THE CARTER administration early singled out Jamaica as a place in which to demonstrate to the generally suspicious (and socialist) Third World that the United States would not shy from befriending socialist regimes -- if they served their people and stayed on the democratic track. Jamaica seemed just the right place to make such a showing: democratic in tradition, favored with a talented middle class, not a basket case, English-speaking, close by.

Well, Prime Minister Michael Manley, reelected as Jimmy Carter entered the White House, has been building socialism democratically. But the economy is an unalloyed disaster. Why? Some attribute it to a 20-fold hike in oil prices in less than a decade -- a painful return, by the way, on Mr. Manley's high-profile Third-Worldy foreign policy. His political and press opposition tend to blame his social profligacy and economic mismanagement; a kind of class conflict stirs the politics of Jamaica and Mr. Manley has replied that his rivals are sabotaging the economy to discredit him. Finally, Mr. Manley identifies the devil as the International Monetary Fund, which in its familiar manner has demanded painful austerity as the price of continuing to service Jamaica's foreign loans.

This last was the issue on which leftists in Mr. Manley's party forced a showdown the other day. The faction inclined to cooperate with the IMB was routed. Mr. Manley found himself swept along by party ideologues with a radical Cuban bent. The result is that Jamaica now has 1) large due debts on whose payment crucial food and raw-materials imports hinge, and 2) a government that, even while it says it will honor its obligations, has rejected the one available way to do so. The Soviet Union and others have been asked for loans -- Mr. Manley has just popped over to Cuba -- but evidently none has come through. In the tension and political violence now spreading in Jamaica, it is being asked whether the elections scheduled for the end of the year will come off. The most recent polls suggest Mr. Manley's party would lose.

The Carter administration has had success in Jamaica in erasing earlier suspicions -- none ever proven -- that the U.S. seeks to "destablize" the country's socialist experiment. It makes no apologies for continuing to show hospitality to ideological diversity now. American officials still insist, however, that democracy must prevail. Jamaica certainly has the right to foul up its economy. But the people must have the right to change their government if they choose. On that foundation American policy toward Jamaica must rest.