When you were a fourth-grader gym was a time and a place for Philadelphia kickball and the President's Physical Fitness Tests. But for the mid-Cambridge children who attend the Longfellow Elementary School, every two years their gym becomes a lesson in civics. But that isn't Cambridge's only peculiarity.

In most cities, you vote and then go home and listen to the returns on the radio. Not in Cambridge, where it takes at least a week to count all the ballots and figure out who's won.

And in most elections all you need to know to vote is how to pull a lever or scratch an X. Not so in Cambridge, where ability to count is required, and a master's degree in logic encouraged.

Cambridge is the last (and first) bastion of strict proportional representation (residents affectionately call it PR) in the country. To understand the system, let's follow a hypothetical voter through the electoral process--from the voting booth to the floor of the gymnasium, where a corps of veteran pollsters gather every two years to count the ballots.

Student voter Jonathan Q. Public III '80 arrives at his precinct's polling center (for most Harvard students this is the firehouse near Mem Hall).

Public accepts his paper ballot and enters the booth. His first task is comparatively simple--yes or no votes on each of six non-binding referendum questions. But just as he has gotten up a head of steam, Public hits a roadblock. "This ballot is like nothing I've ever seen" he muses as he peruses the list of city council and school committee candidates.

Next to each of the names on the ballot is a blank box, in which voters must pencil a ranking. ("Do Not Use X Marks," the ballot warns.) Instead, pick your favorite candidate and mark him down as number one. The second-best person for the job should get your number two, and so on, all the way up until 23. Many people give up after eight or nine names because votes are unlikely to be meaningful after that point. "People do all kinds of crazy things--they mark X's, they cross out names, they write slogans on the ballot," one election official explained recently, adding that any deviation from a legible number ranking invalidates a ballot.

But despite its eccentricities, the process so far is relatively simple. It is not until the ballots reach the school gymnasium that PR gets really tangled up.

The first rule to remember is that you are really only voting for one city councilor and one school committee member. The extra rankings are essentially meaningless unless your number one choice does not need your vote to win or if he has no chance of victory. If that happens, your number two vote will automatically be counted. And if that vote is unnecessary or wasted, the number three vote will be used, and so on. No matter how many candidates you voted for, the ballot will only end up being counted for one of them.

Election workers begin by sorting the ballots by first choice vote. If any candidate receives over a certain quota of first choice votes (set by tradition at ten per cent of the total vote), he is automatically declared a winner. Two years ago, only one candidate, Walter Sullivan, managed this feat on the first round.

If a candidate exceeds this quota, the extra ballots are redistributed to the piles of ballots for number two choices. If no one tops the quota figure, then the candidate with the lowest number of ballots is declared defeated and his ballots are redistributed, again to the second choice candidates. This process of eliminating the lowest candidate and redistributing his ballots is repeated until all positions are filled with candidates who have reached the quota mark or until eliminating another candidate would leave a vacancy on the nine-member council.

The counting usually takes five days, as candidates watch election workers pore over the ballots. Rumors--usually unsubstantiated--fly around the gym like bouncing basketballs, and often workers have to retrace their steps to find where an error has been made. But Cantabrigians love the system. One election commission handout calls it a "much more sophisticated way to choose representatives than the more common methods. It guarantees representation to minorities, whether they are political, ethnic or racial, and prevents voters from wasting their votes on candidates who have more than enough votes to win or who have no chance of winning."

Proportional representation in the Cambridge sense of the phrase is a dying art--the Cambridge law, thanks to a glitch somewhere in the state processing system, was never officially published as a law and no recent statute exists which adequately lays down the rules. But Cambridge politicians adore it, even if they have to spend the week in an elementary school gym.