While the presidential campaign was intolerably long, it may, at least, have finally convinced the country that our way of running elections is a mess. hIt may have generated such a consensus for reform, even among the politicians, that there is hope for relief.

If President-elect Ronald Reagan is looking for a popular and constructive initiative with which to launch his administration, he could do worse than present the incoming Congress with a comprehensive package of long overdue electoral improvements. In the present political climate, he might succeed where Jimmy Carter failed.

Shortly after his inauguration in 1977, Carter submitted to Congress the most sweeping election changes ever proposed by a president. The package included a constitutional amendment to elect the president by popular vote and abolish the anachronistic electoral college.

In addition, he proposed the elimination of restrictive state laws on voting registration and urged federal financing of Senate and House campaigns, along the lines of the government's subsidy of presidential elections. Carter also called for amending the Hatch Act to permit federal government employees to run for political office, hold party office and serve as campaign volunteers.

Carter's message was hailed by many citizen groups and won bipartisan approval on Capitol Hill. Reform bills were sponsored jointly by Democrats and Republicans in both the Senate and the House. For a time the legislation appeared to have clear sailing but in the end was derailed by filibusters and other blocking tactics that a bungling White House couldn't cope with.

The 97th Congress, however, provides a new opportunity. The leading congressional Democrats are already comitted to most of the changes Carter proposed. Prominent Reagan-backers in Congress also endorsed much of the program. The most controversial change -- simplication of registration -- originally won the approval of Bill Brock, the GOP national chairman; Sen. Howard Baker, who will be the new Senate majority leader; and Rep. John Rhodes, the present minority leader of the House. Later on, they hedged.

Reagan could well embrace an additional change, proposed by Baker himself, that would make Election Day a national holiday and keep the polls open for 24 hours. Still another welcome change would be the substitution of a national presidential primary, or several regional primaries, for the countless state tests that stretch over six months.

The voting turnout in the United States is always being compared unfavorably with that in the European democracies, and this year is no exception. In recent U.S. presidential elections, the turnout has averaged only 55 percent of the voting-age population, which is widely seen as indicating an alienated, disillusioned public or, at best, an apathetic one. A closer look, however, suggests the trouble may lie elsewhere, chiefly in the discouraging registration obstacles Americans have to overcome to vote in most states.

In England and Europe, the turnout of "eligible" voters usually exceeds 70 percent, and in some cases 80 percent. But in those countries registration is not a problem; nearly everybody is automatically eligible.

In the United States, though, an eligible voter is one who is registerd and able to get to the polls on Election Day. This year the voting-age total was 160 million, but the eligible (or registered) total was far less, an estimated 112 million. Hence, while 84million votes cast on Nov. 4 were only about 52.2 percent of the total adult vote, they added up to 75 percent of the eligible vote, or well in the European range.

In appraising the U.S. turnout, it should be kept in mind that the voting age total in America is substantially swollen by including millions of aliens who are barred from the ballot, plus millions more who are in prisons and other institutions.

Several states have made it possible to register by postcard or by simply displaying some form of identification (such as a driver's license) at the polls on Election Day. The result: a voting increase of 10 to 20 points over the national average, with no fraud.

Before registration was introduced in the United States more than 50 years ago, the turnout in presidential years was 80 percent or more of the eligible voters. The obvious moral is: don't just scold our citizens; make it easier for them to register.