Does the best man win?

When I am asked whom the Democrats will nominate for president next year I turn to a book published 90 years ago, ''American Commonwealth'' by James Bryce. So far as I can see, Bryce indicates Sen. John Glenn of Ohio, the astronaut. Of course it's a bit early yet so we can't count too much on Bryce; it's the pattern that counts.

In a recent thumbnail poll of Democratic delegates at the party convention in Wisconsin, Senator Glenn did well by the Bryce criteria - he lost. As I interpret the Bryce rules, that was the indicated course. Victor in Wisconsin was Sen. Alan Cranston of California; he gave former Vice-President Walter F. Mondale an embarrassing surprise defeat. (Sen. Gary Hart of Colorado was third.) So what? Presumably the result at this early date will irritate the supporters of the three ''winners''; Senator Glenn just stays in the background. This could , of course, turn into a pattern for victory - in the Bryce outline.

James Bryce was British ambassador to the United States, 1907-1913, and was made a peer in 1914. He was enormously popular and his two-volume interpretation of America is a delight. He liked America. He begins chattily telling about the big country with its 60 million: ''I have never met a European of the upper or middle classes who did not express astonishment when told that America was a more agreeable place than Europe to live in.'' He explains, ''In cities like Cleveland or Chicago one finds miles on miles of suburb filled with neat wooden houses, each with its tiny garden plot, owned by the shop assistants and handicraftsmen who return on the horse-cars in the evening from their work.'' Little class consciousness exists. He likes Americans' buoyancy and cheerfulness. In a footnote he tells an incident: ''In a small Far Western town the stationmaster lent me a locomotive to run a few miles out along the railway'' to see a prized view. There was no self-consciousness, no condescension in the exchange, he said. His locomotive host talked with equality and intelligence. (Thank goodness, Bryce adds, ''that I had resisted, in the forenoon, the British impulse to bestow a gratuity.'')

Now about this 1984 election: Senator Glenn may not welcome the implications of the Bryce analogy. Bryce titled his famous 8th Chapter: ''Why Great Men Are Not Chosen Presidents.'' He goes over contemporaries and they are a rather depressing list: Chester A. Arthur, Garfield, Hayes, Benjamin Harrison - not a world-shaker in the lot. (In a reverie the reporter today compares Eisenhower, Lyndon Johnson, Nixon, Carter, and Reagan.)

Bryce says bluntly that the Old World thinks ''the proportion of first-rate ability drawn into politics is smaller in America than in most European countries.'' Why, he asks? Because ''the method of choice does not bring them to the top.'' He continues:

''Fiercer far than the light which beats upon a throne is the light that beats upon a presidential candidate, searching out all the recesses of his past life. Hence, when the choice lies between a brilliant man and a safe man, the safe man is preferred.'' The ''ordinary American voter,'' he asserts, doesn't object ''to mediocrity.'' (That, of course, was 90 years ago.)

Continuing the argument, he says that ''the total quantity of talent devoted to parliamentary or administrative work is larger (in Europe), relatively to the population, than in America . . .''

In the British election just held, 72.7 percent of the eligible voters voted. It is interesting to note that in the 1980 US presidential election only about 54 percent voted. (In each of the five latest US presidential elections, incidentally, the percentage has declined.)

Back in 1893 Bryce said rather unflatteringly that the American voter ''likes his candidate to be sensible, vigorous, and above all what he calls 'magnetic,' and does not value, because he sees no need for, originality or profundity, a fine culture or a wide knowledge.'' He adds, rather discouragingly, that ''to a party it is more important that its nominee should be a good candidate than that he should turn out a good president.''

Right or wrong? It is a challenge that still exists.