Jose Ortega Y Gasset, writing in the 1930's, preached that access to educational and economic opportunities should be premised on one's lineage, up bringing, wealth, and social responsibilities.
A succession of societies and cultures discriminated against the ignorant, criminals, atheists, females, homosexuals, members of ethnic, religious, or racial groups, the old, the immigrant, and the poor. Communism - ostensibly a strict egalitarian idea - foundered because it failed to reconcile strict equality with economic and psychological realities within an impatient timetable.
Philosophers tried to specify a "bundle" or "package" of goods, services, and intangibles (like information, or skills, or knowledge). Justice - though not necessarily happiness - is when everyone possesses an identical bundle. Happiness - though not necessarily justice - is when each one of us possesses a "bundle" which reflects his or her preferences, priorities, and predilections. None of us will be too happy with a standardized bundle, selected by a committee of philosophers - or bureaucrats, as was the case under communism.
The market allows for the exchange of goods and services between holders of identical bundles. If I seek books, but detest oranges - I can swap them with someone in return for his books. That way both of us are rendered better off than under the strict egalitarian version.
Still, there is no guarantee that I will find my exact match - a person who is interested in swapping his books for my oranges. Illiquid, small, or imperfect markets thus inhibit the scope of these exchanges. Additionally, exchange participants have to agree on an index: how many books for how many oranges? This is the price of oranges in terms of books.
Money - the obvious "index" - does not solve this problem, merely simplifies it and facilitates exchanges. It does not eliminate the necessity to negotiate an "exchange rate". It does not prevent market failures. In other words: money is not an index. It is merely a medium of exchange and a store of value. The index - as expressed in terms of money - is the underlying agreement regarding the values of resources in terms of other resources (i.e., their relative values).
The market - and the price mechanism - increase happiness and welfare by allowing people to alter the composition of their bundles. The invisible hand is just and benevolent. But money is imperfect. The aforementioned Rawles demonstrated (1971), that we need to combine money with other measures in order to place a value on intangibles.
The prevailing market theories postulate that everyone has the same resources at some initial point (the "starting gate"). It is up to them to deploy these endowments and, thus, to ravage or increase their wealth. While the initial distribution is equal - the end distribution depends on how wisely - or imprudently - the initial distribution was used.
Egalitarian thinkers proposed to equate everyone's income in each time frame (e.g., annually). But identical incomes do not automatically yield the same accrued wealth. The latter depends on how the income is used - saved, invested, or squandered. Relative disparities of wealth are bound to emerge, regardless of the nature of income distribution.
Some say that excess wealth should be confiscated and redistributed. Progressive taxation and the welfare state aim to secure this outcome. Redistributive mechanisms reset the "wealth clock" periodically (at the end of every month, or fiscal year). In many countries, the law dictates which portion of one's income must be saved and, by implication, how much can be consumed. This conflicts with basic rights like the freedom to make economic choices.