The Sandanista dictatorship believed its press clippings and submitted to a free election. And, to the astonishment of the usual suspects, lost by 20%-80%.
The sooner a voter registry is compiled for Iraq, and a legitimate concensus on reconstruction (and US participation in it) is obtained, the better. Presumptively the Ba'ath regime was even more oppressive than the Sandanistas--and so I would expect the favorable vote to run higher than 80%.