Political equality means that the individual rights of all the citizens are equally recognised, and protected by the Government. It is the essential condition for existence of a free society, and the only kind of equality possible between individuals.
Remember that the concept, “rights” only pertain to the Freedom to take actions: the individual’s freedom to live, to think, and consequently take actions to produce and trade values, without compulsion or intrusion from other individuals, including and especially, the Government.
If a group of individuals is accorded any exclusive rights, that are denied to others, its meaning and unavoidable logical consequence is a state-sponsored monopoly on production and trade.
Observe that the violation of your freedom to produce and trade, by others(especially the government), essentially implies and requires the violation of all your rights: It implies the violation of your right to think(since the purpose of thinking is to take action, and your freedom to think is redundant if you are not free to act and produce values in accordance with your judgements), and the violation of your right to live(your life, ie., a life proper to man: a non-parasitic life, requires that you think and act to produce and trade values, in order to sustain your own life). This is the reason why a free mind and a free market necessitate each other.
In this context, economic equality may be understood only in the sense that all men must possess the same political-economic right: the right to free trade. ie., the freedom to produce and trade any values with other individuals, with the voluntary consent of both the parties involved in the trade.
This doesn’t mean that all the individuals should be equally wealthy. It only means that all the individuals must possess the same freedom to think and act, to produce and to trade: the same freedom to live. In a laissez faire capitalist society, —ie., a society where individual rights are absolutely protected, and the government is completely separated from trade: making the state-sponsored monopolies impossible— your wealth is a consequence of your competence in exercising your freedom to produce.
– Avinash Kumar, 7 June 2020.
Note: This article is originally my answer on Quora to the question: “What is the relationship between political equality and economic equality?”