Monotonicity and its Cognates in the Theory of Choice

The standard requirement of monotonicity of a voting procedurestates that an improvement in the ranking of the winningalternative, ceteris paribus, should not make itnon-winning. A concept apparently closely linked tomonotonicity is known as the participation axiom whichrequires that it should never be advantageous for a voter toabstain rather than to vote according to his/her preferences.Situations in which a group of voters may end up with a betteroutcome by not voting at all than by voting according to theirpreferences are called instances of the no-show paradox. Astrong version of the paradox occurs when the abstainers endup with their most preferred outcome by abstaining. A thirdrelated concept is invulnerability to preference truncation.This is satisfied by such procedures that make itadvantageous for voters to always reveal their entirepreference rankings. The fourth concept, Maskin monotonicity,plays an important role in mechanism design literature. Wediscuss these requirements in the context of votingprocedures. Particular attention is paid to the plausibilityof conditions guaranteeing various forms of monotonicity. Copyright Kluwer Academic Publishers 2004