The first free elections in Libya have been a substantial success, with the voting passing off without violence and a broad acceptance of the surprising result that the liberal National Forces Alliance, led by former prime minister Mahmoud Jibril, may well win a majority in the parliament.

Jibril has even started to act as a future national leader, calling for all parties to come together for a national dialogue and commenting that there was no loser or winner this week, that “Libya was the real winner of these elections”.

The complicated process of counting is expected to continue over four days, under a complex system in which, out of the 200 seats in national assembly, 80 are reserved for party candidates and 120 for individual representatives, even if many of these people have close ties to the larger parties.

The National Forces Alliance was in the lead in many constituencies in Tripoli, as well as the eastern city of Benghazi, according to unofficial exit polls by Libya Herald.

This was accepted by Mohammad Sawan of the main Islamist party, Justice and Construction, who said: “The National Forces Alliance achieved good results and have a net lead in Tripoli and in Benghazi.”

The exception to this trend was the coastal town of Misrata where a faction of local politicians has done well in the competition to win the four seats from that town.

The elections are far from over, but it is notable that the Islamists have not done well. Preliminary reports suggest that Libya will not follow the same post-Arab Spring route as Egypt or Tunisia, where elections handed power to Islamists.

Some have attributed what seems to have happened in Libya to the personal standings of liberal leader Jibril and his good performance as prime minister in the immediate aftermath of the revolution.

Others have looked to large number of women who were worried that they might lose the high standing that they held under Muammar Gaddafi’s dictatorial but secular regime.