It's a moment of great celebration that Egypt is today voting in the most important presidential election in its history. For the first time, these are transparent elections with candidates representing a broad spread of opinions, and no one knows who will win. For decades after the 1952 Revolution, the elections were fixed by the ruling party, but this time the public has been riveted by the spectacle of open debate about the important issues facing the country.

Despite the political decay of the Hosni Mubarak years, Egypt's size and vigour still make it the intellectual leader of the Arab world. Therefore what happens in Egypt this week and in the next round two weeks later, will resonate all over the Middle East. The start of Egypt's second republic, based on transparency and democratic values, is an extraordinary moment for the whole Arab world.

The public meetings have attracted vast crowds, and the televised debate between two presidential candidates — the secularist Amr Mousa and the break-away Islamist Abdul Moneim Abu Al Fotouh — have transfixed Egyptians, who have been used to having their political leaders tell them what is good for them. After decades of this ‘take-it-or-leave-it' treatment from their political bosses, people loved the sight of the open arguments between the candidates.

Looking ahead, there are some priorities. First, it is vital that the elections must remain honest, and the integrity of the democratic process is respected. It would be a tragedy if the military interim government misused its powers to try and fix the result. Secondly, the elections should pass off peacefully. There must be no violence on a day when supporters of all parties should be celebrating their new ability to register support for their favourites.

Thirdly, the Supreme Council of the Armed Forces should accept the result even if it is uncomfortable for its vision of how the armed forces should be above the law. It is very possible that the winner may be an Islamist who is deeply antagonistic to Mubarak's armed forces.

Lastly, Egypt needs a new permanent constitution and this has to be written by a re-convened Constituent Assembly with a clearly defined inclusive agenda. The new president will do his country a huge service if he helps to form a lasting constitution that does not promote the interests of any one party over others.

Whoever wins the presidency will not have an easy job. Egypt's economy is in dire straits after more than a year of continual internal upheaval: unemployment is high and growing, and investment has fallen to new lows. And while the new president tries to tackle this monumental task, he will get very little support from a recalcitrant parliament and a firmly entrenched military establishment.