One man, one vote is a political statement demanding the right to vote for all, and equal weighting to those votes.
One person, one vote is a more accurate phrasing, indicating that all people over the minimum age be allowed to vote.
One person, one vote in a unitary state is the slogan used by the ANC in South Africa in the late 1980s and early 1990s to state what they wanted: everyone to vote, and all the votes to go into the same pot. At the time the reformed Apartheid system had a silly tricameral parliament whereby some non-whites could vote, but not in the same elections as the whites.
It is a simple statement of mass-democracy in the least adulterated form: everyone votes, all the votes are counted together, and the party with the most votes wins. So many political dirty tricks depend on adulterating this ideal - e.g. having some constituencies have equal weight despite differing populations; removing people from the voters roll or otherwise stopping them voting; and winning the election with less than half of the popular vote by winning not much more than half the constituencies, and getting not much more than half of the vote in those.
Here's an example of the slogan:
Nelson Mandela: In the document which I gave to the government last year, shortly before I met the state president, P.W. Botha, I said that two issues will have to be addressed by the ANC and the government: firstly, the demand of one person one vote in a unitary state; and secondly, the fears of whites, the concern of whites that the realisation of this demand will result in the
domination of whites by blacks. And, I feel that that fear is genuine; it will be wrong, but it is genuine; and the ANC must address that fear.
- Nelson Mandela - Interview by Johannesburg Television Service, 15 February 1990
If you want a more sophisticated system, try single transferrable vote