Arrow's impossibility theorem
Result that no ranked-choice system is spoilerproof / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Arrow's impossibility theorem?
Summarize this article for a 10 year old
Arrow's impossibility theorem is a key impossibility theorem in social choice theory, showing that no ranked voting rule[note 1] can produce a logically coherent ranking of more than two candidates. Specifically, no such rule can satisfy a key criterion of rational choice called independence of irrelevant alternatives: that a choice between and should not depend on the quality of a third, unrelated outcome .
The theorem is often cited in discussions of election science and voting theory, where is called a spoiler candidate. As a result, Arrow's theorem implies that a ranked voting system can never be completely independent of spoilers.
The practical consequences of the theorem are debatable, with Arrow himself noting "Most [ranked] systems are not going to work badly all of the time. All I proved is that all can work badly at times."[1][2] Spoiler effects are common in some ranked systems (like instant-runoff (RCV) and plurality), but rare in majority-vote methods (see below).
While originally overlooked, a large class of systems called rated methods are not affected by Arrow's theorem or IIA failures.[2][3][4] Arrow initially rejected these systems on philosophical grounds, but reversed his opinion on the issue later in life, referring to score voting as "probably the best".[2]