It's a highly dubious principle if you think about it.
Suppose you have two people, A and B. A is intelligent, well-informed, and serious. He does his level best to form correct opinions about the issues of the day. He is an independent thinker, and his thinking is based in broad experience of life. B, however, makes no attempt to become informed, or to think for himself. He votes as his union boss tells him to vote. Why should B's vote have the same weight as A's? Is it not self-evident that B's vote should not count as much as A's?
The problem, however, is that there is no obvious criterion that one could employ to segregate those who are worthy of voting from those who are not. A friend of mine once proposed that only Ph.D.s should be allowed to vote. That is a hopeless proposal for several reasons. First of all, specialized expertise is no guarantee of even minimal competence outside of one’s specialty. Second, there are Ph.D.s who are not even competent in their own disciplines. Third, there are plenty of non-Ph.D’s who are more worthy of voting than many Ph.D.s. There are Ph.D.s I wouldn’t hire to run a peanut stand let alone cast an intelligent vote.
The same holds for any other academic credential. Would you want to exclude the likes of Eric Hoffer from voting on the ground that he had no formal schooling whatsoever?
Sex and race are obvious non-starters as criteria for separating the worthy from the unworthy.
What about owning property? Should owning property, or once having owned property, be a necessary condition for voting? No, for the simple reason that people eminently qualified to vote may for various good reasons remain renters all their lives. It is obvious that, generally speaking, property owners have a better and more balanced understanding of taxation and cognate issues than non-owners do; but if we follow out this line of reasoning, then only property owning married persons with children should be allowed to vote.
There are people whose experience of life is very rich but who are too conceptually impoverished to extract any useful principles from their experience that they could bring to bear in the voting booth. And then there are people who have deliberately restricted their range of experience (by not having children, say) precisely in order to be in a position to develop fully their conceptual powers. Now to adjudicate between cases of these two sorts with an eye to determining fitness for voting would require the wisdom of Solomon. So forget about it.
We live in a culture in which adolescent immaturity often extends through the twenties and into the thirties and beyond. So one might think to exclude the unfit by allowing only people of age 30 or above the right to vote. But just as being 30 years old is no guarantee of maturity, being 18 is no guarantee of the opposite. In general, older people, being more experienced, are more judicious and thus more likely to vote intelligently. But the counterexamples to this are legion.
I’ll insert an historical aside here. The right of 18 year olds to vote is guaranteed by the 26th Amendment to the U.S. Constitution. Before that, one had to be 21 years old. The 26th Amendment was ratified on July 1st, 1971 during the Vietnam war, a fact which is of course relevant to the Amendment’s proposal and ratification. Some of us remember the words of Barry McGuire’s Eve of Destruction (1965): "...you’re old enough to kill, but not for votin’...."
Once we exclude educational credentials, sex, race, property-ownership, and age as criteria, what do we have left? Nothing that I can see apart from the standard criteria of voter eligibility. ‘One man, one vote’ though certainly a flawed principle, may be the best we can do.
We would make it worse, however, if we went the way of the Aussies and made voting mandatory. As it is here in the USA, roughly only half of the eligible voters actually vote, though this is changing with the exacerbation of political polarization. This is good inasmuch as voters filter themselves similarly as lottery players (quite stupidly) tax themselves. What I mean is that, generally speaking, the people who can vote but do not are precisely the people one would not want voting in the first place. To vote takes time, energy, and a bit of commitment. Careless, stupid, and uniformed people are not likely to do it. And that is good. Of course, many refuse to vote out of disgust at their choices. My advice for them would be to hold their noses and vote for the least or the lesser of the evils. Politics is always about choosing the least or the lesser of evils.
I'll conclude by considering an objection. I said that 'One man, one vote' is a flawed principle. For it implies that the vote of a sage and the vote of a dolt count the same. It might be objected in defense of the principle that both are equal in point of both having an equal interest in the structure of the society in which they live. Granted. But not all know their own best interest. So from the mere fact that A and B have an equal stake in a well-ordered society it does not follow that each person's vote should count the same.
What's more, this sort of reasoning proves too much. For children and felons and illegal aliens also have a stake in a well-ordered society, and only the seriously benighted want to extend the vote to them. Of course, this does not stop many contemporary liberals from wanting to extend the vote to children and felons and illegal aliens. It merely shows that they have lost all common sense. (Presumably they would make an exception in the case of the unborn!) So if equality of interest entails right to vote, then we have a reductio ad absurdum of 'one man, one vote.'