The Vatican's Sistine Chapel chimney has released white smoke and church bells have rung, indicating that a new leader of the 1.2bn Catholic Church has been elected after the second day of secret deliberations.

Thousands of people gathered at the rain-soaked St Peter's Square erupted in cheers at the sight of the white smoke on Wednesday evening.

The 115 cardinals had been deliberating throughout the day to find a successor for Benedict XVI.

As a sign of the election of a new pope, the Vatican has also reactivated the Twitter account @Pontifex.

While the voting for the pope is billed as secret, with each cardinal guided only by his faith in God, the process is ultimately a closed-door exercise in consensus-building that cements fidelity to the Church's new leader among the inner circle.

The papal election resembles how decisions were made in Europe some 700 years ago, before elected monarchies were replaced by hereditary monarchies, according to Bruce Bueno De Mesquita, professor of politics at New York University who uses a computer model based on game theory to predict the outcome of elections.

Though it is more a product of tradition than design, it has turned into an efficient system for consolidating the power of the pope and the Church's other elites, De Mesquita said.

Just as in the corporate world or autocratic governments, the small number of electors who are deciding on the leader of the Catholic Church can expect specific rewards - promotions, assignments and other perks - for their loyalty, Bueno De Mesquita said.

The idea is that the smaller the number of electors, the greater the relative advantage of siding with the winner.

Cardinals used to sign their names to ballots, but stopped doing so "due to an old history of intrigues and tensions when people used to fear the most serious reprisals for their choices", Michael Bruter, who teaches political science at the London School of Economics, said.

Even so, factions make their views known during informal discussions between votes.

Because the proceedings are secret, researchers know little about what exactly motivates cardinals to switch their votes, but Romain Lachat, a political scientist at Pompeu Fabra University in Barcelona, says the formation of coalitions, where electors slowly rally around a man who may only be their second or third choice, is inevitable.

Before the doors of the chapel were shut, all the cardinals below the age of 80, when the papal seat was declared vacant on February 28, made an oath of secrecy in Latin before the voting started.

All the "Princes of the Church" were appointed by Benedict or his predecessor and ideological soulmate John Paul II.

In interviews given before the conclave, voting cardinals pointed to new job requirements arising from the problems facing a Church that is struggling in many parts of the world with scandals, indifference and conflict.

"Managerial skills will surely be useful," Vienna Archbishop Christoph Schoenborn told La Stampa.

And in an indication of a faultline between Vatican insiders and those running far-flung dioceses, Nigeria's John Onaiyekan spoke of "new and innovative methods to boost collegiality".

"In this regard there is a lot of room for development," said Onaiyekan, the archbishop of the Nigerian capital Abuja.