Arrow's Impossibility Theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

  1. If every voter prefers alternative X over alternative Y, then the group prefers X over Y.

  2. 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).

  3. There is no "dictator": no single voter possesses the power to always determine the group's preference.

It seems like the theorem can be proven by assuming the 1st and 2nd condition holds for an electoral system, and then showing that the 3rd doesn't. In this case, the resulting dictator would end up being nothing more than a special drinker, guaranteed to exist but not actually possessing any power. Like the drinker, his special status is fake and merely represents the fact that someone like him must exist among the voting populace.

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    $\begingroup$ I'm not understanding what relationship you think these concepts have. Arrow's Impossibility Theorem only applies to rank-order electoral systems where there are 3 or more choices. The drinker paradox, there are 2 options ("drinking" or "not") and there is no "voting" (everyone is individually either drinking or not), there is no single "special" drinker... I'm not seeing any connection. $\endgroup$ – Morgan Rodgers Apr 19 at 5:38

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