Three kinds of people want a head-to-head debate between Mayor Marion Barry and his front-running challenger, Patricia Roberts Harris.

First are those who believe, naively, that things we call debates (but which, in reality, are more like disjointed panel discussions, enlivened only by an occasional potshot) give voters a clearer understanding of candidates' positions on the key issues.

Second are those who are following the mayoral race the way I follow Saturday afternoon boxing on TV: caring less who wins than that it be a good, close fight.

And third: those who want Pat Harris to be mayor.

There are, on the other hand, only two groups of voters who are roundly opposed to a Barry-Harris debate: those who are backing one of the other candidates and who resent the implication that only two serious contenders remain in the race, and those who would like to see Barry re-elected.

One-on-one debates are a political crapshoot, a gambler's last spin of the wheel. It isn't the guy who's comfortably ahead on points who abandons caution in an effort to achieve a last-round KO; it's the guy who knows that unless he can land that haymaker, he'll go home a loser.

Political debates, while occasionally good theater for the voters, are not staged for the benefit of voters. They are a campaign device for candidates, to be welcomed or avoided depending on whether a particular candidate thinks they will help or hurt the cause. Sometimes a candidate will want a one-on-one (Jimmy Carter wanted--needed--to take on Ronald Reagan, but refused to include independent John Anderson; George Bush wanted to debate Reagan, but not the other challengers for the Republican nomination). Sometimes it seems politically wiser to go against the field: Reagan wanted to go against both Carter and Anderson; Walter Washington, Barry's mayoral predecessor, preferred forums that included both Barry and Sterling Tucker.

The preferences have everything to do with political strategy, and nothing to do with voter enlightenment. Hardly any voter can remember the philosophical or policy differences brought out in a debate. What we remember are the telling one-liners (Reagan's ". . . are you better off than you were four years ago?") and the fiascoes (Gerald Ford's goof on the freedom of the Polish people).

Harris, quick-witted, articulate and behind in the polls, wants a chance to go head-to-head with Barry. Barry, a less-gifted orator with a lead in the polls, would be crazy to give it to her. Chances are he won't.

Unless the public pressure for a one-on-one debate forces him to. It would be first-rate entertainment, and it just might afford us the chance to see a knock-out. (Will he mispronounce a key word? Will she lose control of her celebrated temper?)

But it wouldn't shed much light on either candidate's qualifications for the job. The skills useful in winning a public debate are not necessarily helpful in running a city, or even persuading congressional committees to vote a bigger D.C. budget.

Personally, I'd like to see them go at it -- not because they "owe" it to me but for the same reason I like to see a good prize fight: it could be a lot of fun, even if somebody gets hurt.