WITH HIS three-to-one victory in Poland's presidential election, Lech Walesa has triumphantly established what American politicians call a mandate. There is no question now who speaks for Poland. When he was running against the patient and thoughtful Tadeusz Mazowiecki, the outgoing premier, it was possible to have some doubts about Mr. Walesa's expansive populism and his tendency to keep too many decisions tightly held in his own hands. But when Mr. Mazowiecki was eliminated in the first round of voting two weeks ago, Mr. Walesa found himself running against the highly questionable Stanislaw Tyminski. At that point a victory for Mr. Walesa, and a big one, became crucial to Poland's democratic future. That's what the voters have now delivered.

Mr. Tyminski, an emigre who had made money in Canada and Peru, became a symbol for instant and effortless wealth. If he had done well in this weekend's runoff, it would have been a very bad sign. Worse, Mr. Tyminski never explained the presence of the former secret police officers who were on his campaign staff. Some of his support obviously came from people who rose to power in the Communist regime and now resist losing it.

As president, Mr. Walesa will be judged above all by his ability to bring the country through the rigorous economic reforms on which it has now embarked. One of the Mazoweicki government's great achievements has been to pull Poland back from the brink of hyperinflation and stabilize the currency. That required it to end the automatic adjustment of wages to inflation, and come to terms with the declining productivity of an economy in a state of peaceful revolution. That wasn't popular, and it helps explain Mr. Mazowiecki's defeat. Now, as a former union leader, Mr. Walesa is going to be under fierce pressure from his supporters to come through with big wage increases. The crucial part of his job will be to explain to Poles, more persuasively than Mr. Mazowiecki managed to do, why restraint is crucial.

Despite its immediate troubles, the present moment is, for Poland, the most promising in its modern history. It is the first time in 2 1/2 centuries in which Poland has been not only a sovereign country but one menaced neither by a suspicious Russian empire to the east nor an aggressive Germany to the west. For some years Poles will be poorer than their neighbors in Western Europe, and that contrast will put a strain on their political life. But wise policy -- in both Poland and the West -- is capable of diminishing that disparity over time. Mr. Walesa takes office in a time of great hope.