence of Smith-dominated alternatives''' (ISDA), which says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the [[Smith set]]. ISDA implies Condorcet, and some Condorcet methods (e.g. [[Schulze method|Schulze]]) |
:- '''Independence of Smith-dominated alternatives''' (ISDA), which says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the [[Smith set]]. ISDA implies Condorcet, and some Condorcet methods (e.g. [[Schulze method|Schulze]]) satisfy ISDA. |
||
:- '''Independence of covered alternatives''' which says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the [[uncovered set]]. Independence of covered alternatives also implies Condorcet. If a method is independent of covered alternatives, then the method fails monotonicity if perfect ties can always be broken in favor of a choice W by using ballots ranking W first. |
:- '''Independence of covered alternatives''' which says that if one option (X) wins an election, and a new alternative (Y) is added, X will win the election if Y is not in the [[uncovered set]]. Independence of covered alternatives also implies Condorcet. If a method is independent of covered alternatives, then the method fails monotonicity if perfect ties can always be broken in favor of a choice W by using ballots ranking W first. |
||