The topology of justice

Several people are complaining about Osborne’s decision to abolish child benefit for higher-rate taxpayers on the grounds that it violates horizontal equity. Under his scheme, a family with a single earner getting £50,000 a year loses, whilst one with two earners getting £40,000 each keeps the benefit. Which seems unfair.
This, though, raises a broader question. What is the relationship between partial justice and wider justice?
In this case, one could argue that Osborne’s move satisfies wider justice - because it means median earners no longer transfer cash to the better off - and yet it violates partial justice.
This is not the only such example. Chris Bertram says:

Many self-described left-wing academics of my acquaintance, though earning in the very highest percentiles of the income distribution, believe they are underpaid and ought to get more. This belief, I submit, is in practice inconsistent with even sophisticated egalitarianisms.

Perhaps, though, what we have here is another trade-off between partial and wider justice. One could argue, from the perspective of partial justice and depending on the case, that a particular professor earning £50,000 is underpaid relative to another one getting £60,000. And yet at the same time, you could argue that both are overpaid from some perspectives of global justice. Giving one a pay rise would then satisfy partial justice but (arguably?) worsen global injustice by increasing inequalities between the worst off and better off. 
The issue here doesn’t merely apply to income equality. Imagine a nation in which libertarian justice were violated - say because private property was illegal. A government then permitted private property, but only for whites. Would this represent a move towards justice - by allowing some private property - or away from it, by introducing racial injustice?
What I’m asking here is: what is the topology of the domain of justice? It’s often thought that justice, whatever one’s conception of it, applies to a smoothly-sloping surface, so that the correction of one injustice moves us closer towards perfect justice. But is this really so? Could it be instead that the topology is hilly, such that moving to the top of a local hillock (local justice) entails moving away from the top of the mountain (global justice)?
There might be a parallel here with welfare economics. It’s well-known that, in theory,  in conditions where Pareto-optimality is impossible, welfare might be increased by a policy which, on its own, introduces another market imperfection. Is what is true of welfare also true of justice? If not, why not?
Another thing: a better way to claw back child benefit from the rich would have been to keep the benefit universal, but simply to raise the top rate of tax. But a Tory Chancellor wouldn't do this.

Comments

[twitter.com/matt_heath]

I think you want a topography of justice. Topologically speaking, hilly is the same as flat (and coffee cups are doughnuts).

[Prateekbuch]

a better way to claw back child benefit from the rich would have been to keep the benefit universal, but simply to raise the top rate of tax. But a Tory Chancellor wouldn't do this.

Or, keep child benefit (and winter fuel allowance, for that matter) universal, and tax it (them), a la IPPR

Currently reading Amartya Sen's Idea of Justice, some answers to be found there I reckon

[Nick Rowe]

Chris: if you take standard optimal tax theory, and just add in an assumption that some people have additional expenses (kids, glasses, whatever), you get universality as a feature of the optimal tax system. See Frances Woolley's post today: http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/10/britains-proposed-child-benefit-taxback-is-inefficient.html

I can't think of any second-best argument for clawback. If you can't raise the top rate of tax, why can you raise the top rate of effective tax on people with children?

[Sam]

"why can you raise the top rate of effective tax on people with children?"

Because people are stupid.

[Leigh Caldwell]

"why can you raise the top rate of effective tax on people with children?"

Because the effective tax rate on people with children is lower, so you aren't actually raising the top rate. You're just unifying the second highest and highest rates.

Or what Sam said.

[Adam Bell]

I think justice would be better modelled by a topology more analogous to that of space time, with the self taking the role of mass. In other words, wherever one happens to be one is always sitting in one's own little hollow of injustice.

[Nick Rowe]

Leigh: the top *marginal* effective tax rate on people with children is the same (under the old system) as people with no children. It's marginal effective rates that have disincentive effects.