Independence of irrelevant alternatives: Difference between revisions
Independence of irrelevant alternatives (view source)
Revision as of 16:45, 26 April 2024
, 1 month agono edit summary
No edit summary |
|||
(2 intermediate revisions by one other user not shown) | |||
Line 13:
=== Cardinal methods ===
[[Range voting]], [[approval voting]], and [[majority judgment]] satisfy the criterion. This implies that if
Note, however, that this means no voter can [[Normalization|normalize]] their ballot. This also requires voters not to vote strategically (which can cause majority failures).
=== Ranked methods ===
[[Arrow's impossibility theorem]] states that no [[ordinal voting]] system
==== Proof for majoritarian methods (simple case) ====
Let's say that we have a majoritarian ranked ballot method, i.e. one that elects the candidate with a majority of the vote (if there are only 2 candidates). With an election that's a Condorcet cycle (rock-paper-scissors situation), like this:
{{ballots|
25: A>B>C
40: B>C>A
35: C>A>B}}
at least one of A, B or C must be elected (or have a chance of winning the election if the method is nondeterministic). There are three cases:
*Case 1: ''A'' is elected. IIA is violated because the 75% who prefer ''C'' over ''A'' would elect ''C'' if ''B'' were not a candidate.
*Case 2: ''B'' is elected. IIA is violated because the 60% who prefer ''A'' over ''B'' would elect ''A'' if ''C'' were not a candidate.
*Case 3: ''C'' is elected. IIA is violated because the 65% who prefer ''B'' over ''C'' would elect ''B'' if ''A'' were not a candidate.
No matter who wins, the method will fail IIA.
== Related criteria ==
* '''[[Independence of Smith-dominated Alternatives|Independence of Smith-dominated alternatives]]''' (ISDA)
* '''[[
* '''[[Independence of Pareto-dominated alternatives]]''' (IPDA)
* '''Local independence of irrelevant alternatives''' (LIIA), which says that if the alternative ranked first or last in the outcome is removed, the relative ordering of the other alternatives in the outcome must not change
* Woodall's '''Weak IIA''': If
Neither the [[Borda count]], [[Coombs' method]] nor [[Instant-runoff voting]] satisfies the less strict criteria above. [[Ranked Pairs]] and [[Schulze method|Schulze]] satisfy ISDA, and [[River]] satisfies IPDA as well. [[Kemeny-Young]] and [[Ranked Pairs]] satisfy LIIA, but the [[Schulze method]] does not.
== Anecdote ==
An anecdote which illustrates a violation of this property has been attributed to Sidney Morgenbesser:
<blockquote>After finishing dinner, Sidney Morgenbesser decides to order dessert.
== Implications ==
Line 39 ⟶ 59:
* A candidate can enter or drop out of the election without changing the result (unless they win in one of the cases).
The second implication is
=== Strategic implications ===
Line 49 ⟶ 69:
* [[Vote splitting]]
* [[w:Gibbard's theorem]]
==References==
<references/>
[[Category:Voting system criteria]]
|