U3 is the official measure because it matched the International Labour Organization definition[1]. Most countries use the same definition.

Measurement is always hard, and always requires caveats. There are good arguments both for including discouraged workers (hidden unemployment) and part-time workers who would prefer full time work (underemployment) in unemployment statistics. There are also good arguments against it, mainly around the fact that gathering those numbers tends to be more error-prone.

[1] http://en.wikipedia.org/wiki/Unemployment#United_States_Bure...