The recent election victory of a conservative, basically Pro-American government in the Indian Ocean island republic Sri Lanka completed the elimination of left-leaning governments throughout volatile South Asia.

The process began in 1975 with a grisly coup d'etat in Bangladesh. Then, in March, India's Prime Minister Indira Gandhi was swept from power in a stunning election. Gandhi's fall was followed by a bloodless coup in Pakistan last month. And now, Sri Lanka.

An analyst examining these major shifts in the Subcontinent is tempted to look for a single cause, a popular desire for Western-style democratic rule.

A close look, however, makes it quite clear that the only real common factor that could have provoked the drive for change in the four South Asian nations was their ruinous poverty.

Poor people are dissatisfied, and dissatisfied people want change. Beyond that, the four cases are distinctly different:

Bangladesh's prime Minister Mujibur Rahman was slain because of his swift slide into corruption.

Gandhi was voted out because she ran roughshod over the most basic human rights of the Indian people.

Pakistan's Prime Minister Zulfiqar Ali Bhutto was toppled because, ultimately, he lost the important support of the army.

Sri Lanka's Prime Minister Srimavo Bandaranaike lost her election because she ran the economy of what should be a rich country into the ground.

Idelogy, of the left-right variety, played little or no role in any of those cases. The essential reason for this was that, despite their left-leaning images abroad, the four South Asian leaders had very little genuine commitment ot any particular ideology.

Mujib's alignment with the Soviet Union through India was dictated by the fact that he owed the independence of Bangladesh - and his own life - to Gandhi and the indian army's intervention in the 1971 war of secession from Pakistan.

Gandhi's own ideology, as an influential newspaper editor in Bombay put it recently was "somewhere to the left of self-interest." By the time her son. Sanjay, had reached the peak of his personal powers she was following his lead to closer relations with the United States and away from the Soviet Union.

The depth of Bhutto's commitment to socialism may be gauged by his sudden concession to his opponents' demands for the most conservative kind of Islamic laws in the weeks just before his fall.

Bandaranaike, despite her party's alliance wiht Trotskyites and other Communists, gradually became identified with Sri Lanka's big business houses. She and her family are probably the wealthiest property owners on the island.

As to a polular commitment to Western-style democrary, the picture is somewhat blurry. Indian voters, no doubt, voted for democracy even though the central thrust of their ballots was negative, against Gandhi's authouritarianism.

The astonishing results of the Indian vote did have a certain influence on pakistanis, who rioted for months against Bhutto before the army took charge. Yet, the army was welcomed. There are now growing doubts among politically astute pakistanis that the present strongman, Gen. Zia ul-Haq will allow voting to take place in October, as he has promised repeatedly.

In its 30 years of existence, Pakistan has spent much more time under military dictators than it has under democratic governments.

Bangladesh, which until six years ago was part of Pakistan, also undoubtedly is more at ease these days under the dictatorship of Gen. Ziaur Rahman than it was with the civilian Mujib in charge This is due, in large measure, to the good fortune of outstanding rice crops in a row. Zia, who like his namesake in Pakistan came to power seemingly against his personal desire, shows no sign of stepping aside.

Sri Lanka, like India, has had democratic governments since being granted independence by Britain. Unlike its giant neighbor, the little country, which used to be named Ceylon, has changed governments in every election.

The SRI Lankans are fond of saying that this see-sawing proves the genuineness of their democracy. They also admit that the constant change has weakened the effectiveness of the democratic system in their country.

Thus, in two of the four South Asian countries, democracy prevails for the moment. Given the slide toward military dictatorships and communism in other parts of Asia and elsewhere in the Third World, it is not a bad average. Why this should happen in a part of the world most distinguished for its poverty is not an easy question to answer.

Perhaps the most obvious reason is that the former British colonial powers in India And Ceylon instilled respect for democratic norms during tier long tenure. They took an active part in developing indigenuous, relatively efficient civil services.

The independence procedure was gradual enough so that by the time they stood on their own feet, the elites in both countries were throughly convinced of the value of the system and, more important, capable of making it work.

Although only two of the South Asian governments are now democratic, all four are, for the first time, notably right wing. What does this imply for the United States and the other Western powers?"

Probably not much. Leaders are likely to tone down their predecessors' attacks on "Western imperialism" in nonaligned conferences. Diplomats may not vote against the West so often in the United Nations. But, for a variety of reasons, none of the four can afford to weaken their ties to the Soviet union and China a great deal.

India, for example, must continue to rely on the Soviet Union to provide its armed forces with spare parts for its arsenal. Pakistan must maintain its friendship with China to counter what it sees as an ever-present threat from India. Bangladesh has begun turning to Peking to replace the friendship with Moscow lost when Mujib died. Sri Lanka is likely to maintain its close relationship with the Chinese for aid and trade.

All this could probably be altered if the Carter administration chose to step up its involvement in the subcontinuet. So far there is no sign of this happening.