The old political maxim in Cambridge was that students didn't vote--a postulate that proved true until last November, when students turned out in force to help elect the City Council and school committee.

That trend continued this week, as local officials reported registration in the three student precincts for the presidential primary was among the heaviest in the city. And there are signs of upsets in the making for March 4 among student voters.

Almost 70 per cent of students, and a plurality of the city, registered as Independents, something of a surprise in a district long regarded as lock, stock and barrel Democratic. And hundreds more students and other residents switched their registration from Democrat to Independent.

One beneficiary of that trend may be Rep. John Anderson (R-Ill.), a moderate Republican running strong on the city's campuses. If Anderson does well, he could rob votes from the city's favorite, Sen. Edward M. Kennedy '54 (D-Mass.).

Almost every politician in the city has endorsed Kennedy--Thursday night they even held a birthday party for him, complete with giant chocolate cake.

But while Kennedy will carry Cambridge by a large margin, it may not be as overwhelming as some predicted--the campus vote, once expected to unite with the vast majority of the neighborhood Kennedy vote, may shrink before the election a week from Tuesday.