Independence of irrelevant alternatives: Difference between revisions

Adding irrelevant (non-winning) candidates should not be able to change the election results. The only time when adding candidates can change the election results is when they change the election result to one in which they are one of the winners.

 

 

[[Condorcet method]]s necessarily fail this criterion, although some, such as [[Ranked Pairs]], satisfy a related but weaker criterion known as [[local independence of irrelevant alternatives]]. [[Borda count]], [[Coombs' method]], and [[Instant-runoff voting]] fail.

 

[[Range voting]], [[approval voting]], and [[majority judgment]] satisfy the criterion if the voters grade or rate the candidates on an absolute scale that doesn't depend on who is in the running. Note that this means no voter can [[Normalization|normalize]] their ballot, and so in a two-candidate election the majority can't vote strategically to make their preferred candidate win.

 

[[Arrow's impossibility theorem]] states that no voting system can satisfy universal domain, non-imposition, non-dictatorship, unanimity, and independence of irrelevant alternatives. Since universal domain implies that the method is an ordinal method, the impossibility theorem only applies to [[ordinal voting]]. In practice, this means that no deterministic ranked ballot system can satisfy independence of irrelevant alternatives without either having a dictator (whose ballot decides who wins no matter the other ballots), failing to elect a candidate that the whole electorate ranks first, or rendering one or more outcomes impossible no matter the ballots.

 

Therefore, less strict properties have been proposed (some of which are incompatible with IIA):

 

Neither the [[Borda count]], [[Coombs' method]] nor [[Instant-runoff voting]] satisfies the less strict criteria above.

 

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. The waitress tells him he has two choices: apple pie and blueberry pie. Sidney orders the apple pie. After a few minutes the waitress returns and says that they also have cherry pie at which point Morgenbesser says "In that case I'll have the blueberry pie."</blockquote>

 

Voting systems which are not independent of irrelevant alternatives suffer from [[strategic nomination]] considerations.