Decision making in international organizations is a multistage and complex process. This paper is confi ned however only to one but the most important stage, either the voting on a one proposal, which may be accepted or rejected, or the choice between two alternative proposals. This seemingly simple, dichotomous decision can be made by many different methods of voting, i.e. simple majority; absolute majority; qualifi ed majority; voting with quorum; weighted voting; voting with a possibility of veto etc. These methods differ in their properties: equal vs. unequal treatment of the participants of decision-making assembly; the manner of respecting of minority rights; equal vs. unequal treatment of possible decisions; sensitiveness to changes of decisions of particular participants; effectiveness and other. These properties express postulates: anonymity; semi-duality; citizen sovereignty; monotonicity and strong monotonicity; unanimity, unrestricted domain etc. Some of these properties exclude the other. The choice of the particular method of voting means an acceptation of some postulates and a resignation from the other postulates.