The city enlists thousands of volunteers for the four-hour, overnight canvass, an undertaking that would cost far more without the unpaid search parties. The decoys shoulder the responsibility of testing the accuracy of a survey carried out by volunteers who are sometimes too timid to approach homeless people or are too inattentive to spot them.

The annual count, scheduled for Monday, is part of a nationwide estimate of homelessness, which helps to determine annual federal grants.

The city uses the percentage of decoys who are not found as a margin of error, one of several factors used to come up with the final estimate. “All of our efforts here are essentially checking our work,” said Steven Banks, the city’s commissioner of social services.

The decoy program is known as the “shadow count,” and the people who brave the cold year after year say they do it not for the pay of $85, but as a civic duty.

The city estimated that 3,900 people lived unsheltered during last year’s census, accounting for about 5 percent of the city’s 77,000 homeless people. Still, there was a 40 percent jump in street homelessness over the previous year, which city officials attributed to unseasonably warm weather. But advocates for homeless people have long argued that the unsheltered population is likely higher, since people find temporary relief with friends and family during inclement weather.