Concept

Independence of irrelevant alternatives

The condition that a verdict between two candidates depends only on how the voters ranked those two. It is one of the conditions Arrow's theorem shows cannot all be met at once, and it is the one most rules give up.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Independence of irrelevant alternatives, broken by Borda. Two profiles that agree on every voter's ranking of two candidates and differ only in where the others sit, with the rule's verdict between the two reversed.

Four conditions, and no rule that has all of them

Five reasonable rules can return five different winners on one set of ballots, which invites the obvious question of which one is right. The answer is that the conditions anybody would write down cannot all hold at once — and here each named rule's own violation is found by search rather than quoted.

applied · Voting rules

Every ballot one voter could submit under instant runoff. One voter's true ranking beside every ranking that voter could submit instead, with the winner each produces and the profitable misreports marked.

A lie that pays

A ballot is usually read as a report of a preference. This one reads it as a move, and walks every move one voter has — all six rankings, the winner each produces, and the ones that beat honesty.

applied · Voting rules

Named alongside it

The objects these essays reach for when they reach for this one.

Condorcet cycle Pairwise majority Preference profile Voting rule Arrows theorem Counterexample Decisive set Proof by contradiction Strategic voting Strategy-proofness

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