Problem 1
Suppose that we say that an allocation \(\mathrm{x}\) is socially preferred to an allocation y only if everyone prefers \(\mathrm{x}\) to \(\mathbf{y}\). (This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.) What shortcoming does this have as a rule for making social decisions?
Problem 1
Suppose that we say that an allocation \(x\) is socially preferred to an allocation \(\mathbf{y}\) only if everyone prefers \(\mathbf{x}\) to \(\mathbf{y}\). (This is sometimes called the Pareto ordering, since it is closely related to the idea of Pareto efficiency.) What shortcoming does this have as a rule for making social decisions?
Problem 2
A Rawlsian welfare function counts only the welfare of the worst off agent. The opposite of the Rawlsian welfare function might be called the "Nietzschean" welfare function - a welfare function that says the value of an allocation depends only on the welfare of the best off agent. What mathematical form would the Nietzschean welfare function take?
