Abstract We
study the existence of a group of individuals which has some decisive
power for social choice correspondences that satisfy a monotonicity
property which we call
modified monotonicity. And we examine
the relation between modified monotonicity and strategy-proofness of
social choice correspondences according to the definition by Duggan and
Schwartz (2000). We will show mainly the following two results. (1)
Modified monotonicity implies the existence of an oligarchy. An
oligarchy is a group of individuals such that it has some decisive
power (
semi-decisiveness), and at least one of the most
preferred alternatives of every its member is always chosen by any
social choice correspondence. (2) Strategy-proofness of social choice
correspondences is equivalent to modified monotonicity.
modified
monotonicity - oligarchy - social choice
correspondences - strategy-proofness - weak dictator