The Beginning of Infinity

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Arrow's theorem

An impossibility theorem proving that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

  • If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
  • If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
  • There is no "dictator": no single voter possesses the power to always determine the group's preference.

Essentially proving that no systems of government are mathematically fair.

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Governing

There's a class of questions that Popper called 'Who should rule?'. For example, 'Who should hold power?', and then lots of derived questions like 'How should they be educated?.' These are questions that have been asked ever since history begun and are at the root of all squabbles around governing. Popper pointed out that this class of questions is rooted in the same misconception as the question ‘How are scientific theories derived from sensory data?’ which defines Empiricism. It is seeking a system that derives or justifies the right choice of leader or government, from existing data – such as inherited entitlements, the opinion of the majority, the manner in which a person has been educated, etc.