“It” is not “the State” but the action you described: redistributing based on merit. To do this there needs to be a standard of merit. This standard is subjective. Hence, the state imposes an objective standard in place of a subjective one.
Necessity is that which is biologically required. Air has no subjective value: we all need it, period. Now, one might say that this makes it have an objective value—I don’t care either way. The context of necessity is “acquire or die.” Shelter, clothing, food, water, and air are good examples. There is, of course, no pure necessity because there are alternatives. If I can’t eat an apple I might eat a pear, some air is cleaner than others, and so on. So even here there is some room for subjective value, but there is no question that this good must be available. Its necessity is determined by our very nature. There is no escape from it, there is no “do without.” Contrast this to cigarettes, automobiles, or paper clips, all of which can basically be done without in the short or long term; resources may be diverted away from these goods. It is possible to choose to do without some goods, but not others. In some sense this is an objective value, in others its value is infinite, in others it is a prerequisite for ascribing value in the first place and so has no value. Choose your poison. I’m easy.
Assume an set of available choices {C}. Assume a set of agents ascribing value {A}. Value is ascribed by the ordering of {C} by each member of {A}. By “the market can handle all possible preferences” I mean to indicate that the market can handle any ordering of {C} for each agent {A}. All permutations are permissible. By " the market will promote that which everyone wants" I mean to indicate that if every agent {A} orders {C} such that some choice x in {C} is always ranked above some choice y in {C} that the market will encourage/promote/etc x over y. The final note, which you didn’t ask for clarification on but I will anyway, is “if aggregate preferences do not change then neither will aggregate valuations.” I mean that if in one permutation the ranking in {C} goes {…, x, z, y, …} and in another permutation the ranking in {C} goes {…, x, y, z, …} (that is, x is still highest but other choices below it have changed) then the market will still select/promote/etc x. Assuming these three conditions there will always exist someone in {A} who can dictate what happens overall. There is no fair method of responding to a system of preferences. In voting, this simply means that preference voting has intrinsic flaws. In a market context, it means that either there will be a controlling force in the economy, or one of the three conditions must fail to apply—in either case, the market cannot be fair (if we assume this is a good standard of fairness).
The problem goes very deep. If we assume, for example, that each individual should, at the very least, have the decisive say over at least one choice, we will still end up in a situation where one of our three requirements fail (actually, the one which says that if everyone prefers x to y then x should be chosen). So much for pure voluntary action!
