Arrow's impossibility theorem
Common misconceptions

Arrow's theorem is not related to strategic voting, which does not appear in his framework, though the theorem does have important implications for strategic voting (being used as a lemma to prove Gibbard's theorem). The Arrovian framework of social welfare assumes all voter preferences are known and the only issue is in aggregating them.

Monotonicity (sometimes called non-perversity) is not a condition of Arrow's theorem (contrary to a mistake by Arrow himself, who included the axiom in his original statement of the theorem but did not use it). Dropping the assumption does not allow for constructing a social welfare function that meets his other conditions.

Contrary to a common misconception, Arrow's theorem deals with the limited class of ranked-choice voting systems, rather than voting systems as a whole.
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