In liberal circles, the wage gap between men and women is a major focus of attention. President Obama references it frequently, and Hillary Clinton has unsurprisingly made it a major campaign plank.

Typically, the wage gap is presented as a median value — the difference between men and women right at the 50th percentile of the income distribution. And since the Census Bureau just released the Annual Social and Economic Supplement (ASEC) for its Current Population Survey (which contains detailed income data for 2015), it's a good time to check in and see how the wage gap is doing. It turns out that in 2015, the median woman made 80 cents for every dollar the median man made. It's a problem that has been improving, but with grinding slowness.

However, the median measure does not reveal how the wage gap breaks down across the income distribution. It might vary between rich and poor — and when you run the numbers, it turns out it does. The wage gap is substantially smaller at the bottom of the income distribution than the top, both in percentage and absolute terms. That means potential intra-left conflict between meritocrats, who would close the wage gap, and egalitarians, who would close it while also flattening the overall distribution.

The same ASEC microdata can also be used to calculate the distribution of the wage gap. Here I've broken it down by 5-point intervals, up to the 90th percentile:

The wage gap at the bottom of the income distribution is much smaller than at the median — a woman at the 10th income percentile makes 87.5 percent of what her male counterpart does. But the gap at the top of the distribution is much larger — a woman at the 90th percentile makes only 73.6 percent what her male counterpart does. In dollar terms, fully closing the wage gap would deliver $2,600 in annual income to the 10th percentile woman — but $33,000 to the 90th percentile woman.

The wage gap is a complex phenomenon, and it's hard to know with complete certainty what is happening here. However, one can formulate some reasonable hypotheses. The lowest-paying work is generally in service jobs where there is little chance for career advancement, and everyone is paid the same low rate indefinitely. The minimum wage is very important here, because it provides a floor beyond which (most) wages cannot fall, prevents employers from capturing welfare benefits like the Earned Income Tax Credit, and serves as an anchor that pushes wages up well past the formal minimum wage level.

At the top, detailed accounts of the wage gap show that it's probably the result of some combination of outright discrimination, unfair social norms around salary bargaining, and especially how child-bearing and disproportionate child-rearing means fewer opportunities for raises. Reaching very high-paying jobs often depends on never leaving that career track for a second, so percentage raises can compound and pile up.

But this presents some potentially tricky questions. Imagine we present two options to a 10th percentile woman: Either we can close the wage gap, or bring the whole bottom 10 percent, men and women, up a single decile bracket to the 20th percentile. For that woman, the choice would be easy. Closing the wage gap would mean an additional $2,600 — but the bracket jump would mean an additional $5,800, more than twice as much.

That's a crude thought experiment, but it illustrates a real ideological fault line between the two broad schools of thought on the left, egalitarianism versus meritocracy. An egalitarian approach would place the greatest moral priority on the poorest women, and hence would close the wage gap while also raising up the bottom and ratcheting down the top. Most obviously, the extreme pay packages of corporate executives, regardless of gender, would be forced down with confiscatory top marginal taxes and re-unionization — thus diverting corporate money to workers, research, investment, and so on. Raising the minimum wage, and running the economy hot to tighten labor markets, would mean more wage income going to the bottom, and less to the top.

Universal paid leave, probably the most important wage gap policy because it makes it much easier for women to stay in the labor force, could be funded with broad-based taxation, though Hillary Clinton's plan says the rich will pay. Other vitally necessary transfer programs to eradicate poverty would not affect wages per se, but would be expensive enough that the rich would have to pay.

But a meritocratic approach would be different. This school of thought is more concerned with ensuring people are allowed to fulfill their natural potential, not the distribution as a whole, and hence would tend toward simply closing the wealth gap without any leveling. This would have the great advantage of making a lot of workplaces far more fair, especially elite ones — no small achievement. However, meritocrats most concerned with female professional success at the very tippy-top of the social ladder would most likely balk at the massive tax increases and assault on the executive class necessary to seriously improve the situation of women at the bottom. It's even conceivable that some ultra-rich female executives would prefer to keep the pay gap rather than take a large absolute pay cut as part of a program to help women at the bottom of the wage ladder.

It's vanishingly unlikely that any of the above policy will be passed soon. But at some point, this dispute will come up. Clinton's paid leave plan, for example, will supposedly be a universal plan funded via taxation on the rich. A likely counter-offer from rich meritocrats is to do it like we currently do most health insurance, with an employer-based tax subsidy that would be far cheaper. That would help maybe the top half of female workers stay on the career track, while doing nothing at all for the bottom half.

So in the future when we're talking about gender and justice, let's remember that the wage gap has a class bias.