Ex Post Fairness not Ex Ante fairness. Which, if you optimize for the former at the cost of the latter, is no longer quite as clear cut which is 'better'.
Imagine if I started with a dollar and you started with nothing.
Ex post fairness is to say that "you started with less than me, therefor you should pay less for an ice cream cone than me"
Ex ante fairness is to say "it is fair that we pay the same for an ice cream, no matter how much money we have in our pockets"
both are a kind of fairness, and if you try to organize your rules to optimize for one, you will not be able to obtain the other -- if you change the price of ice cream for everyone depending on their pre-existing finances before they come up to you, first of all you're going to be fighting an uphill battle against history on every level, but second of all you're going to be actively discriminating against people in ways that a neutral third party is going to see is bizarre, unjust or just plain "unfair"
If you choose to charge everyone the same for ice cream no matter what people are going to judge you as unjust, cruel and "unfair" for not taking pity on people who cannot afford it
you usually cannot have it both ways - you usually have to choose. Sometimes you can get lucky and have a situation where you can be fair in both ways, but it is unusual for things to be so pleasant