I thought that the end result is that since any change would not be a pareto improvement the function can’t recommend any change so it must be completely ambivalent about everything thus is the constant function of every option being of utility 0.
Pareto-optimality says that if there is a mass murderer that wants to kill as many people as possible then you should not do a choice that lessens the amount of people killed ie you should not oppose the mass murderer.
Ah, I should have made more clear that it’s a one-way implication: if it’s a Pareto improvement, then the social choice function is supposed to prefer it. Not the other way around.
A social choice function meeting that minimal requirement can still do lots of other things. So it could still oppose a mass murderer, so long as mass-murder is not itself a Pareto improvement.
Ah, I should have made more clear that it’s a one-way implication: if it’s a Pareto improvement, then the social choice function is supposed to prefer it. Not the other way around.
A social choice function meeting that minimal requirement can still do lots of other things. So it could still oppose a mass murderer, so long as mass-murder is not itself a Pareto improvement.