On the eve of the poll the government explained that it had long been committed to "constitutional legitimacy and political pluralism".
It had failed to introduce them merely because of the Iran-Iraq war which broke out in 1980 and lasted for eight years. Two years later it had once again been forced to curb its democratic instincts after the invasion of Kuwait. Nobody in Baghdad takes these claims seriously. One of the few street demonstrations in the city (naturally in favour of voting "yes" to the presidency of Saddam Hussein) was made up of Egyptian labourers. Saddam's control is total and is likely to remain so. Iraqis say privately that they are pleased that Uday, the son of the Iraqi leader, has lost influence after shooting his uncle Watban in the leg in August and forcing Hussein Kamel, his brother-in-law and head of military industries, to flee to Jordan.
But the fear is still there. A taxi-driver did not want to drive past the 10-storey building on Palestine Street which houses the Iraqi National Olympic Committee and is Uday's headquarters. Iraqi sources say that when Saddam sent security men there they discovered Uday was maintaining his own prison, from which they released three men.
Iraq remains rigidly controlled from the top. For instance, Watban, Saddam's half-brother, who may lose his leg because a nerve was severed by the bullet, is being treated by his own Iraqi doctor assisted by Cuban medical staff. But the doctor had to return to jail after each visit to Watban's hospital bed, because he was serving a six-month sentence for illegally owning a satellite dish for foreign broadcasts.
The law has since been modified. Illegal possession of a dish now leads to confiscation and a fine of about pounds 300. The government can still enforce its will. All but a few restaurants in Baghdad keep to the ban on alcohol even though it means few customers.
Diplomats say that through the referendum and the curbing of Uday, Saddam means to send a message to Iraqis that in future "government will be in the hands of bodies like the Revolution Command Council and the Ba'ath Party Regional Command, and not his inner family".
This will not necessarily mean a change in policy. A Russian diplomat with long experience of Iraq once said that even the most sophisticated member of the Iraqi leadership "always has to be 10 per cent tougher than the boss, because this is the only safe thing to be".
There are signs that Iraq wants to present a more moderate image. For the first time since 1991 it has allowed in large numbers of foreign journalists. Even the mosaic of the face of George Bush, on which those entering the al-Rashid Hotel had to step as they came into the lobby, has been covered by blue carpet.
Saddam has always had a fondness for symbols of his unshaken grip on power. The referendum and the herding of eight million people to 1,662 polling stations - outside the three Kurdish provinces, which the government does not control- is the latest.
But a more impressive symbol of his power in the face of adversity is planned. At Baghdad's old municipal airport in the centre of the city, 10 design teams are working on what is to be the world's largest mosque. "It is the only construction project in the country at the moment,'' said an Iraqi engineer. The design is for a concrete dome covering an area the size of a football pitch. Lack of piledrivers, excavators, high-tensile steel or concrete additives may force Saddam to adopt a less ambitious alternative, but a pavilion is being built from which he can view the work.
The real basis for his power is Iraqis' fear of the security services. But he has other strengths. The 20 million Iraqi population is divided into Sunni Muslims, Shia Muslims, and Kurds, who dislike and fear each other. This has made a united opposition impossible. Eight million live in Greater Baghdad, making it more difficult for a revolt in distant provinces to succeed. The very dependence of people on the official ration for 50 per cent of their diet gives the government control over their lives.
Impoverishment of the urban poor and much of the professional middle class has so far had little political impact. In one vast market held every Friday under a Baghdad flyover, families sell their furniture. "As soon as it is sold they go and buy fruit to eat,'' said a bystander.
Senior government officials and landowners make money from the embargo. Sheikh Hatem al-Jerian, head of a tribe 100,000 strong near al-Hillah, south-west of Baghdad, says farmers are doing well and "everything is available on the black market".
But the government is growing weaker because it has failed to breach the embargo. Last week's strong UN report that Iraq has concealed evidence of many more weapons of destruction makes it inevitable sanctions will continue. Like a besieged medieval city, Iraq grows feebler every year but is still far from capitulating.