Given the choice between trying to maintain military superiority over the Soviet Union and signing an arms pact that gives both superpowers "equal . . . military strength," Americans chose the treaty by a ratio of 50 to 42, according to a new poll conducted by The Washington Post.

At the same time, Americans prefer by 53 to 31 a policy of getting "tougher" with the Russians rather than trying "to relax tensions with Russia."

These results suggest that popular support for the new strategic arms limitation trety (SALT II) exists but that it is weaker than the Carter administration has been saying and weaker than some polls whose questions are worded differently might suggest.

The extent of popular support for SALT II will be a factor in the coming Senate debate on the treaty, though spokesmen for both sides already have demonstrated that they can offer statistical support for widely differing interpretations of the true state of public opinion.

The Post poll-a survey of 1,808 adults conducted by telephone during the first half of May-suggests uneasiness in the country about America's world position in relation to the Soviet Union. By a ratio of 64 to 30, the respondents agreed with a statement that the United States has failed to do enough "to maintain our position as the number one nation in the world."

The poll produced an intriguing indication that reservations about President Carter among active members of his own Democratic Party have produced significant skepticism about a new strategic arms agreement with the Soviets.

Generally speaking, the more liberal a respondent said he was, the more likely he was to favor an agreement with the Soviets instead of U.S. military superiority. People who considered themselves conservative favored an agreement by 48 to 45; moderates by 49 to 42, and liberals by 55 to 40.

However, strong Democrats, the group in the political spectrum that includes the largest number of self-styled liberals-the group that might be expected to most favor an arms agreement-instead turned out to be the only group in the spectrum to favor military superiority, not equality.

The poll suggests that these strong Democrats-potentially Carter's most important political constituency-express strong reservations about a treaty because of an apparent disapproval of Carter's conduct of the presidency.

Strong Democrats who gave Carter a low performance rating also came out strongly against an arms treaty with the Russians. Stron Democrats who gave Carter high ratings expressed approval of the treaty, but the negative group was sufficiently large to tilt strong Democrats as a whole against a treaty.

Overall, strong Democrats favored "superiority" over a treaty based on equality by 49 to 41.In contrast, other Democrats favored the treaty, 54 to 36.Strong Republicans favored the treaty by 48 to 44. Independents chose it by 57 to 38.

For these other groups there appeared to be no linkage between their view of Carter's performance and support for the treaty.

As the SALT debate quickens in the months ahead, of course, the strong Democrats could fall in line behind the SALT II accord even if they remain unenthusiastic about Carter. This aspect of The Post poll may indicate more about Carter's own political problems than it does about the public's eventual attitude toward SALT II.

The Post poll's overall finding that by 50 to 42 Americans prefer a treaty giving both countries "equal strength" to a policy of trying to maintain U.S. superiority does not necessarily mean the public supports SALT II by that ratio. SALT II does not give both countries equal military strength, but only roughly equivalent strategic nuclear arsenals. Critics of SALT II contend it gives the Soviets an advantage in strategic weapons.

It appears to be all but impossible to draft a brief definition of SALT II that could be put to the public in a poll and that both critics and supporters of the treaty would agree was fair and accurate.

Questions about whether people favor "an agreement limiting nuclear arms," for example, regularly elicit high percentages of support, 70 percent and more. On the other hand, a more detailed poll exploring citizens' specific knowledge of the contents of SALT II has found widespread ignorance of the details.

A new poll conducted by the president's pollster, Patrick Caddell, has found that some of the administration's arguments for SALT II have failed to make a deep impression on the public.

This poll-distributed to some senators this week-found that only 22 percent of the public accepted the administration argument that U.S. national security would be diminished by Senate rejection of SALT II.

Caddell's poll also found that Americans believed-by a 31-to-25 plurality-that the United States is "behind the Russians in nuclear arms development." CAPTION: Chart, How People Feel About Salt II, By Robert Barkin - The Washington Post