Monotonicity paradoxes discussed above consist in counterintuitive changes in the sets of alternatives chosen (the choice sets) as a result of changes in the preferences of individuals. In other words, once certain modifications are made to the preference profile the choice sets ‘respond’ in unexpected ways. In another class of paradoxes one performs various modifications in the alternative set, considers various subsets of alternatives or subdivides the voter set, while holding the preference profile constant, and observes counterintuitive or undesirable changes in the choice sets. These latter paradoxes are, thus, related to monotonicity ones, but there is a crucial difference between these classes: the monotonicity paradoxes are inter-profile ones, while the paradoxes encountered when holding the profile constant are intra-profile ones. In intra-profile paradoxes the preference profile remains the same and something else, e.g. alternative set, is changed. In inter-profile paradoxes, in contrast, the preference profile, but not the alternative set, undergoes a change. Of course, not all changes in either profiles or alternative sets result in paradoxes.
KeywordsCondorcet Winner Preference Profile Borda Count Plurality Vote Simple Majority Rule
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