There are some coherent approaches without picking and choosing, though. For example, according to luck egalitarianism any major (dis-)advantage that someone has in life that is given by sheer coincidence is not deserved. The policy of the state should then be to make society more equal by reducing advantages and disadvantages that stem from pure luck.

To address your examples, the state should try to help people with abnormally low life expectancy achieve higher life expectancy, try to equalize different wealth and education levels by making education available/affordable to everyone, by severely limiting wealth distribution by inheritance, and so on, and help people with mental illness to lead a normal life as others (which could include all kinds of measures from tax-funded mental health care to changes in work law).

I don't really want to defend luck egalitarianism here, although I personally consider it a reasonable position. It's an example to point out that relative to a theory of fairness the solutions can be fairly clear. The "picking and choosing" is rather the result of disagreement about the respective theory of justice.

The groups selected as help-worthy are often arbitrary.

The largest inequality I see in real life is between first-born women and their younger siblings. First-born women are often hyper competitive and earn way more than their siblings, including brothers.

Should we discriminate against first-borns in university admissions?

I see no evidence for the claim that the selection of help-worthy is often arbitrary. Anyway, I'll accept your example for the sake of the argument.

Of course, why shouldn't we help people who are second, third, or fourth born if they are at a systematic disadvantage according to robust data?

AFAIK, many societies have changed hereditary law over the past centuries to compensate for former advantages of first-borns in favour of other family members.

> To address your examples, the state should try to help people with abnormally low life expectancy achieve higher life expectancy

But we don't, and that's generally accepted, isn't it? There's a strong (and recent!) difference between male and female life expectancy, but we accept that, because "men" aren't one of the chosen minorities.

The issue is exactly what you mentioned there: "abnormally low life expectancy". Once we declare something normal, we're done, no more intervention necessary. We could just do the same with poor people and only help those that are abnormally poor. But we don't, because reasons.

> We could just do the same with poor people and only help those that are abnormally poor. But we don't, because reasons.

I have to disagree. If at all, the people who make the decisions whom to help and whom not to help are Prioritarians (due to the popularity of Rawl's famous book), which is exactly the position you describe. I have inadvertantly slipped into Prioritarian language when I used "abnormally."

What I had in mind and you criticize is Luck Egalitarianism. That's a fringe position that I've never heard from any politician or decision maker. Larry Temkin defends it, for instance, in case you're interested in the actual reasons rather merely dismissing them with a phrase like "because reasons." There are good reasons for it, and I personally find luck egalitarianism more compelling than Prioritarianism.