Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped...

For a social decision problem we define a new aggregation procedure--the threshold rule--for the construction of an output ranking from the individual m-graded rankings with an arbitrary integer m >= 2. An axiomatic characterization of the procedure is given.

Within the framework of the axiomatic approach three types of voting schemes are investigated according to the form in which the individual opinions about the alternatives are defined, as well as to the form of desired social decision. These types of rules are Social Decision Rules, Functional...