How well does theory explain reality? - A case of Arrow's impossibility theorem

In this paper, we investigate how well Arrow's impossibility theorem, a typical no-existence proof, can explain real human decision-making. Since the conclusion of a no-existence proof is universal, it may also be useful to examine instances of illogical decision-making which are actually handled in reality if an Arrovian approach is seriously considered. Then, we try to modify the framework to reflect the actual decision-making situation as much as possible by allowing individuals to have their own sets of alternatives. Since individual sets of alternatives are varied in nature, Arrow's framework is not satisfied in general because a social ordering of all alternatives does not normally exist. Therefore, it may be concluded that Arrow's impossibility result holds not only in theory but also in reality. This conclusion may open up a way to manage an illogical social decision such as cyclical decision-making and strategic negotiation, among others which are popular and effective in actual decision-making.