Why not have the eugenics institute(s) find people of merit on whatever sets of measures they want and pay those they choose to have kids or to supply sperm/eggs/parenting (whichever they think important for the traits)? Maybe also give subsidized child-care to their progeny. This would allow for competition of metrics between and inside such organizations.
Sure only using positive feedback might be a bit slower than also availing ourselves of negative ones. But negative ones seem more tricky to implement, and we don't actually know what the species will need in the future, i.e. if we even have a single goal in this search space. Ethically less complicated to nurture the flowers you want to see blooming than to have a hand in cutting off others.
2. Yes, amplifying possibly unfair advantages is a nasty side-effect of this, but in a "mostly clean an functioning" capitalist society with not that much corruption, mafia and stuff this could be mitigated (I even goes the US comes close enough to this... by comparison on a global scale).
3. I don't think this will "put us at each other's throats"... poorer people to which the tax is targeted at should feel more motivated to have a better life, like swimming pool and better sports car than to have kids... or we'll need to fix this with more "pro-consumerist propaganda"!
4. And about positive versus negative feedback/motivations... I might have an overly "dark" view of human nature, but I think only negative/pain/punishment will work for those that need to be discouraged in having children (benefits might make the other change their minds and have more children but my intuition tells me it won't work - yes, we need some sort of controlled social engineering experiment to check this assumption, of course).
On the other hand, the eugenics institutes I mentioned ("organizations" maybe you like that word better?); well, those could be lots of different groups of like-minded people/sub-groups spending their own resources the way they want to increase the frequency of traits in the world that they value.
If I and some friends want to pay to subsidize progeny of our choosing, how is that more scary than the various states of the world financially penalizing people (even sterilizing or jailing people in other suggestions of yours) toward similar ends?
a tax is centralized, but the fact that some can pay it and some cannot it not dictated by a central authority, that's the reasoning. The state would not decide who has enough money to pay the tax, and this would be an emergent effect from economy. NOBODY would decide and this I think would be a good thing!
Your group of friends could just as well finance the poor people that nevertheless they think have desirable traits.
NOTE: I still would'n support such my proposed soc-eng strategy in any current society because the erosion of human rights and possibility for abuse is far too great, so the discussion is entirely theoretical anyways, but it was fun
NOTE: The only eugenics I am for are those based on voluntary gene replacement.