[asuidyasiud]

The point is that invoking an impossibility theorem oftentimes - and also in this case - demonstrates that the formalization one has chosen to work with is not a desirable one.

For example, if a group of people by some social process comes to a consensus then arguably this represents the "will of the people". Thus it makes sense to reason about this concept without requiring the existence of ranked preferences.

[yummyfajitas]

So for you, "will of the people" represents a consensus preference? And following this idea, if there is no consensus (i.e., at least one person in Portland wants to ride an Uber), there is no "will of the people"?

The whole point of Arrow is that you need some very strong assumptions (e.g., cardinal preferences) to define a "will of the people". The only real world expression of cardinal preferences is a set of supply&demand curves, however - based on this the "will of the people" says Uber should exist.

[asuidyasiud]

You misread, I made the converse claim.

[thaumasiotes]

"If there is no 'will of the people', then there is no consensus"? That doesn't make a lot of sense to me. Groups make decisions all the time, but that doesn't mean those decisions were all endorsed by everyone in the group. Was splitting off from the Catholic Church to form the Anglican Church really the will of the people of England? Because there was a consensus.

[asuidyasiud]

If a group of people comes together, discusses, and comes by some process to a unanimous decision ("consensus") then it does usually make a lot of sense to regard the outcome as the "will of these people".

The point I am trying to make through the last n posts is that Arrow's theorem does concerns the impossibility of a certain, narrow-minded formalization. It is therefore incorrect to conclude that 'the "will of the people" is a nonsensical concept by Arrow's Impossibility Theorem', which is what you had claimed.

I have nothing to say about the people and churches of England.

[yummyfajitas]

Your claim is that if a unanimous decision has been arrived at, it constitutes the will of the people. No one disputes this - the case where everyone agrees is trivial and uninteresting. It also does not describe the situation with Uber in Portland, Delhi, or anywhere else. I want Uber in Delhi, some politicians don't. Hence there is no consensus.

You either have a coherent definition of "will of the people" that goes beyond consensus, or you don't. If you do, give the definition.

[fugigig]

For the moment I am content having pointed out the flaw in your argument.