That’s nuts, and he knows it. His county simply needs to build some mixed-income units, enact fairer zoning laws and combat discrimination seriously. But through inaction and legal nit-picking, Westchester has bristled repeatedly at the conditions of the agreement. Its most recent breach involves a numerical benchmark. By the end of 2014, the county was supposed to have had in place building permits for at least 350 affordable units and financing for 450. The county has been slowly inching toward that goal, with developments here and there. But when it tried to claim that a planned 28-unit development in New Castle, called Chappaqua Station, should count toward its goal, it went too far. Local resistance to Chappaqua Station is strong, approvals have not been granted and financing is nowhere to be seen.

Image The site of a proposed 28-unit affordable housing development in Chappaqua. Credit... Uli Seit for The New York Times

The court-appointed monitor in the case, James Johnson, has determined that the county cannot count those units yet. He reported in April that because progress was lagging overall, the county was courting a possible contempt-of-court finding and steep fines. One condition of the order is that the county has to use “all available means” — including legal action — to meet the decree’s objectives, which in Mr. Johnson’s view includes pushing New Castle to get moving on Chappaqua Station. But the county has done no such thing.

Westchester got into this mess because for years it took tens of millions in federal housing funds while falsely claiming it was meeting the conditions under which the money was given: that is, lowering the barriers to fair housing in its predominantly white towns and villages. An advocacy group in New York City sued. The county — facing certain defeat in federal court and the prospect of immense fines — signed the 2009 decree that not only compelled it to build the new units but also to “affirmatively further fair housing” by dismantling the obstacles to integration, like the onerous zoning laws that its towns and villages have erected against outsiders.

Mr. Astorino was not in office when the decree was signed, but once elected, he became bound to uphold it. His efforts to obstruct it have damaged his county’s reputation and squandered or imperiled millions of dollars in housing funds that could benefit many county residents — all because he and the decree’s other implacable foes cannot seem to reconcile “affordable housing” with their vision of Westchester as a place of leafy privilege.

One encouraging development in this continuing stalemate was the recent publication of a paper commissioned by Mr. Johnson pointing to a way forward. The report, “Collaboration and Affordable Housing,” highlights numerous design and planning solutions, and mixed neighborhoods around the country where brittle resistance has melted away and integration’s benefits are well accepted.