What is the fundamental implication of Arrow's theorem?
A) No alternative can beat the one preferred by the median voter in pair-wise majority-rule elections if the number of voters is odd, voter preferences are single-peaked over a single policy dimension, and voters vote sincerely.
B) If there are two or more issue dimensions and three or more voters with preferences in the issue space who all vote sincerely, then it is likely (except in very extreme case) that there will be no Condorcet winner.
C) There is no possible decision-making rule satisfying a minimal standard of fairness that is guaranteed to produce a rational decision for a group.

Question

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Arrow's theorem states that there is no possible decision-making rule satisfying a minimal standard of fairness that is guaranteed to produce a rational decision for a group. This means that any decision-making process that involves multiple individuals with different preferences and opinions will inherently lead to some form of unfairness or irrationality. This has significant implications for democratic systems and highlights the difficulties in designing a system that can truly represent the interests of all individuals within a group. Option A and B are specific cases that can occur under certain assumptions, but the fundamental implication of Arrow's theorem is the impossibility of a perfect decision-making rule for any situation.

What Is the Fundamental Implication of Arrow's Theorem