Was Mnogabukav, vyhodil here it is:
“…Further development of the mathematical proofs of the incorrectness of democracy as a tool to reflect the interests of society received in 1951 by Kenneth arrow ( for which he received the Nobel prize in 1972). In the study “Social choice and individual values”, he considered democracy as a social choice model that combines individual preference. Describe without mathematical apparatus.
The axiom of universality: the election system must allow any distribution of votes. An obvious requirement.
The axiom of unanimity: if there is the unanimous opinion of all voting, the vote should lead to this choice. Even more obvious, isn’t it?
The axiom of independence from unrelated alternatives: the preference of the voter is of a particular vote should not depend on its relation to alternative options. Although the requirement is logically correct, in practice it can be disturbed for psychological reasons. However, now we consider an ideal democracy, and mathematics; and, if we are talking about political elections, candidate feedback is a prerequisite of informed choice.
Axiom of completeness: the voting system should provide for comparison of any pair of candidates, including the case of equal attractiveness for the voter. It is also difficult to imagine a democratic electoral system without such a mechanism.
Axiom of transitivity: “if in accordance with the opinion of the voters, the candidate In no better candidate, And (worse or equivalent), the candidate With no better candidate, then the candidate With no better candidate, And”. Simple logic statements, essentially just affirms the rationality of the behavior of voters.
All five axioms describe fully democratic electoral system in General, isn’t it? But then arrow proved that all the axioms simultaneously. More specifically, he added a sixth axiom about absence of the dictator — the person who has the ability and the desire to impose their views throughout society, and mathematically proved that the simultaneous implementation of all six axioms is impossible. Ie, if both the first five — the choice is performed as a result of obedience to dictator — that is why the final output arrow is called “theorem of impossibility”.
The three objectives of democracy, namely, collective rationality, the ability of the voter to make decisions and equality of power, as it turned out, contradict each other. If we start from equality and the ability to make decisions (the essence of the electoral process), we have to reject collective rationality of choice (see Condorcet paradox discussed in the beginning of the article). If you insist on collective rationality, the principle of equality will be available only at the approach, when the result of the vote is determined only by full consensus of the electorate. And, in the end, based on the ability to make decisions, you have to focus it right for an increasingly narrow range, i.e. essentially moving to the same dictator in the limiting case.
In the role of a dictator does not have to act a certain chief, etc. — in General the condition of freedom of choice may be removed by any sufficient global foreign influence: religion in fundamental countries, a threat to all the people outside, etc. — including the so-called public opinion, which is often inspired by external forces for their own purposes. Looking ahead: this is how modern democracy.”
Who is not tired, the rest here->