Among the many objections raised by public school groups when Gov. Andrew M. Cuomo began pushing his tax cap last year, perhaps the weakest was the claim by teacher unions that the law would “erode democracy.”

Even before Tuesday’s statewide school budget vote, it was clear the cap had empowered voters to an unprecedented degree.

Before this year, school boards could impose a state-mandated contingency budget without voter approval, subject only to a limit on spending growth equal to the lesser of 4 percent or 1.2 times the rate of inflation. In some cases, especially after state aid was reduced, this led to tax increases even larger than those rejected by voters. In too many districts, the annual budget vote had become an exercise in fiscal determinism.

The cap has now decisively shifted the focus from school spending to school taxes, giving district residents the ultimate power to decide whether there will be any tax increase at all. If the budget is rejected twice, taxes must be frozen.

Tuesday’s votes were a display of democracy in action. Turnouts reportedly were high despite rain in much of the state, and at least 96 percent of budgets passed.

This positive result was not surprising. Anxious to avoid triggering the 60 percent “supermajority” requirement to exceed the tax cap, most districts were careful to hold their hikes safely within allowable limits. Taxpayers appreciated the effort. As an added benefit, like NFL teams that avoid splurging on free agents, most districts will have unused cap space (up to 1.5 percentage points) to carry forward into next year.

This was exactly how the cap was supposed to work: instilling more restraint in the budgeting process right from the start.

Not surprisingly, the rejection rate was higher among the 48 districts seeking tax increases above their adjusted caps. At least 19 of them saw their budgets defeated. But in at least seven of those districts, including Suffolk County’s East Islip, the cap-busting proposal failed to win even a simple majority. In at least five districts, including East Ramapo in Rockland County, voters rejected tax increases below the cap.

The real impact of the cap — a maximum of 2 percent per year, which can vary depending on local allowances and exemptions — will be felt in the longer term. For example, projected over the next 10 years, the difference between a 3 percent and 4 percent average annual levy increase would equate to a statewide savings of $3 billion.

It’s not too early to observe that the cap has broken a trend. In the past, school districts generally sought higher property taxes when hoped-for state aid failed to materialize. Annual tax levy increases averaged nearly 8 percent between 2001-02 and 2004-05, when state aid growth slumped.

The increase in school aid included in the latest state budget won’t fully make up for the cuts Cuomo had to make last year. Yet, in nominal terms, the 2.3 percent average school tax levy increase for 2012-13 will be the second lowest since school districts were unionized in 1967, according to data from the state comptroller’s office. Even adjusting for projected inflation, this shapes up as the second smallest increase in 30 years.

Spending is another matter. Per-pupil expenditures under next year’s proposed budgets will rise by about 1.5 percent, slightly more than in previous years. Nonetheless, as described in a recent report by the New York State School Boards’ Association, districts “have had to slash staff . . . eliminate or reduce sports and extracurricular activities, cut or trim back on elective courses such as art and music, increase class sizes, defer maintenance and curtail pupil transportation.”

The reason: Employees salaries and benefits are rising considerably more than inflation, and current collective bargaining provisions make them difficult to restructure.

Of course, the cap is far from perfect. It doesn’t do anything to help districts control expenses shaped in part by state mandates, for instance. But this will only increase the political pressure on Albany to meaningfully address the mandate issue.

Meanwhile, property owners across New York finally have added protection from tax increases they can’t afford.

In short, the cap is working.