Interpretation of Dictator as Representative
The lack of dictator in the infinite model implies that the part of properly dictatorial decisions is small if the number of individuals is large. Consequently, the denomination of dictator is justified in rare cases which can be considered as non-typical. Therefore, the interpretation of the model based on the common understanding of the dictator is not precise. On the other hand, the fact that a dictator can be taken into and away from the infinite model, not affecting its properties, indicates at the subsidiary character of the concept of a dictator itself. As shown in chapter 5, the dictator coincides with the upper level of deciding hierarchy, which can be unattainable in the infinite model. In contrast to the dictator, the deciding hierarchy is invariant with respect to isomorphisms of the model, finite and infinite as well. Moreover, since the function of the dictator is shared by the coalitions of the deciding hierarchy, his personal contribution to decision-making becomes to a great extent limited. Thus the dictator appears to be not so much opposed to other individuals, from which its prohibition was postulated originally.
KeywordsBoolean Algebra Mathematical Expectation Significant Pair Preference Probability Independent Individual
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