But this is the "people's government" and it has decreed that the people must decide what should go on the empty plinth in Trafalgar Square in London.
And so for the past five years the suggestions have been flowing in thick and fast. The collective mind of the Great British Public can definitely be seen behind most of them: A giant David Beckham; a statue of Idi Amin. Or rather more bizarrely - a stiletto-heeled shoe. Other ideas to have reached the desks of the think- tank that has to decide what to recommend to the Government, include representations of Dolly the cloned sheep; Winnie the Pooh and a "British stiff upper lip".
Until a few months ago, when a life-size figure of Christ was installed on the plinth as part of a rolling exhibition, it had stood naked since the 1840s, when the square was designed by the architect Charles Barry.
He created two large plinths at the bottom of steps leading down to the square (two other, smaller, ones sit on the other side) with the intention of exhibiting groups of statues.
Three years later a statue of George IV went up. The fourth plinth was supposed to have William IV on it but he died leaving no money to pay for it and no one else felt like paying for it. And so it lay empty. Over the next 150 years or so there was a succession of proposals but no one could agree on the final installation.
Then Prue Leith, the cookery writer and deputy chairman of the Royal Society of Arts, drove past one day and decided something must be done. She formed a committee and started badgering people for their ideas, the most popular of which was a sculpture of the Queen Mother holding the reins of Red Rum.
That was followed by a plan for a 24ft pigeon by Fernando Botero, famous in South America for his paintings of big bottoms. Then someone suggested a giant abstract sculpture which could double as a pigeon-feeder.
Eventually, everyone calmed down. The Departure of Culture, Media and Sport set up an advisory group headed by Sir John Mortimer, and started to ask people what they really, seriously, wanted.
And it appears that the pigeons may yet have it their way. In all, 275 different suggestions have been submitted by 550 people to the advisory group. Naturally, this being Britain, the leader, with 45 separate nominations, is the desire for a statue paying tribute to animals involved in warfare - horses, dogs or carrier pigeons. Next in line, with 18 votes each were the explorer Captain James Cook and the Queen.
Her Majesty has never agreed to be sculpted in her life and is thought unlikely to change her mind. It has even been suggested there is a royal decree preventing the royals from being sculpted in their lifetime in Britain. For some reason the Commonwealth countries can create their likenesses in bronze, but not here.
That means there is no bar to creating Diana, the People's Princess of Wales, but, surprisingly, and despite the involvement of the people, she received only 11 votes. Nelson Mandela garnered 13 votes and Mahatma Gandhi 10.
Many respondents were keen to pursue war themes and one of the most popular suggestions, with 15 votes, was a portrayal of children evacuated during World War II. Similarly, there were calls for Women in the War or the Women's Land Army.
Others wrote in asking for Batman, the actress Helen Mirren and, inventively, a statue of the "Unknown Hooligan". The advisory group will make its recommendation in early summer and in the interim the space is being filled by three temporary statues.
Currently standing on the plinth is the life-size statue of Christ by Mark Wallinger. Next year this will be replaced with an allegorical bronze sculpture by Bill Woodrow. Regardless of History shows a toppled human head, representing Mankind, pressed down by a giant book representing knowledge and experience and bound to the roots of a tree.
The final exhibit to fill the plinth will be an inverted cast of the plinth itself in a clear resin. Created by the Turner Prize winner Rachel Whiteread, it is designed as a point of calm in the bustle of the square.
Sir John paid tribute to the "imagination and individuality" of the new suggestions yesterday, but said the process was not a straight vote and that the committee would have the final say on what to recommend to the Government.
Then, with nary a hint of desperation, he stressed that the nominations were still open and added that he would welcome more ideas. And if they are not forthcoming perhaps the people will end up with what they deserve - three people did vote for a giant Maggie Thatcher, presumably complete with handbag.
FROM SUPERHEROES TO MIRACLES OF SCIENCE: BRITAIN CHOOSES ICONS FOR 21ST CENTURY
The cream of Manchester?
Ugandan dictator now living in exile
Led India out of the British empire
Winnie the Pooh:
The children's favourite
A vote for tradition
The People's Princess
Dolly the sheep:
A stroke of gene-ius
Symbol of a struggle, father of a nation
Captain James Cook:
He put Australia on the map
Gotham City's caped crimefighter