While the world's attention Tuesday focuses on the outcome of the U.S. presidential race, balloting begins here for an election in which only the 268 Labor Party deputies in the British House of Commons are eligible to vote.

At stake in the voting is the selection of a new party leader and potential future prime minister if the Labor Party returns to power. Tuesday's balloting, however, is only the first step in a convoluted and uncertain process that could leave the leadership of the deeply divided opposition party in doubt for many more months.

Labor's leadership contest and the underlying struggle for the soul of the 70-year-old, union-based, left-of-center party that created Britain's postwar welfare state could be crucial for Britain's future and its relationship with the rest of Europe and the United States.

Although Labor has little chance of regaining power before 1984, the bitter ideological battles shaping up between the party's left and right wings could tear the party apart by that time.

One of the leading contenders to succeed former prime minister James Callaghan, who resigned as Labor's leader last month, is former chancellor of the Exchequer Denis Healey. Like Callaghan, Healey supports Britain's participation in NATO and the European Community. He backs retention of the nuclear deterrent and Britain's mixed economy, while pressing to reverse Conservative Prime Minister Margaret Thatcher's erosion of welfare state benefits and of the government's involvement in the economy.

The party's insurgent left wing, however, which has already captured control of many grass-roots constituency organizations and its policy-making national executive, wants Labor to be more radically socialist.

The left wing wants to take Britain out of the Common Market, ban nuclear weapons from British soil, nationalize much more of its industry, and eliminate private medicine and education. One left-winger suggested at the party's recent annual conference that venerable elite private boarding schools such as Eton and Harrow be turned into residential centers for trade union apprentices or homeless refugees such as the Vietnamese boat people.

Healey's strongest opponent in the balloting that begins Tuesday is deputy party leader Michael Foot, who is being supported by much of the left wing plus deputies who believe that the eloquent, self-effacing and sometimes compromising Foot would be more successful in holding the party together than the often abrasive Healey.

With two other contenders in the race, party foreign affairs spokesman Peter Shore and former agriculture minister John Silkin, neither Foot nor Healey are expected to receive an absolute majority in Tuesday's secret ballot, although Healey could come close. A runoff vote between Healey and Foot is expected a week later.

Foot, a 67-year-old journalist, gifted orator, skillful parliamentarian and veteran campaigner against both Common Market membership and nuclear arms, is regarded by the left-wingers primarily as a stalking horse for their long-range leadership candidate, former energy minister Tony Benn, an aristocrat who renounced his peerage and became a tireless anticapitalist polemicist and grass-roots campaigner for structural change in the party.

The radicals, with Benn as their titular leader, have gained control of Labor's organizational apparatus but not its parliamentary delegation. At last month's party conference, however, they succeeded in winning narrow majority approval to eventually take the selection of the party leader away from the Labor members of Parliament and give it to an electoral college, whose representation of deputies, labor unions and constituency organizations is to be decided by a special conference in January.

The electoral college is then to pick a new party leader, who must be a Labor deputy but not necessarily the same person chosen by the Labor deputies' balloting beginning Tuesday.

"What is happening now is not the real election," Benn said. "When there is a real election, I will be a candidate."

A poll by The Times newspaper this week showed that a majority of party organizations in constituencies with Labor members of Parliament favor Foot in the deputies' voting but back Benn in a later electoral college contest.

The right wing intends to campaign at January's special party conference for direct election of the leader by all paid-up Labor Party members as an alternative to Benn's proposed electoral college.

Healey, who has accused Benn and the left wing of being "out of touch with the average Labor voter," said that if he is elected leader by the Labor deputies he would remain leader as long as a majority of Labor legislators wanted him.

Foot has emphasized his support for unilateral nuclear disarmament by Britain, a campaign that has recently gained increased although still minority support, judging from opinion polls and the growing size of prodisarmament public demonstrations here this summer and autumn.

Benn, silver-haired, pipe-smoking, professorial and an effective, although deadly serious speaker, said the party is undergoing an inexorable reformation whose "moral appeal" eventually will defeat the resistant right wing and win the support of a British electorate battered and disillusioned by Thatcher's harsh survival-of-the-fittest economic policies and priority for defense over welfare state spending.

A Foot supporter and left-wing former Labor Cabinet minister who does not necessarily want Benn as leader also argued that the party would continue moving leftward no matter who wins the current leadership struggle.

Other observers, including some of Britain's leading pollsters and political commentators, offer three other possible scenarios: Healey will win and consolidate the leadership, eventually quashing or papering over much of the leftist dissent, as has happened in past left-right party clashes; Foot will win and postpone a showdown; or, no matter who wins, the leftists will gain enough ground to force the right-wingers to split off and create a significant new political force in the wide-open center of British politics, which now is occupied only by the struggling Liberal Party.