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Arrow's Impossibility Theorems
 Žárský, David ; Pražák, Dalibor (advisor) ; Vejnar, Benjamin (referee)
In 1950 Kenneth Arrow proved a famous theorem which states that if we impose certain rather natural conditions on an electoral system, then there must be a dictator amongst the voters. In other words, no electoral system is flawless. In this thesis we first formalise the notion of an electoral system and formulate the conditions we impose thereon. After laying out and proving the auxiliary theory, we show a more modern proof of Arrow's theorem which uses set ultrafilters. On the last pages we look into the case of infinite number of voters. In this case, it holds that there exists an electoral system fulfilling all of our requirements including nonexistence of a dictator. However, the problem of dictatorship in the infinite case doesn't completely disappear. We show that under certain circumstances instead of a dictator there exists an arbitrarily small dictatorial group as well as an individual whom we call an invisible dictator. 1
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