This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions (...) which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication. (shrink)

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. (shrink)