The problem of an elusive general will

1
The problem of an elusive general will

• Arrows 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