You have a some/none/all problem. If every agent has a set of preferences that is disjoint from every other, then there is no pleasing all the people. But that is vanishingly likely, as is every agent having identical preferences...in all likelihood, agents have some preferences in common.
You have a some/none/all problem. If every agent has a set of preferences that is disjoint from every other, then there is no pleasing all the people. But that is vanishingly likely, as is every agent having identical preferences...in all likelihood, agents have some preferences in common.