Will integrity fly in Massachusetts?

On the face of it, the issue seems routine enough: the Massachusetts Port Authority (Massport, which runs busy Logan International Airport and the Boston seaport) will probably announce the name of its new director by the end of this week.

But this is Massachusetts, where everything is political and nothing is routine. Did you imagine that America had outgrown its sordid traditions of lame-duck patronage, machine politics, and hardball chicanery? Listen, then, to the following sorry tale - whose (perhaps upbeat?) denouement is unfolding even as you read it.

It begins with outgoing Gov. Edward J. King. A pro-business Democrat, he once headed Massport. He worked singlemindedly to develop Logan into one of most active airports in the world. But he rode roughshod over community groups, sparking antagonisms that still smolder. When a former governor appointed enough supporters to the seven-member Massport board in 1974, the new majority dumped him.

The board then hired David W. Davis. Davis, by most accounts, was a fine director whose staff made Massport a decent place to do business. It also made a pile of money, and was entirely independent of state funding. And Davis managed to accommodate the interests of the community groups - partly by abandoning some development plans dear to King's heart.

Normally, offending your predecessor hardly matters. But shortly after being bounced, King defeated then-governor Michael S. Dukakis. King's dislike for Davis, a Dukakis ally, was profound. So when, last July, he appointed his fourth supporter to Massport's board, retribution was certain.

It was not, however, swift. The 4-3 King majority on the board finally voted Davis out in October - and would instantly have voted in a pro-King director, except for a public outcry demanding a nationwide search. In the meantime, however, something else had happened: King had lost the September gubernatorial primary to Dukakis, who will come see-sawing back into the governor's chair next January 6.

Into this cross-fire, then, wades a 14-member group known as the Executive Search Advisory Committee. Its charge: beat the nation's bushes and find the best director available for Massport. It has only advisory powers. But, as committee member and community activist Bernice Mader notes, the Massport board would be ''very, very ill-advised to appoint somebody if the majority of the committee did not approve.''

For this committee is one of the most potent ever assembled in Boston. It comprises representatives from business, airlines, community groups, unions, women's groups, and minorities. It includes such luminaries as Richard Hill, chairman of the First National Bank of Boston - the kind of man who (as a colleague says), if he merely hints that he needs to talk to some South American government, finds its officials in his office the next morning. Nor has it been idle. A list of more than 100 candidates assembled by an executive search firm has been winnowed to six - three local names, and three outsiders.

So far, so good: there is, at least, a process. But nothing, remember, is routine in Massachusetts. The board decided that each of its own members could add one name to the list of finalists. Members of the pro-King majority added two - names which, says one insider, the executive search firm had earlier twice rejected as unqualified.

And that, as they say, is where the shooting started.

Why? Three reasons:

1) These are the last days of the King administration. Massport's directorship pays $75,000 a year - and King's supporters need good jobs, fast. ''Their carriage,'' quips one anti-King board member, ''turns into a pumpkin January 6.''

2) King wants an ideological ally at the authority's helm, so that the development projects he favors - another runway, a third tunnel under Boston Harbor - won't be foreclosed by alternative construction.

3) Massport has lots of noncivil-service jobs to fill. It is also plugged into contacts that range from US House Speaker Thomas P. O'Neill and Sen. Edward M. Kennedy to state legislative committees and potent business groups. So it's a fine power base if King should decide in four years to run for governor again - and a useful ally if he should land (as he thinks possible) a post in the Reagan cabinet in Washington.

It might seem inevitable, then, that one of the added names would get the job - that the nationwide search is a charade, that minds are already cast in concrete. Even that, however, would be too routine for Massachusetts. Consider the individuals:

* William T. Hogan. He has served King in several posts, most recently as Human Services Secretary. Though he has little experience in transportation, he is ''without doubt the best manager to come out of the King administration,'' says one businessman on the search committee. Insiders say he wants the job badly. For insurance, however, King has offered him a judgeship.

He might well be acceptable to the search committee. And the board could give him four votes. That's enough to win, but not (many feel) enough to govern well. One of those four votes, after all, resides with Teamster official William F. Lyden, who at times will have to vote for his labor constituency rather than for King policies. And nobody sees a fifth Hogan vote. Moreover, there is legislation pending to reorganize Massport operations entirely, which Du-kakis has hinted he would push. Mr. Hogan could find himself jobless within four months - a consideration which must make a lifetime judgeship look most attractive.

* Louis R. Nickinello. As chairman of the Transportation Committee of the state House of Representatives, he has some background in the field. And he, too , needs a job. Having failed to get a newly-created House leadership position two years ago, he is owed one by legislative leaders. They would like to see one of their own sitting atop such an attractive source of patronage jobs, community influence, and overseas junkets.

But Nickinello is roundly disliked by community groups, who cite his consistent opposition to bills intended to limit airport noise. And some in the business community find him unpalatable. So far, the search committee has operated in commendable privacy. But if the job goes to Nickinello over their strong objections, a number of the community-minded members of the committee have threatened to ''go public'' and expose the entire process as a useless charade. More worrisome is the rumor that, if they do so, one of the business-leader committee members - a man with considerable clout - will join them.

All of which puts the pro-King board members between a rock and a hard place. They are under intense pressure from the governor and the legislative leadership. But they will also have to live in a Dukakis world. And they have their own careers to consider. Board member John W. Arata, a lawyer, is well-placed to expand his practice within the business community - unless he is perceived as stiff-arming them. And David S. Paresky, who owns a large travel service, has already seen his establishments picketed by angry community groups.

Is there an out? Yes, indeed. When all the power-plays are exhausted, the board just might have to settle for a dark-horse, compromise candidate. It might , in other words, be driven back to that original list of candidates. It might, in the end, have to listen to the advice of its advisory committee and select a professionally-qualified director of Massport.

That, to be sure, would violate the routine. But this, after all, is Massachusetts.