The argument is statistical, which is why it has taken so long to become political.

Post-enumeration analysis by independent demographers suggests that several Midwestern urban counties, including Hennepin, were counted short of their actual population. The estimated gaps are small in percentage terms — generally between one and three percent — and large in consequence, because federal funding formulas for transportation, housing, health and education distribute money on a per-capita basis for a full decade.

A one percent undercount in a county of 1.3 million is roughly 13,000 people who exist, pay taxes, use roads and hospitals, and are invisible to the formula until the next count.

The Census Bureau does not dispute that differential undercounts occur. Its own quality reports acknowledge persistent difficulty counting renters, young children, immigrant households and residents of multi-unit buildings — categories that overlap heavily and concentrate in cities.

What the bureau resists is adjustment. Statistical correction of census counts has been litigated for decades, and the legal and methodological objections are serious. A corrected number is an estimate, and estimates carry their own error.

Local officials counter that an uncorrected number is also an estimate, one whose error runs in a known direction.

"We are not asking for a number we like," a Hennepin County commissioner said at a hearing this summer. "We are asking that the known bias not be treated as zero simply because correcting it is inconvenient."

The practical remedies available are narrow. The bureau's Count Question Resolution program allows jurisdictions to challenge specific errors — a missed apartment building, a misassigned block — but not sampling-based shortfalls. Several Midwestern counties have filed challenges of this kind and recovered modest population adjustments.

A coalition of mayors is pressing instead for a change in how funding formulas themselves handle uncertainty, proposing that agencies use the bureau's own population estimates program, updated annually, rather than the decennial count alone.

That proposal has the advantage of avoiding the constitutional argument over apportionment entirely, since it touches only money and not congressional seats. It has the disadvantage of requiring dozens of separate statutory changes across agencies.

Preparation for the next count has already begun. Local officials say the lesson they have drawn is not about statistics but about staffing: the counties that fared best were those that funded their own outreach, in the languages their residents speak, well before the bureau arrived.