Unless you mean everyone will get only one cup of water. But then, the farmer will be fucked, because one cup of water is not enough to farm. And if the farmers can't farm, then you'll have another set of problems on your hand: NOT ENOUGH FOOD.
If a rich person wants to buy extra water to use on their lawn, they can. But they need to find someone willing to sell it, and offer them enough money to make it worth it.
If it really gets to the point there is only 1 cup of water per person per day, well then so be it. Everyone gets exactly 1 cup of water. That's perfectly fair. What's not fair is giving 1.5 cups to one person and 0.5 cups to another. Just because they are rich or a farmer or whatever.
Such a situation would create huge economic incentives to find more water, to conserve existing water, to reuse waste water, etc. The point is to get the benefits from a free market with incentives, but to distribute the benefits equally among the population.