When Federal Reserve Board governor Manuel H. Johnson wants to figure out how to win a colleague to his point of view, he follows an approach that is gaining in popularity in the Reagan administration.

James C. Miller III, director of the Office of Management and Budget, said he took the same path last fall when he was drawing up the fiscal 1987 budget.

Rep. Phil Gramm (R-Tex.), coauthor of the Gramm-Rudman-Hollings budget-balancing law, said Congress should go in that direction when searching for solutions to hard decisions on the budget. And William Niskanen, former member of the Council of Economic Advisers, said he relied on that route to outflank the bureaucracy, not only at the CEA, but also at OMB.

The philosophical road they travel is called "Public Choice," which has been around since the 1950s, but is attracting new interest as the belief in the government's ability to improve society has dimmed.

The academic headquarters for the philosophy is at George Mason University in Fairfax County, but its proponents are scattered throughout the Reagan administration and Congress. Public Choice provides the intellectual underpinnings for much that the administration and some members of Congress will attempt to do in coming months on the budget. Its followers support a balanced budget amendment, a flat tax and efforts to limit government.

Public Choice applies economic analysis to political problems. Instead of trying to predict how buyers and sellers will act in the marketplace, analysts focus on decision makers. They use statistics, mathematics and economic models to determine not only the result of a particular political action, but also why it was taken.

Using mathematical models and other econometric tools, Public Choice adherents examine such issues as how individuals and legislatures vote, which benefit programs should be cut and how society, rather than interest groups, can get a bigger bang for its tax dollar.

For example, instead of measuring a tariff's impact on the economy, Public Choice would analyze why a tariff should be erected and why industries seek protection from imports.

Gramm claims Public Choice theory will be important in deciding how to cut the federal budget. For instance, a Public Choice follower might oppose higher taxes to reduce the deficit, believing that government spending still would grow at a rate faster than the economy, and "that ultimately means the growth potential of the economy is used up by the government," Gramm said.

Public Choice would educate policy makers on the costs and benefits of raising taxes, Gramm said. "Public Choice does not give you the conclusion," he said. "It simply gives you a means of assessing the options."

Public Choice argues that people act in their own interest, rather than for the public good. The budget deficit was allowed to grow, Public Choice economists argue, because lawmakers spent money on projects to enhance their chances of election, rather than cutting spending for the benefit of all.

To solve the problem, they argue, Congress needs to be reined in, either by Gramm-Rudman-Hollings or a constitutional amendment requiring a balanced budget.

It sounds at first like cost-benefit analysis applied to politics. But Public Choice followers say the program focuses more on the biases that can result from cost-benefit analysis by bureaucrats and others, who tend to overstate costs or benefits for their own interests. Public Choice tries to eliminate those biases, said James M. Buchanan, one of the theory's founders who teaches at George Mason.

Public Choice scholars congregate at the University of Chicago, Washington University in St. Louis, the University of Rochester and the University of California at Los Angeles, in addition to other schools in the United States and Europe, according to Robert Tollison, director of George Mason's Center for Study of Public Choice.

But George Mason's center has grabbed the spotlight in attracting scholars and students. Two prominent economists, Buchanan and Gordon Tullock, were lured away from Virginia Polytechnic Institute in 1983 to teach Public Choice at George Mason. Both are listed in British historian Mark Blaug's book, "100 Great Economists Since Keynes," and are two of only 51 scholars listed who are living, Tollison said.

Many mainstream economists consider Public Choice adherents to be a fringe element, although Buchanan and others have held prestigious positions and are respected professionally.

Allen Sinai, chief economist for Shearson Lehman Brothers, said that Public Choice adherents are not "crazies" or "weird," and that, as a scientist, he is interested in their work. "I'm always looking for something worthwhile, whether it's in the mainstream or not," he said.

"Generally they've been thought to be Republican, conservative, free market-oriented," Sinai said. "Their approach is certainly sympatico with the current administration."

Princeton University professor Alan S. Blinder, a visiting fellow at the Brookings Institution, said that Public Choice is serious economics. "But there is a lot of craziness that goes on with serious economics," he said.

"It's mainly the extremism that leads a lot of people, including myself, to believe that they go overboard," assigning selfish motives to the actions of all bureaucrats, Blinder said. Many people are in the government for public service and act accordingly, Blinder said.

Public Choice advocates insist that they are not just out to eliminate government, although many of them favor cutting programs. They also say Public Choice is not espoused only by conservatives, although it seems that conservatives are most receptive to its theories.

According to Tollison, who was a Federal Trade Commission official when Miller was the agency's chairman, Public Choice assumes that neither the government nor the public sector are perfect; therefore, neither can provide the solution to the country's problems.

"Virtually everything I've done in public policy, even as an economist at the Department of Transportation or Council on Wage and Price Stability or CEA or FTC, benefited from this sort of perspective," said Miller, who added that he often consults with George Mason scholars on budget matters. "That's the way I sort of think of public policy issues."

Tollison said he used Public Choice principles to help him understand how bureaucracy works. During the previous administration, the agency took many initiatives to regulate certain industries and break up others, Tollison said.

"We went in there with a heavy dose of economic analysis as a guide," Tollison said of himself and Miller. "We took a hard look at those initiatives. We took a look at that menu of proposed rule-making on a case-by-case basis.

"Are these large-scale structural assaults on American industry worth anything?" Tollison said he asked. "We went through those things on a case-by-case basis. We were guided by our economics in what we did there."

What Miller and Tollison did was deregulate many industries and dilute many of the antitrust laws to allow big mergers, FTC observers have said.

Public Choice believers also are skeptical about how the Federal Reserve Board controls monetary policy, Buchanan said. "You look at the way unbridled agents work without constraints," Buchanan said of the Fed members.

Monetary policy needs more predictability, which he said could be provided by something like a legislative rule to direct the Fed what its monetary targets should be, or by placing the Fed under the Treasury Department.

Fed's Johnson said he uses Public Choice analysis to try to determine how his Fed colleagues will vote, by deciding what their interest is in voting a particular way. "I try to understand what might be affecting peoples' decisions," Johnson said. "It's useful in trying to know how the Fed acts as an institution . . . and why people are voting the way they are."

Although Fed members are not supposed to be influenced by public interest groups, as many in government are, Johnson said the Fed is affected by the general interests of farmers, energy-related business, trade and exchange rate movements and banking problems.

"All the board members don't have the same views," Johnson said. "It's important to try to figure out their thinking on an issue." He said an argument can be lost when the reason for an opponent's resistance is not understood.

"The bureaucracy" is a favorite target of Public Choice analysts. As bureaucracies expand, these analysts say, they more effectively impose their own views of the public interest on the rest of the country; in fact, the analysts argue, they are committed to special interest groups rather than to the public.

"What the bureaucracy would do in order to get its way in the budget process is try to put the administration in the position of accepting or rejecting a whole package of proposals, where some intermediate proposal would be better," Niskanen said.

Miller said: "Public Choice will tell you that the existence of deficit finance tends to lead to the government being at the margin larger than optimum." The best ways to address deficits is by constitutional amendment or to require the decision-making body to restrain itself, Miller said.

"Whether one agrees with the particulars of Gramm-Rudman-Hollings, the Gramm-Rudman-Hollings Act was a kind of device . . . that a Public Choice scholar would have advanced," Miller said. "It's an institutional device that forces the decision makers to gradually get out of the deficit and imposes a penalty if they don't."

Some of the more recent work from the Public Choice center has focused on the deficit. The center has looked into an interest group theory of government, which holds that regulations are imposed to favor consumer interest during economic expansions, but that, during contractions, new regulations tend to protect producers.

This theory also contends that the Immigration and Naturalization Service's goal is to protect domestic wages, because it increases deportation activities during difficult economic times.

Other areas of research include studies on the effect of televised legislative sessions on the introduction of bills, and another that concluded most final votes are held at the end of the legislative sessions to control legislators' tendency to renege on legislative transactions.

But to dispel any notion that Public Choice can't be fun, the center is studying sportometrics -- the economic research of play and institutions of sports. One paper "explains the process by which runners decide to supply effort during a race," according to the center's annual report. "They test their theory with positive results using data on track evets in the modern Olympic Games."

Another paper, entitled "Homo Basketballus," argues that professional basketball players who competed in states with open high school basketball competition -- teams are not limited to playing schools of the same size -- survive longer in the National Basketball Association than those who don't.