A fair distribution of resources and opportunities. I believe that if we do not address this problems soon enough we will be (soon) living in a cyberpunk dystopia.
A Pareto distribution with alpha >= 2 (and likely alpha < 5, because that's starting to look too much like Communism) and x_m >= the cost of basic necessities for one person--including shelter, water, food, sanitation, medical care, education, and their share of upkeep for the transportation and communications networks.
No one suffers from lack of vital resources. Yet it is still possible to get rich via a combination of luck, skill, and tenacity. Seems fair to me.
Of course, this leads to bickering about how to calculate the numbers, so....
At the point where you said "and likely alpha < 5, because that's starting to look too much like Communism", we're back on politics.
This is a blind-spot I see in a lot of technically-minded folks: politics as an evil to be avoided via technological solutions, as opposed to politics as the natural side-effect of needing two or more people to come to consensus on combined action. You can definitely improve the space of possible solutions if you have technology at your disposal, but you can't remove the human from the equation if you're solving human problems.
So merely saying "Communism" is sufficient to make it political? In terms of fairness, my opinion is that alpha less than 2 puts too much wealth in the hands of the rich, hurting the baseline quality of life, and alpha greater than 5 probably doesn't concentrate enough capital to support innovation, competition, moonshots, and luxuries.
I was defining an objectively measurable middle ground between two economic antipodes that have each had extensive political backing now or in the past. This contrasts with those who decry any movement in the direction of redistribution to be greasing the slippery slope to Abhorrently Evil Communism, and any movement in the direction of concentration to be greasing the slippery slope to Abhorrently Evil Capitalism.
When you define numeric values, it becomes harder to hijack the discussion by throwing around loaded words and charged phrases.
Politics with concrete numerically-quantifiable values is much better politics.
But you can't replace the politics with the math, as the exercise of deciding the alpha value in the Pareto distribution demonstrates. The numbers don't tell us what people will value; that's where the politics comes in. It's the art of figuring out human values and coming to terms to try to satisfy as many as possible.
In theory, the optimal alpha could be determined experimentally. It would be an expensive experiment, though.
For now, we just have anecdotal historical examples, like the Soviets, and the European monarchies, and the ruins of ancient empires, and the banana republics, and the resource-curse countries.
We have already determined that the extremes at either end are bad. Concentrate the wealth too much, and you get slavery or serfdom, and stagnate. Distribute it too much, and you get socialism or communism, and stagnate. Follow some happy medium somewhere between them, and your economy grows.
In the absence of an experiment that would require extensive political maneuvering to even begin to conduct, we substitute less extensive political maneuvering in order to make some reasonable assumptions. It is better than just allowing the person that derails the discussion with the loudest distraction to win.
Besides that, experiments undertaken to determine the optimally fair distribution of wealth are as likely to be used to craft an illusion of fairness as they are to create a real environment of fairness, so even if we knew, we wouldn't necessarily be able to do.