There he was, the new mayor of New York, standing in his cramped kitchen, washing his own dishes. It made an irrestible news photo. Let Jimmy Carter or Jerry Brown top that for folksiness.

Until recently, the President of the United States and the governor of California appeared to have few rivals in the anti-elitist, man-of-the-people sweepstakes. But now other politicians, the latest being New York's Ed Koch, are getting into the act.

As yet there are no established rules for playing the game, but if there were, Koch's ploy in spurning his fine official residence, Gracie Mansion, would probably be ruled out as unsportsmanlike conduct, for it is unfair to other contenders, like the President.

After all, how could Carter abandon the White House for an efficiency flat without deserting or seriously inconveniencing his wife, daughter and assorted other relatives who have taken up residence at 1600 Pennsylvania Aveneu?

On the other hand, Koch should feel perfectly free to walk to work (as Carter did after his inauguartion) or carry his own luggage, as our populist' chief executive does so uncomplainingly - at least on his domestic travels.

Sleeping, however, raises additional competitive problems: New York's new mayor, for instance, can dramatize the Spartan simplicity of his lifestyle by stretching out on that now well-photographed iron cot in his threeroom, rent-controlled Greenwich Village apartment.

California's governor has got even greater mileage out of the bedless mattress he is reputed to sleep on in the pad he uses in preference to living in high style at the elegant governor's mansion in Sacramento that the taxpayers provide.

What excuse, though, would Carter have for emulating them? Even if he wanted to go them one better by sleeping on the floor, there would be carping critics complaining that if Lincoln's bed was good enough for the Great Emancipator it ought to be good enough for Jimmy Carter.

The Presdient will just have to face up to the fact that it's not easy for any moderan White House incumbent, or his family, to project an image of plan living. Gone are the days when the first occupants of the White House, the John Adamses, hung the family wash in the now glittering East Room. Before the time of Teddy Roosevelt, the First Family could correspond on any old writing paper, but today all the stationery is majestically headed "The White House."

When it comes to transporation Carter is also handicapped. Koch, for example, can rub elbows with the common people by using a crowded public bus to commute between his apartment and City Hall. Jerry Brown, as the world well knows, drives himself around in a battered old compact, after having rejected the big limousine and chauffeur that come with the governorship.

The best Carter could do was to take the limousines away from the White House staff. The Secret Service would go crazy if the president insisted on driving himself around or taking a bus. This problem has been weighed by a former White House aide, William Safire, who says:

"Envision Jerry Brown as Presdient - having refused to live in the pretentious White House like other politicians - surrounded by limousines loaded with Secret Service agents and cops on motorcycles, driving his own little car to work from his bachelor pad. It would vividly symbolize the Spartan life, but it would cost a fortune every morning."

No matter how hard Carter and Brown and Koch try to identify themselves with the common man, it's obvious that they are actually most uncommon men. All three are notably intelligent, well educated and politically sophisticated. There's not an average bone in their bodies.

Do the people really want an ordinary man in the White House? They had one in Jerry Ford, who effortlessly projected the image of a simple, sincere, unassuming, average man, but where did it get him? He was the first incumbent President to be defeated since Herbert Hoover in 1932.

No one can deny that Lyndon Johnson had a genuine "commin" streak. It was prefectly natural for him to confer with his staff and others while sitting in his White House bathroom. Although he was "just folks" with a vengeance, it didn't help him much in the politics of 1968.

President Eisenhower's image-makers persuaded him to wear a homburg instead of a top hat as his first inauguration, but after that Ike happily went back to golfing, hunting and cardplaying with the millionaire cronies whose society he so unfeignedly enjoyed. Four years later he was re-elected by a landslide.

That master politician Richard Nixon confidently backed his hunch that the American people secretly liked presidential pomp. He even dressed up the White House sentries like a Ruritania palace guard, which inspired sophisticated laughter, but in the next election Nixon carried 49 out of 50 states.