This November the relentlessly thoughtful citizens of Montgomery County will swarm to their neighborhood voting booths. There -- faced with a choice between two candidates who burn with camparable ardor to represent them in the halls of the U.S. House -- they will jab their computerized ballots for the man who they think best personifies their values, their outlook on the world, and their life in this celebrated suburb.

The race between Newton I. Steers, a well-heeled financier and former congressman, and Michael D. Barnes, the industrious and monochromatic young incumbent who knocked him out of office in 1978, is more than just another political rematch. One of several intriguing aspects of this race is that the players run not so much against opponents of flesh and blood as the memories of former congressmen Charles McC. Mathias and Gilber Gude, the two liberal Republicans whose blend of views Montgomery countians favored for 16 years despite the two-to-one ratio of registered Democrats to Republicans.

And there is an extra measure of emotion invested in the outcome for Republican Steers, a man who does not seem comfortable with the speechifying and gladhanding of a campaign, who could be working in his study or perfecting his net game on his private tennis court, but who at 63 years of age is even more determined to avenge a defeat he blames on his own complacence.

Just as their is more than a replay, the seat Steers would rest back from Democrat Barns itself has a cachet. The representative from Maryland's Eighth District is the congressman's congressman whose constituents include about 75 of his House colleagues and 20 U.S. senators, not to mention droves of union presidents, undersecretaries, diplomats and corporation bigshots. It is, says longtime county Democrat and former McGovern campaign director Frank Mankiewicz, who sought it unsuccessfully in 1976, "the best seat in the country."

Such a prize is not won easily or cheaply, and the two contestants have engaged each other in a scientifically diagrammed duel comprised of "lit drops," mailings, voter attitude surveys, television ads and sundry other gambits overseen by paid staffs and full-time campaign managers. Steers, who has loaned his own campaign $80,000, expects to spend upwards of $400,000 to recapture his old seat, and Barns, who took a second mortgage on his Kensington home to erase the debt left after his victory two years ago, expects to shell out more than $250,000 to stay where he is.

Should the 37-year-old lawyer prevail, he would become the first Democrat in more than 40 years in Montgomery to serve back-to-back terms in the House, an astonishing fact that is a reflection not so much of the success of the outnumbered Republican party as of the peculiar personality of the county as a whole.

By and large, Montgomery is a place where people have arrived, and where the image of affluence is as important as the fruits. "Down in Annapolis," said Howard Denis, the baby-faced Shakespeare-spouting state senator who is Steers' campaign chairman, "they think we're all a bunch of plutocrats."

Few counties in the country take as much pride in their reputation of integrity as does Montgomery, and none has a higher level of education among its residents, or a higher per capita ncome -- the last thing something local politicians try to play down. "What else can they do?" says Mankiewicz. "Otherwise when they ask for state revenue sharing funds the agencies will say, 'What do you want it for, brie'?"

What makes representing Montgomery so unusual is that, along with being a bastion of wealth, it also is a model of good government where people are so determined to make up their own minds that some uncharitable observers say they think there's a state law against voting the party line. Ticket-splitting is a way of life in this place where issues have perennially eclipsed the role of parties. Montgomery has 450 civic organizations; when the national activist group Commmon Cause was founded there were more members from Montgomery County than there were from the rest of the nation. It's a place where issues sometimes get "due processed to death," yet only howls of outrage would greet suggestions for more expeditious treatment.

Representing such a well-read, conscientious, and politically manic populace is especially difficult for the U.S. congressman. His constituents are not the sort to shy away from expressing their views and it doesn't cost them anything to make the local telephone call. They pore over the newspapers of the nation's capital and won't be placated by a fortnightly newsletter from their man in Washington. They themselves are usually employed in Washington, and according to one poll, nearly four in 10 households of registerd voters in the county have federal employes in the family.

Every candidate in Montgomery who has been to a coffee klatch in Potomac or Chevy Chase has a horror story abuot outlining an incipient position on some issue, when a hand rose in the audience and a division chief of some obscure agency who worked on nothing else asked haughtily, "What about section 402, paragraph 17 of the revised regulations published last spring."

The congressman even gets it from his Capitol Hill colleagues who call him about school closings, garbage pickup and public works projects in their neighborhoods. Once an 8th District officeholder got a call from a colleague who wanted him to fix a ticket.

"I can't do that," the Man from Montgomery said.

"Whaddya mean you can't do that" said the offending fellow pol.

"This is Montgomery County," came the response. "I couldn't do it even if I wanted to."

"You mean you don't fix tickets?"

"No, not in Montgomery County."

The congressman was perplexed, and finally said incredulously, "Well then, what Do you do for your people?"

Mostly the Montgomery congressman speaks to the infinite number of organizations in the country and responds to the more than 200 phone calls a day from constituents.

"Montgomery County is an exhausting place to be a public official," said Gilbert Gude, former five-term congressman from the 8th District -- he of the fabled "Mathias-Gude" tradition that Newton Steers cast himself in, and that Lanny Davis, the man he defeated in 1976, largely blames for his loss.

"You would not believe the civic associations," said Gude, who is now director of congressional research at the Library of Congress and is still beloved in Montgomery. "Something happens and they form groups. De Tocqueville said Americans are the greatest organizers he ever knew of. He would have felt right at home in Montgomery County. He would have said, 'Look! it's all true'!"

As much as the success of liberal Republican candidates can be laid to the traits of the candidates themselves, it also has a lot to do with the two-fold interests of voters who pride themselves on their enlightened social thinking on such issues as civil rights, but don't necessarily want anyone to go fooling around with the economic machinery that has performed so smoothly for so many of them. A liberal Democrat is, after all, a Democrat. sWhat if he flew completely off the handle and tried to nationalize the estates in Potomac?

"On a scale of 1 to 100 from conservative to liberal I rank the classic Montgomery voter as a 48 percent conservative," said Davis, who formed a polling business called Potomac Survey Research after his own polls told him two weeks before the election that his campaign against Steers was foundering. "They're liberal in the heart and conservative in the head. The voters do not perceive themselves this way but they're more conservative than they think."

Davis may owe his wrenching electoral failure not just to Gude and Mathias, who endorsed Steers and draped their exemplary arms around him for television spots, but to his immodest and undisguised ambition. It just didn't jibe with the aristocratic element of the country that prizes the gentry image of the congressman born to the role. Newton Steers, whose "personal fortune" is valued at $2 million, looks "like Mr. Montgomery County," says campaign chairman Denis, himself one of a crop of younger Republican can heirs apparent.

But Steers won't be able to bless future Republican leaders such as Denis unless Democrat Mike Barnes is dislodged. And Barnes -- who would substantially reinforce his hold on the House seat with a second victory -- has an image of a hard-working analytical issue-bent algebra teacher who is not a whit less typical of this reform-oriented county than Steers' avuncular aristocrat.

At this time, Barnes is apparently ahead of his older challenger. Steers claims polls show the two neck and neck, but Barnes swears his latest soundings put him even further ahead than the roughly 10-point margin he had before the Democratic convention and his foray into presidential politics. h

Steers, who had branded Barnes a "rubber stamp for the Carter administration" had to shift gears when Barnes emerged as one of the main figures in the open convention bid. The Steers campaign recoverd quickly and came up with a new charge that Barnes had displayed "ethical inconsistency." And they crowed over what straw polls said was a gain in support for Steers among disaffected die-hard Carter lovers.

And so for the next seven weeks the two contenders for the best seat in the country will be wondering what's on the mind of that invaluable segment of ticket-splitting Montgomery Democrats who in some elections have amounted to as much as 30 percent of the party's registered total. And they'll be worrying about inexhaustible variables, the "the coattail effect," the new computer each race separately, the "Anderson factor," the Jewish vote, the county's proof or lack of it against economic misfortunes -- or even some hidden jack-in-the-box regulation tucked a few fiendish paragraphs down in section 402.