It's a quiet little squabble, unlikely to generate much publicity. But it provides a useful insight into one of Washington's hottest controversies: the arithmetic of fairness or, as some might see it, the fairness of arithmetic. On the one hand is the Justice Department, whose top officials are squarely on record as opposing numbers. On the other is the Equal Employment Opportunity Commission, whose chairman insists that he cannot perform his congressionally mandated duties without numbers.

One result of the conflict is that the Justice Department has so far been unable to send to EEOC what is required from all federal executive agencies: an acceptable affirmative action plan for dealing with discrimination. To date, the only plan submitted by Justice dealt with the disabled. And that one was bounced right back in part because it contained no numbers. EEOC Chairman Clarence Thomas says he needs the numbers "to fulfill our responsibilities under the statute to report to Congress on progress in the executive branch in the area of affirmative action."

"We don't think that there's any way we can report to Congress accurately if we don't know where an agency is today, where it plans to be five or six years from now, and where it is in terms of progress based on that plan," says Thomas. "Justice seems to think that they don't need those numbers. We disagree."

As long as two years ago, William Bradford Reynolds, assistant attorney general for civil rights, was preaching his anti-numbers gospel. "We no longer will insist upon, or in any respect support, the use of quotas or any other numerical statistical formulae designed to provide nonvictims of discrimination preferential treatment based on race, sex, national origin or religion," he said at that time. His remarks, which dealt with equal employment opportunity in private industry, obscured a crucial point: the purpose of the "numerical statistical formulae" he excoriated was not to facilitate preferential treatment but to ensure that employers were in fact not discriminating.

The industry EEO reports, like their federal counterparts, constituted a requirement on the part of employers to say: "here's how many women and minorities we have working for us at various levels; here's how many one would expect us to have based on their availablity in the labor pool, and here's what we plan to do to bring the two numbers closer together." Reynolds' reformulation amounts to having employers simply state that they would no longer discriminate. And while his agency would prosecute proven violations, it would be up to the victims to prove they had been discriminated against--often an impossible burden.

The opposing view, shared by the conservative Thomas, a Reagan appointee, is that numbers tell you a good deal about progress in eliminating discrimination, whether or not specific victims come forward to complain. "It's just like companies having to report to the Environmental Protection Agency on their (hazardous) effluents or whatever," Thomas said in a recent interview. "It's all numbers. . . . If Congress expects us to monitor the entire affirmative action program, the only way we can do it is to do it with aggregate numbers."

You'd think the point would be obvious, even to the numbers-hating Reynolds. Unfortunately, he has gotten himself into a trap between his philosophical view that fairness is individual and the practical fact that numbers can be a useful measure of fairness. The upshot is that, in employment opportunity, the Department of Justice is having trouble living up to its name.