If the definition of insanity involves doing the same thing repeatedly and hoping for a different result, maybe the long-troubled New York City Housing Authority, the nation’s largest, isn’t entirely insane after all. 

Rather than pouring yet more money into repairs of the crumbling Fulton and Elliot-Chelsea Houses, among the nation’s oldest public-housing projects, NYCHA has — boldly — decided to tear them down, as it announced Wednesday.

Unfortunately, the replacement that it plans, likely a model for future demolitions in the aged system, perpetuates some of the suspect principles of traditional public housing, including lifetime tenure for tenants.

What’s more, it keeps prime property off the tax rolls at a time when New York City desperately needs revenue.

The logic of replacing 2,000 public-housing apartments with a $1.5 billion high-rise complex is deceptively seductive: Building anew will cost less than rehabilitating the existing structures.

But the decision to guarantee all the current tenants brand-new, modern apartments overlooks an alternative that could not only compensate tenants but also put the real estate in the hands of private, tax-paying owners.

NYCHA is turning its back on a real-estate gold mine.

Like many of its properties, Fulton-Elliott-Chelsea sits on land so valuable that it could be sold, provide generous buyouts for current tenants and be cleared for private development.

Based on property assessments from NYCHA, the Chelsea Houses land is worth $67 million; the Elliott Houses, $77 million; the Fulton Houses, $101 million.

Selling the sites could provide Chelsea tenants up to $157,000 each — and allow the sites to be put on the tax rolls. 

(The Baruch Houses on the Lower East Side are worth even more — $111 million, enabling tenant buyouts of a staggering $564,000 each.)

Of course, tenants needn’t get such large sums.

And by retaining some of the proceeds, the sale of these and other properties could provide a windfall for NYCHA, endowing it with a renovation fund to sustain a smaller but better-maintained system, rather than the current one plagued by falling bricks, heat and hot water outages and elevator breakdowns.

Why, after all, simply based on the coincidence of their happening to live in Chelsea-Elliott-Fulton at the time of its planned demolition, should these tenants in particular qualify for the sort of brand-new unit that low-income households across the city would pine for — and then have the right to stay there in perpetuity?

While tenants in the Jackson Houses (Bronx), Queensbridge Houses (Queens) and Brownsville Houses (Brooklyn) live with rats and roaches, a lucky few hit the housing jackpot. 

Far better to compensate current Chelsea-Elliott-Fulton tenants, provide them time to find new housing and “unfreeze” some of NYCHA’s frozen real estate.

In the private housing markets (in which most Americans live), tenants and owners must face difficult choices when taxes or rents rise along with heating and maintenance costs.

To buffer a select group of public-housing tenants from such pressures simply because they happen to live in a project too dilapidated to repair “privileges” them, as the left would put it.

NYCHA culture must change, from one in which some people get to live for a lifetime in subsidized units to one where they live only temporarily in transitional housing, while striving and saving for a return to the private market.

Nor is the windfall for existing tenants the only problem with the new plan.

As is the city’s pattern, the replacement high-rises would include a range of specific income-restricted apartments, not just for those of lowest-income.

This mixed-income approach overlooks an essential truth about housing markets: New construction of any kind increases overall supply and brings down median prices.

Releasing land to the private sector for new housing will help buffer rents everywhere.

It will also boost the property-tax rolls, reaping new revenue the city desperately needs.

None of these options, of course, can fully solve NYCHA’s long-term woes overnight: The authority lacks the funds to rebuild or replace all of its buildings that need work, and it surely can’t reap enough revenue in some neighborhoods, even by releasing private land.

But as the city faces looming and growing budget constraints, it must start to make choices that seemed politically unimaginable not long ago.

Revenue shortages that spark cuts in services will drive even more New Yorkers to Florida.