The Big Question: Does the rise of Tzipi Livni make peace in the Middle East possible?

Why are we asking this now?

Because Tzipi Livni has just won the contest to lead the currently ruling party Kadima in sucession to the outgoing Ehud Olmert. It doesn't mean that she will automatically become Prime Minister. But she has a real opportunity to form a coalition in the coming weeks. And even if she fails, the polls suggest she is still the politician in Israel with the best chance of winning a general election against Kadima's strongest opponent, Benjamin Netanyahu's Likud.

So is that good for peace hopes?

At the minimum, the record suggests that Livni, as foreign minister, has been more interested in diplomacy and serious negotiations with the moderate West Bank-based Palestinian leadership under Mahmoud Abbas than the Kadima runner-up Shaul Mofaz, who as a hawkish former Army Chief of Staff and Defence Minister is rooted in the security establishment.

Livni has actually been taking part in talks started by Olmert and aimed at some sort of agreement on the outlines of a future "final status" two-state solution to the conflict with the Palestinians; Mofaz indicated during the campaign this was not the time to be talking about final status. And if anything that is even truer for Netanyahu.

Although Livni comes from the hard right – her parents were prominent in the right-wing Irgun Jewish underground organisation – she does seem, like Olmert, to have come to the conclusion that dividing land with the Palestinians is the only option for guaranteeing the long-term future of the Jewish state. And because she is – so far – popular, in contrast to Mr Olmert, whose standing was badly damaged both by the Lebanon war and the financial allegations against him, she might be able to deliver things he couldn't.

So we should expect a dramatic breakthrough?

If only it were that simple. First the nature of Israel's political system means she will find, as Olmert did, that it's difficult to form a stable government without at least one party, like the Sephardic ultra-orthodox Shas, which is basically opposed to the kind of deal that Mr Abbas could sell to his own people.

Shas's opposition is one of the reasons that the talks that Livni and Olmert are embroiled in haven't even got serious yet about the key issue of Jerusalem, which the Palestinians want as a shared capital. True, she could dispense with Shas – and she certainly dislikes their constant demands for increased family allowances – and instead opt for the left wing Meretz. But Meretz has only half as many members as Shas's 12 which would mean her relying on the acquiescence of some Arab Knesset members. That probably isn't the mix she would like to make her essentially centrist pitch at a general election, whenever it comes.

Isn't that a crucial point?

Not quite. You have to assume that if there was a deal of any kind, the Prime Minister making it would have to take it the country. So in theory, if Olmert – who is likely to stay in post as an interim PM until a new one is actually sworn in, either after forming a coalition or winning an election – made one which Livni signed up to, or if Livni as PM made one herself, that could be the centerpiece of the next Israeli election. And of course we aren't exactly talking yet about a Camp David-type deal (had it succeeded) which could usher in a Palestinian state the next day.

If, say, an agreement were to be struck before Olmert, George Bush, and perhaps even Abbas were to leave the stage in January 2009, then the maximum it would probably do would be to agree some principles on borders and refugees, and create some "mechanism", probably underwritten by Arab states, for taking the negotiations onto to the next stage.

Isn't this a bit academic as long as Hamas is running Gaza?

Livni certainly isn't going to start talking to Hamas as long as it refuses to recognise Israel. On this she is a hawk. Israel's talks with its Fatah rivals were kick-started at Annapolis, the international summit convened by the US late last year. And the theory behind Annapolis, such as it was, was to negotiate a two state "proposition" with Abbas which would be attractive enough to the Palestinian people for him to put it to a referendum or an election, so bypassing Hamas's opposition. That still seems to be a long way off and it's notable that Livni has cautioned against expecting too much, too soon, from the talks with Abbas's team.

Where does Livni stand on the rest of the region?

On Iran, she has refused to take any options, including the military one, off the table – but she also hasn't gone in for the kind of bellicose rhetoric ramped up before the leadership campaign by Mofaz. She has actually taken a tough line on Syria, criticising Olmert for opening talks with Damascus before it has taken tangible steps to stop its "support for terror".

On the other hand, it's worth recalling that at the time of the Lebanon war she argued before any of her colleagues – though not to the point of threatening resignation – that an urgent diplomatic solution was needed. And she showed some healthy scepticism, in internal discussions, about the claims being made for a military one.

Finally, Livni was notably negative in an interview last week about the case for a military invasion of Gaza .There is some evidence, at least, that she isn't about to make the same mistake as Olmert did in Lebanon – over-compensating for his lack of military experience by being more of a warrior than the warriors.

So has she got what it takes to make big bold steps for peace?

That really is the Big Question. What we don't know about Livni is how much of a risk-taker she is. Some people believe, for example, that to implement the kind of withdrawals of West Bank settlements that would be needed to make a reality out of any peace agreement, you would need someone of the authority and mettle of Yitzhak Rabin, or – if he had had both the time and the inclination – Ariel Sharon. Particularly given the political constraints we have already talked about.

When Livni called on Olmert to resign in the wake of the Winograd inquiry into the Lebanon war, she then failed to press her demand home by walking out of the government herself. On the other hand, this week's result – narrow as it was – indicates that she didn't do herself any harm. At least the difficult period ahead should tell us rather more about Livni's character than we know so far.

So can Livni bring peace?

Yes...

* A self-confident woman, she is not scared of preferring diplomacy to militarism

* Though a Zionist she believes a peace agreement with the Palestinians is essential

* Most Israelis want the conflict to end. Livni's popularity will help her to sell peace

No...

* Israel's multi-party system and the disportionate power of the right will stop her

* Only a powerful general on the Sharon-Rabin model could beat settler opposition

* It will be easier to keep people quiet with a drawn-out process than by concluding a deal