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Why do some people expect a universe full of randomness to be fair?
What is fascinating about the claim that the universe is "random" is that we only understand "randomness" in terms of order and purpose. And where did we get that notion from? It is commonly said, for instance, that we are random as we came from, say, one particular out of many sperm. A tree is random because one seed happened to land in the right place and sprout. But is it the case that the seeds fell randomly? Rather, isn't randomness a function of a greater order and purpose? That one seed sprouts may be random, but that seeds fall from trees with the obvious purpose of sprouting new trees does not seem random at all. We'd have to miseducate ourselves to see the world this way. And so we do these days. But the desire for justice is not random because we see that an order is present amidst much that seems to happen by chance or arbitrarily. Geometry and math are similar. We discern order in the universe, and chaos within it. Are they in tension? Sure. But it is the kind of tension that leads to lines of predictable occurences. It is the kind of tension that occurs within purposes that are not adequately described as random, since they incorporate randomness into themselves. That human being developed a certain way as opposed to others may be random, or a reaction to a particular environment over time. But that this then dicates what justice is - this is not random. Or so it seems to me. And to every child who says "but that's not fair."
-Matt Peterson, founding editor of The American Mind
This expectation—that right order superabound in a cosmos where chaos abounds—is not something we can talk about too explicitly. One thing we can say about it is that it is a decayed or debased form of hope, a hope so afraid of itself in the risk of disappointment it entails that it converts into a demand or the stipulation of an entitlement.
Yet there is something itself proper to us in its orderliness about even acting as if the evidently disorganized aspects of life in the cosmos can only be understood in the context of a greater, indeed fully constitutive, schema.
Understanding how to approach the totality and reality of such a scheme is something that demands much of individuals as well as the groups and institutions that develop to cultivate, raise up, and guard this discipline (as it makes these demands too on the guardians of these groups and institutions).
-James Poulos, executive editor of The American Mind
The old joke about the town where all the kids are above average speaks to a habit of mind that people have about odds. Like a form of confirmation bias, people tend to assume that they will wind up on the positive side of events, at least in the long term. As in, "I probably won't get brain cancer, my wife probably won't get early-onset Alzheimer's at age 40, my kids probably won't get kidnapped, my industry probably won't implode," etc.
It's funny to think that there's a whole science based about what "probably" will or won't happen, because it's such a basic part of how we think about everything that happens in our lives. But we aren't very scientific in our own estimations and allow our emotions and wishes for desired results to inflect our evaluations.
In a universe of randomness, "fairness" is the average result of everything that happens. People would be much happier if they were satisfied with what they got rather than what they wanted. However, most of the time their expectations exceed reality. 
-Seth Barron, managing editor of The American Mind
Strictly speaking I don't think people expect a completely random universe to be fair. I think they expect it to be cruelly indifferent, which is perhaps why they so strenuously demand that people be fair. Perhaps this is a kind of compensation: purely Darwinian nature is indifferent; it has no commitment to delivering anything that resembles justice. So we must furnish all the justice ourselves. If there will be no cosmic answer, no ultimate design which at its final revelation rights all wrongs, then the task of righting wrongs falls in its entirety to us.
People should be fair, of course. But wisdom brings with it the sad knowledge that no matter how fair we are capable of being, the universe will not be brought into order. Besides which, history suggests we are not all that capable anyway. In any case, there will be injustices beyond our foresight or prevention, natural disasters and personal heartbreaks that cannot be abolished by sheer force of will or city planning. Hence the intolerable burden many young people seem to feel now, of righting global wrongs all on their own. They are exhausted by an imperative to fix things that are completely outside their control.
In any case what seems remarkable is that people who believe in a random universe think anyone or anything "should" be fair, be it people or systems. The modal verb "should" implies not merely an "is"—"things just are this way"—but an "ought"—"things are this way but should be better." There is no such "ought" in the material world. It is contained nowhere within a purely random, merely physical universe. To posit the validity of any "ought" at all is to imply a standard outside the ironclad machinery of "is"—beyond just how things are and how they work.
That aspirations to the beautiful and the true and the good persist among people whose metaphysics furnishes no cause for believing in any such things is a wonder indeed. Perhaps it is a hangover from outdated Christian assumptions, now rightly jettisoned but still peskily embedded in our lizard brains. Or perhaps it indicates that no one really believes in a random universe after all—that try as we may, we cannot help suspecting the universe is not random, and things like fairness ought to exist whether they currently do or not. If so then it follows that such standards come from a place beyond us, and the burden of meeting them at a universal level does not fall entirely upon our own narrow shoulders.
-Spencer Klavan, associate editor of The American Mind

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