WASHINGTON — The most interesting political meeting this week may be the one between Valerie Jarrett, the closest confidante of President Obama, and Mark Holden, the general counsel for Koch Industries, the conglomerate owned by the anti-Obama Koch brothers.

This will be their fourth meeting. They correspond regularly and have developed a mutual respect while working on the most sweeping reform of the American criminal justice system in decades.

Addressing the economic and social cost of the huge prison problem — 2.4 million people are incarcerated in America, a higher share of the population than almost anywhere else — is a priority for the White House and the Kochs.

The effort is advancing in both houses of Congress; Speaker Paul D. Ryan of the House of Representatives and Mitch McConnell, the Senate majority leader, are committed to bringing legislation to the floor.