What is Equality? Is it a state such that some market operation exists such that agents are left indifferent between their own endowment/preference set and that of other agents? If Preferences are at least partly determined by Society, clearly this definition fails because then Equality, as a Policy Objective, would be best pursued by tampering with Preferences- i.e. reconciling people to their lot. This cashes out as amor fati and Religion has already shown it is unbeatable at that gig.
To avoid this, one might postulate some other set of Preferences that people 'ought to have' based on their meta-preferences and work backwards from there. This fails immediately because you'd have to know the whole future fitness landscape- i.e. you'd have to have access to the sort of computing power which, if it exists, would make Evolution redundant. But this would mean that your solution would be apophatic- something outside language- because collocational Language use is clearly an Evolutionary process of some sort. So this cashes out as some apophatic Tetragramaton or Mathesis Universalis and once again Religion does that shite best.
Another approach, that of the Economist, would be to look at equality from the incentive/mechanism design p.o.v. This is just pi-jaw tarted up with some Statistical guesswork still it's good enough for the Great and the Good. Is it good enough for the rest of us? Inequality could give rise to two different Social effects
1) Tardeian 'imitation' or Girardian 'mimetic desire' whereby the agent having less of some good adopts the mores or modus operandi of the better off while from time to time requiring the sacrifice of some scapegoat to preserve Social Cohesion and prevent an envy based uprising. The problem with looking at the World like this is that you soon feel an overwhelming sense of disgust- the game is not worth the candle- and so we're back to Religion by way of Stoic dysphoria.
2) Learned Failure- agents adopt an Information assimilation model such that any new inequality gradient they notice convinces them that this is yet another chute they're going to slide down and this expectation is self-fulfilling. Actually, for me personally, this is the, Rational Choice, best in class, Solution and I'd download an app for it except I never got round to upgrading to a smartphone coz. like telephoning is so difficult? and how they have all these little buttons and I'd just probably lose it anyway or else the tough kids will take it off me along with my lunch money even though I'm 50 years old and don't actually go to the local Primary School
Learned Failure isn't Religion but it's the best defense against it. It's also good at reducing inequality coz it encourages fucking up and goofing off- both of which disproportionately affect the yield upon the Wealth gap to the better off- i.e. their Matthew effect Rent Take an example. If low paid people think they just can't do stuff better off people do then they won't imitate them or else they will fuck up when delegated work by them. This means the return on Income disparity to the Rich turns low or negative.
Clearly Learned Failure is what Secular Society has to push to survive. This is the true meaning of Enlightenment as Education.