“The classic result of social choice theory is Arrow’s (...) impossibility theorem, which states that ordinal noncomparability of individual welfare orderings implies that a consistent social ordering must be dictatorial, corresponding to the preferences of a single individual.”
Not everybody falls for dictatorship. The impact of the AGV generally comes from the fact that people find themselves, either from moral obligation or from reasonableness, wanting the impossible. And many simply stay in that fixture.
Note the subtlety in that fixture. The impossibility is logical and not just empirical. An example may help. Let me confide that I want to found a new university on the island of Crete. However, I am not that rich, so I want something impossible. This however does not put me into a fixture, since I am used to the fact that I cannot afford some things that I want. However, the Arrow general view concerns a logical impossibility, which is something quite different.
We can usefully recognise:
reasonable = rational & realistic
Reasonableness is the intersection of rationality and empirical realism. Nonexistence may derive from empirical circumstances or from logical impossibility. Irrationality however is always unrealistic. Inconsistency cannot exist, in the true empirical sense. For example a round square cannot exist. The nonexistence of the Arrowian constitution similarly derives not from empirical reality but from logical necessity.
Given the AGV, the question arises what the reasonableness and moral presumptions of Arrow’s claims actually are. Are these claims as strong as conjectured ?
My position is as follows:
1. As has been said on ‘round tables’, it is not rational to postulate inconsistent properties. People involved in a learning process may indeed make inconsistent assumptions. However, once the inconsistency is discovered, it is no longer considered to be rational to adopt those assumptions. People may enjoy ‘roundness’ and ‘squareness’, but having both simultaneously is seen to be inconsistent, even inconceivable, and hence unreasonable. The Arrowian properties are unreasonable in the exactly same manner. Arrow’s pitfall is to confuse the learning process, his context of discovery, with real world applications by educated people.
2. Similarly, one cannot be morally obligated to a logical impossibility. Hence Arrow’s properties are morally undesirable.