FORTUNATELY, the strike for majority rule seems to have failed in Northern Ireland. Fortunately - because majority rule in Britain's unhappiest province does not mean what it might mean in other places. The Protestant majority votes as a bloc and, whenever given the opportunity, has used its power to discriminate against the Catholic minority. The purpose of the failed strike last week was to re-establish this highly peculiar local version of democracy.

The Northern Irish case is a reminder of the conditions essential to democratic self-government. It doesn't work well everywhere. It's a vulnerable enterprise and takes a lot of tending. In India, for example, the British constitution only produced a loose and tolerant one-party system - until Mrs. Gandhi made it temporarily less tolerant and created an opposition by throwing politicians into jail. In Canada, national democracy is currently jeopardized by the rising quarrel over languages. In Ulster, the menace is the endless guerrilla warfare between two communities whose differences, despite the labels, have very little to do with religion. Both sides have long since embraced terrorism and mutilation as legitimate tactics of politics.

There was a time, some years ago, when it seemed that the British government might work out a compromise. But the enmities have proved too hard and bitter. An experiment in sharing power was destroyed in 1974 by a massive strike organized by some of the Protestants. It was that triumph that last week's effort attempted to repeat. But the strike's failure still leaves the peacemakers very little to work with.

The repeated collapse of one negotiation after another has been deeply disheartening to the British government and to everyone else who has tried to take a hand. The record is a victory for nothing but the narrowest and least attractive kind of ethnic loyalties - which, in this case, divide people who are of the same race, speak the same language, belong to much the same social class, and have shared the same corner of a small island for hundreds of years.

What can Americans do? Not much - except, of course, refuse contributions for the guns and explosives that keep the bloodshed going. This country's most prominent Irish-American political leaders marked St. Patrick's Day this year by urging an end to American support for the gunmen. Neither side lacka armaments, to the deep misfortune of the whole population.

Nothing seems to be changing greatly. Meanwhile, two silent trends continue. The paramilitary organizations are expanding into common criminality. Gangs of young men increasingly prey on frightened neighborhoods, extorting money for protection and various causes - mainly their own pockets. There is also the steady trickle of emigration. As you might expect, the people who leave tend to be the best educated and the least wedded to crippling traditions. The longer the violence and the political stalemate continue, the more impoverished Northern Ireland becomes.