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The problem of an elusive general will

The problem of an elusive general will. Arrow’s theorem: Assumption: any ‘reasonable’ system of preference aggregation must include a set of conditions (see below). Theorem: no system can satisfy these conditions and simultaneously guarantee group coherence. The Stupid Conditions.

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The problem of an elusive general will

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  1. The problem of an elusive general will Arrow’s theorem: Assumption: any ‘reasonable’ system of preference aggregation must include a set of conditions (see below). Theorem: no system can satisfy these conditions and simultaneously guarantee group coherence.

  2. The Stupid Conditions • ST: Social transitivity • If xPiy and yPiz  I, then the social choice function must choose xPz • U: Universal admissibility • The set of preference orderings includes all possible orderings of x, y, and z (including indifference) • P: Pareto optimality • If xPiy for all in the group, the social choice function must not choose y. • I: Independence of irrelevant alternatives • If we add a new alternative a, it should not change the relative rankings of x, y, and z, and by implication the social choice. • D: (non)-dictatorship • There exists no i such that if xPiy, the social choice function chooses x regardless of other preferences

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