At the conclusion of a spirited meeting of his Cabinet Council on Economic Affairs May 18, President Reagan announced that he had decided not to raise gasoline taxes as proposed by his secretary of transportation, Andrew L. (Drew) Lewis Jr.

The president's decision was presented as an example of the much-ballyhooed "Cabinet government" that Reagan promised during the 1980 presidential campaign and which he has continued to proclaim ever since. It was supposed to be the textbook ideal of a Cabinet of wise men debating a proposal on its merits and making recommendations that the president, as chairman of the board, could ratify or reject.

But the reality was different. As Lewis entered the Cabinet Room, a White House staff member took him aside and whispered in his ear.

"Drew, the president's decided not to go with it," he said.

Lewis nodded and went on with his presentation anyway. So did his colleagues, some of them unaware that the decision had already been taken. Afterward, one of them said admiringly that the president had "made the decision on the spot."

Instead, following a discussion of the issue in the influential White House legislative strategy group held before the Cabinet council meeting, Reagan made his decision in consultation with a handful of White House staff members who thought the proposal both dubious in policy terms and politically ill-timed.

The incident, typical of many, is illustrative of the gap between the theory of "Cabinet government" in the Reagan White House and the actual practice of decision-making. It demonstrates why many Cabinet officers and other administration officials--when speaking behind the anonymity of "background" or "not for attribution"--readily acknowledge that many of Reagan's most important decisions, like those of other presidents, are arrived at not in a corporate-style board of directors meeting but in private consultation with a small cadre of trusted advisers.

"Cabinet government is an illusion," said one of these officials. "It is an illusion useful for keeping people in harness and for maintaining esprit de corps. It is useful for gaining participation and framing policy options. But it is not the way decisions are reached in the Reagan administration."

It is an irony that the administration's actual operating process, rather than the illusion proclaimed by Reagan that Cabinet secretaries would be "managers of the national government," is widely praised even by those who are unsympathetic to the president's policy objectives.

Some students of government credit the six Cabinet councils devised by White House counselor Edwin Meese III for keeping Reagan's agenda in the forefront. They say the councils also reduce the role of traditionally influential interest groups and make it less likely that Cabinet secretaries will become captives of their constitutencies.

Stuart E. Eizenstat, chief domestic adviser for President Carter, observed that the Carter administration struggled for more than a year with Cabinet government before deciding, in the spring of 1978, that the White House should exercise control and write the decision memos.

"You want a guy in there without turf concerns, someone looking for the prime client, the president," Eizenstat said.

Bradley H. Patterson Jr., Cabinet secretary in the Eisenhower administration and subsequently an executive assistant in the Nixon administration, believes the Reagan Cabinet council system is effective largely because the White House plays such a central role.

"This system is run by the White House staff," he said. "They in effect write the option papers. Meese controls the Cabinet agenda. As in Eisenhower's White House, even though you say you have Cabinet government, you come to the point where the White House does it."

By and large, this dominance is accepted--and even applauded--by members of a Reagan Cabinet noted more for its fealty than for its independence.

"The president was elected to run this country; I wasn't elected," said Secretary of Commerce Malcolm Baldrige, considered by several of his colleagues to be the Cabinet member most willing to differ with Reagan. "The president is accountable to the country. We're accountable to the president."

Secretary of Interior James G. Watt, accepting a reporter's description of the Cabinet council system as "a noose" around the necks of Cabinet officers, said: "I think it should be. I think that's good. I don't think that Jim Watt or Carter secretary of health, education and welfare Joseph A. Califano Jr. had a mandate to do anything other than carry out the will of the president under the statutes on the books.

"Too many secretaries get to thinking they are the elected officials to carry out the will of the people. They have no rights. That's why you have the backbiting and see Cabinet officers in the past get co-opted by the bureaucracy and the special interest groups."

When this remark was mentioned to Meese, the administration's most ardent apostle of Cabinet government, he smiled and said: "I wouldn't think of it as a noose. I would think of it as a means of management guidance and management communications and policy guidance from the president."

"Noose" or "management guidance," the councils are a distinct modification of the "super-Cabinet" that Reagan and Meese toyed with and soon abandoned at the beginning of the administration. Full Cabinet meetings, scornfully referred to as "dog-and-pony shows" by one Cabinet member and as "pep rallies" by another, were largely informational. The busier Cabinet members and White House staff members alike tended to regard them as a waste of time.

"I can't think of a single major decision that has been made at the full Cabinet meeting," said one secretary.

In this respect, the Cabinet meetings emulated similar gatherings that, wrote Carter's attorney general, Griffin Bell, helped in "trivializing" the Carter presidency.

"When President Carter took office, he conducted weekly meetings of the Cabinet secretaries at which we would go around the table, each usually mentioning an activity of the past week or something that might be coming up in the immediate future," Bell wrote in "Taking Care of the Law."

"The discussions were too disjointed, given the range of Cabinet positions, to produce any coherent themes. It was adult Show-and-Tell, and as a result President Carter became entangled in trivial, technical minutiae that occupied too much of his time and attention."

No one has ever accused Reagan of becoming too entangled in detail. He is a delegator, by executive preference and personal inclination, and he used the early Cabinet meetings as a forum for storytelling and morale-building.

However useful for this purpose, they were never forums for decisions. Even actions announced with fanfare at Cabinet meetings, such as the lifting of the Carter ban on grain sales to the Soviet Union, were decided beforehand in small groups of advisers.

Before the Cabinet meeting at which the ban was lifted, Meese pulled aside then-secretary of state Alexander M. Haig Jr. and Secretary of Agriculture John R. Block for a brief private meeting in which the president told them what he was about to do.

The Cabinet councils more truly reflect the size of Cabinet government as it was practiced during the eight years Reagan was governor of California. Unlike Richard Nixon, who preferred written memos, and unlike Jimmy Carter, who was comfortable in large meetings, Reagan prefers to make his decisions in consultation with a small group of trusted advisers--notably Meese, national security adviser William P. Clark, chief of staff James A. Baker III, deputy chief of staff Michael K. Deaver and such principal deputies as Tom Reed (Clark), Richard G. Darman (Baker) and Craig L. Fuller (Meese).

Like Reagan's Sacramento cabinet, the Cabinet councils are meetings of 15 or so people in which four or five Cabinet secretaries or their chief deputies participate. In theory, and sometimes in practice, they explore policy options and refine differences on issues, sometimes among themselves and sometimes directly in front of the president, who is the chairman of all councils. A designated secretary is chairman of each group and presides over the many meetings that the president does not attend.

The councils are consciously designed to be an instrument of the presidency and not of the Cabinet secretaries. They meet in the West Wing of the White House. They are staffed by the president's men, who also write the summaries of their deliberations. They are flexible instruments--a quality praised by such students of Cabinet government as Patterson--and any Cabinet secretary is welcome to attend councils of which he is not a member.

Meese contends that virtually every administration policy decision is thrashed out in the councils, and others in the White House have produced elaborate statistical studies designed to emphasize their importance.

These studies, as of last week, show that there have been 50 full Cabinet meetings and 228 Cabinet council meetings, with the Council on Economic Affairs holding 112 of these sessions and the newly created Council on Legal Policy only five. Reagan attended approximately one-third of the meetings. One in-house study determined that these councils have produced 262 "process actions" and 128 "substantive actions."

Whether this impressive-sounding compilation of statistics actually represents decision-making in the Reagan administration is another question.

Many administration officials say that vast numbers of the council meetings are largely informational. They dispute the notion that the "actions" of the councils are representative of decision-making. They say the councils ratify or refine a spate of secondary decisions and regulations but that the big-ticket items are decided by the president after ad hoc consultations or in bodies that, like the legislative strategy group, are not Cabinet entities.

As Treasury Secretary Donald T. Regan, one of the most highly regarded Cabinet members, put it, the "smaller decisions" are made in the councils while "the more detailed, more complicated decisions are given to the president."

Rep. Dick Cheney (Wyo.), chief of staff in the Ford White House and now a member of the House Republican leadership, said the major objectives of the Reagan administration in economic and national security affairs were not susceptible to being managed by Cabinet government.

In fact, the most fundamental Reagan initiatives -- the priority-shifting budget bills, the income tax reduction, the decision to revive the B1 bomber and build the MX missile, most foreign policy decisions and all personnel decisions, including the resignation of Haig -- were decided outside the framework of the Cabinet.

Several administration officials said the Cabinet councils were not the decision-making arenas even on many actions that technically bear a council imprint. Among the examples:

* Enterprise zones. This proposal to create tax-incentive business development zones in depressed urban areas was based upon a Reagan campaign promise. A computerized chart of its progress through the Cabinet council system shows 23 separate meetings or reports beginning March 19, 1981, with a working session in the Council on Commerce and Trade, and ending March 23, 1982, with submission of the legislation to Congress. While some administration officials point to this process as a model of Cabinet government, others contend that the chief effect of the deliberations was to delay the proposal.

* New Federalism. Though a plan was debated for many months in councils, the actual proposal put forward was chiefly the product of separate initiatives that came from Office of Budget and Management Director David A. Stockman and Richard S. Williamson, the administration's intergovernmental specialist. "Federalism gets mixed up in the budget; it was taken out of our hands," said one official associated with the councils.

* Natural gas deregulation. The Council on Natural Resources and Energy produced an elaborately researched paper that won in-house praise for fairness and completeness. But while this paper was still being drafted, White House aides consulted with congressional leaders and the president decided that the political timing was not right for deregulation.

* Synthetic fuels. When Stockman learned that Secretary of Energy James B. Edwards wanted to give energy companies loan guarantees for synthetic fuel development agreed to during the Carter administration, he took the issue to the Council on Natural Resources and Energy, where he hoped to block it. At one meeting Stockman lined up support for his side of the argument. But the president attended the next meeting and agreed with Edwards--and the synthetic fuel lobbyists--that the commitment should be kept.

* Housing. Various proposals to help the housing industry were considered in a Cabinet council without resolution. Intending to force action by the administration, deputy chief of staff Deaver and Cabinet secretary Fuller scheduled a Reagan speech before the National Association of Realtors, which brought about the development of an administration housing proposal.

* On-shore oil development. Watt, more candid than most of his colleagues about use of the councils, said: "Off-shore oil I took to the Cabinet council on two instances because it has such interdepartmental impact and, frankly, because of the politics of it. On-shore leasing for oil and gas, coal, geothermal, I have not taken to council because the president gave that such prominence in his campaign, and in the Republican Party platform."

Meese, creator and defender of the councils, argues that most of these actions are part of the "Cabinet government process," whether or not the decision is actually made by the president in a council meeting. Meese's definition of this process is so broad that he considers the National Security Council a seventh Cabinet council and its recommendations part of the Cabinet process.

Few others in the administration would argue that the NSC, an institution that has its modern origins in the Truman administration, would qualify as an adjunct of Cabinet government. But the NSC measures up more to Reagan's concept of a board of managers than do the domestic councils.

Reagan, unlike many of his predecessors, was without experience in foreign affairs. His first national security adviser, Richard V. Allen, was not a towering figure in the mold of Henry A. Kissinger and Zbigniew Brzezinski. Haig, the dominant force in foreign policy until his resignation, was an outsider. Clark, the longtime Reaganite who replaced Allen, is skilled in process without having a background in foreign affairs. The result has been a collegial, if contentious, process, in which no single adviser dominates.

Beyond this, Reagan believes that foreign policy should not be the exclusive province of experts. His top staff trio of Meese, Baker and Deaver are members of the NSC. At the time Haig was calling for an expanded U.S. role in El Salvador, the president's top trio of advisers was calling attention to the negative domestic political impact of such involvement.

Even so, Reagan makes many of the most important foreign policy decisions outside the NSC. While Meese contends that the president made his far-reaching decision extending sanctions on the Soviet natural gas pipeline within the NSC, others say he arrived at the meeting with the decision already made. As is his custom, Reagan had discussed the issue first with close advisers.

In passing judgment on how Reagan arrives at any decision, two points stand out. One is that the president came into office with his agenda in place. His most important decisions, one longtime Reaganite observed recently, were his campaign promises to lower taxes and increase the defense budget.

The other point is the difficulty of defining exactly when any particular decision is made. "Policy," which is Meese's responsibility and "implementation," which is Baker's, intersect. Some of the most important decisions that the administration has made--on the tax bill, for instance, or on AWACS radar planes for Saudi Arabia--were strategic ones that became policy.

"I think it is incorrect to try to impose on the activities within any administration--and I would say within any government--an order and rationality that is not there," said Roger Porter, director of the Council on Economic Affairs and author of a book on the economic policy board in the Ford administration. "Government is messy. Things do not come in neat little compartments. . . . "