Many, if not most, problems in group decision making can be translated into MCDM problems by substituting criteria for voters. Yet, there has been very little discussion about the implications of various types of voting paradoxes to MCDM. The classic voting paradoxes, viz. Borda's and Condorcet's, have obvious implications for certain MCDM situations. The latter implies that the notion of the best alternative, given a set of criteria and information about the ordinal ranking of the alternatives on those criteria, can be essentially arbitrary. The former, in turn, demonstrates a particularly clear case of conflict between reasonable intuitions. Completely unexplored are implications of compound majority paradoxes to MCDM. The paper deals with Ostrogorski's and Anscombe's paradoxes which result from non-bisymmetry and non-associativity of the majority relation. Moreover, we shall discuss the implications of paradox of multiple elections which is a situation where the result of multiple-item election may be a policy alternative that nobody voted for.