Editing Arrow's impossibility theorem (section)

==== Generalized stability theorems ====
The Campbell-Kelly theorem shows that Condorcet methods are the most spoiler-resistant class of ranked voting systems: whenever it is possible for some ranked voting system to avoid a spoiler effect, a Condorcet method will do so.<ref name="Campbell2000" /> In other words, replacing a ranked method with its Condorcet variant (i.e. elect a Condorcet winner if they exist, and otherwise run the method) will sometimes prevent a spoiler effect, but can never create a new one.<ref name="Campbell2000" />

In 1977, [[Ehud Kalai]] and [[Eitan Muller]] gave a full characterization of domain restrictions admitting a nondictatorial and [[Strategyproofness|strategyproof]] social welfare function. These correspond to preferences for which there is a Condorcet winner.<ref>{{Cite journal |last1=Kalai |first1=Ehud |last2=Muller |first2=Eitan |year=1977 |title=Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures |url=http://www.kellogg.northwestern.edu/research/math/papers/234.pdf |journal=Journal of Economic Theory |volume=16 |issue=2 |pages=457–469 |doi=10.1016/0022-0531(77)90019-9}}</ref>

Holliday and Pacuit devised a voting system that provably minimizes the number of candidates who are capable of spoiling an election, albeit at the cost of occasionally failing [[Monotonicity criterion|vote positivity]] (though at a much lower rate than seen in [[instant-runoff voting]]).<ref name="Holliday23222"/>{{clarify|reason=Needs a quote saying what is claimed, for instance how it has fewer spoilers than other Smith methods.|date=November 2024}}