Underinflation should not cause any problems. The circumference of the
tire remains the same independent of low air pressure, so the number
of wheel revolutions per mile remains the same.
Here's something that should settle some of these raging arguments.
At dmses.dot.gov/docimages/pdf68/135285_web.pdf is a US Department of
Transportation report on tests of tire pressure monitoring systems (TPMS).
It's a 161 page .pdf document; if you don't want to download it, Google's HTML
conversion is at
http://tinyurl.com/ke1a
This report says:
"As was mentioned in the preceding section, TPMS can be divided into two main
categories, Wheel-Speed Based - WSB (Indirect) and Pressure-Sensor Based - PSB
(Direct). WSB systems infer tire pressures by using the vehicle's ABS
hardware, specifically the wheel speed sensors, to measure tire-to-tire
differences in tire rotational velocities that indicate that a tire is at a
different pressure from the others."
The report also says that WSB sensors don't work very well:
"Four WSB systems installed as original equipment on 2000 or2001 vehicles were
evaluated. Testing showed that all of the WSB systems would warn of a single
tire being significantly underinflated (50 percent low) on a winding road
course. However, on the 7.5 mile oval test track, which requires little
turning input, only three of the four systems could detect tire pressure as
low as 14 psi. The WSB systems also did not warn of two tires equally
underinflated on the same side of the vehicle or on the same axle. Three of
four systems warned of two underinflated tires in diagonal positions. All of
the systems warned of three tires equally underinflated. None of the four WSB
systems were able to warn of all four tires equally underinflated. The
observed warning capabilities of these systems corresponded to the theoretical
limitations of the sensing algorithm documented in this report."