Administration officials are trying to figure out an affirmative action compromise that will improve hiring opportunities for minorities and women without reducing job opportunities of white men.

After that, they can start working an omelet recipe that does not entail the breaking of eggs.

The thing that Labor Secretary William Brock, Attorney General Edwin Meese and other officials are looking for does not exist. They can draft an executive order that will pressure government contractors into a greater effort to integrate their work forces, or they can draft an order that will sound fair while producing no useful result.

They will do the latter, of course. If the administration had been interested in the former, it would have left in place the existing goals-and-timetables formulation.

It doesn't necessarily follow that the administration officials are bigots who wish to continue favoring white men over women and minorities, though there are some bigots in high places. What makes this issue so hard to resolve is our different, often irreconcilable, perceptions of the problem.

One group begins with the premise that employers, left to the dictates of the marketplace, will choose to get their work done in the most cost-efficient manner: with the very best workers the prevailing wage will buy.

Under that assumption, race and gender discrimination will take care of itself. A garage owner would be a fool (the reasoning goes) to prefer a male front-end specialist over a woman who could do 5 percent more front-end alignments for the same pay.

If that is your assumption, then what victims of "discrimination" need is not affirmative action but better skills and work habits.

Another group will take as a given that people tend to hire people who remind them of themselves. And since the hirers are disproportionately white men, white men, given anything like an equality of merit, will get a disproportionate share of the best jobs -- unless some outside force intervenes. That outside force could be anything from a stricken conscience to the threat of a boycott to a presidential order.

There are a couple of positions whose main utility is to confuse the issue. One is that discrimination is the right of free men, and that it is up to the marketplace, not the government, to extract a price for that bigotry. The other is that it is proper to parcel out society's goodies strictly on the basis of demographics. But while debaters often invoke these straw-man positions to make their own positions look good, few people actually believe them.

What most of us believe is that discrimination on the basis of race, gender or other irrelevancy is wrong, and that government has a role in mitigating it. The questio is: How do you establish that the discrimination exists?

One side, the side now in political power, believes that the only discrimination the government needs to be concerned with is the demonstrable discrimination against an individual. Prove that you lost a job to an obviously inferior candidate on the sole basis of race or sex, and even Brad Reynolds will agree you deserve relief.

The other side, recognizing that it is seldom possible to prove who got "your" job, let alone whether that person was better qualified, takes a different approach. It assumes that the easiest way to tell whether an employer discriminates is to look at his work force.

Does it reflect, in general terms, the available pool of qualified hopefuls? If not, is there an explanation? If there's no reasonable explanation, how much improvement might we expect, and when?

That has been the government's approach for two decades. Those to whom it makes sense describe it as "goals and timetables." Those who want the government out of the affirmative action business brand it "quotas," and hope that will be sufficient to kill it.