Barring some extraordinary electoral reversal, all the signs seem set for Hamas, the militant Islamist movement, to emerge from Wednesday’s Palestinian elections with about one-third of the popular vote. Even if the organisation does not top the poll, it will break the stranglehold of Fatah, the nationalist movement that has grown tired and corrupt after years of political domination.

The democratic breakthrough of Hamas, responsible for almost 60 suicide bombings in Israel in the past five years and still officially committed to destruction of the Israeli state, would seem on the surface like a devastating setback for the peace process. Israeli politicians of all persuasions have condemned the willingness of the international community – including the US and the European Union – to tolerate the participation in the Palestinian poll of an organisation that has yet to renounce the armed struggle, even if it has observed a year-long ceasefire.

Hamas may not demand a role in the future Palestinian Authority – it is not clear that its leaders want to participate – but it will be able to wield powerful influence on the future government, most likely then to be a fragile coalition of Fatah, itself riven by factionalism, and much smaller independent groups. Hamas could readily block attempts to revive the road map towards a two-state peace settlement to which both the Israeli government and Mahmoud Abbas, the Palestinian president, are committed.

That might seem a nightmare scenario for Israel. Yet all is not quite as it seems. The Israeli reaction is far more equivocal than one might expect. Israeli politics are also in a state of extraordinary flux following the stroke suffered by Ariel Sharon, the prime minister. Kadima, the new centre party he launched, has transformed the old left-right division between Likud and the Labour party, and even without its founder is favourite to win the March election.

That outcome, however, will be profoundly influenced by the Palestinian poll and the unpredictable behaviour of Hamas. “They will face a terrible dilemma if they win,” says Shimon Peres, the former Labour prime minister who has now thrown in his lot with Mr Sharon’s Kadima. “What can you do with public support if you do not translate it into real terms? Without a partner, their victory is worth nothing.”

Israeli analysts, not least in the powerful intelligence services, admit they are uncertain how Hamas will react. “The probability is that we will see a combination of Fatah and Hamas,” according to a senior military officer. “Fatah will keep the security apparatus and central offices, while Hamas takes over social services. The terror will continue.” But at the same time he admits it could turn out very differently: “The better Hamas do, the more difficult it will be to return to violence. It will force them to talk responsibly.”

Ehud Olmert, Israel’s acting prime minister and acting leader of Kadima, left his options open on the eve of the Palestinian poll. “I am not a partner to all the doomsayers who are already telling us how hard and horrible it will be here after the elections,” he said on Tuesday night.

If Hamas does return to violence, it would probably help Benjamin Netanyahu, leader of the rump of Likud, who fiercely opposed Mr Sharon’s decision unilaterally to close down the Israeli settlements in the Gaza strip. “He rewarded the terrorists and punished the moderates, because the Palestinian streets see the Jews fleeing from terror,” Mr Netanyahu said this week.

On the streets of Gaza, however, the success of Hamas seems to be as much due to its campaign against corruption in the Fatah ranks and its success in providing welfare services to its supporters as to its militancy. A vote for Hamas may very well not be a vote for violence, but simply a vote for clean hands.

Whatever the outcome, the message of the Palestinian elections for Israeli voters is that the two democratic processes are inextricably linked, even though the level of communication between politicians on either side of the divide is depressingly low. At the prestigious Herzliya conference held outside Tel Aviv this week, all the great and good of the Israeli political and security establishment were there, but not a single Palestinian face was to be seen. Political analysis of the elections taking place barely 20 minutes drive from the seaside venue was almost entirely absent.

Instead, the debate focused overwhelmingly on questions such as identifying where to draw the most defensible borders for the future state of Israel; how changing demographics would affect the two-state solution; how to ensure that an Israeli state would always preserve a Jewish majority; and how Israel’s international relations were affected by the current state of the peace process and the wider conflicts in the Middle East. It was as if Palestinian opinions were entirely irrelevant.

Perhaps it was too much to expect, given the history of mistrust. Yet a huge part of the Arab-Israeli problem is that so often the two sides are talking completely past each other. Tzipi Livni, the newly appointed foreign minister and rising star of Kadima, dared to point it out. The whole debate in Israel, she said, was on how to adjust the 1967 borders of the Israeli state. On the Palestinian side, however, the real focus is still on the refugees who fled their homes in 1948. If they cannot even agree on the starting point, they will carry on a dialogue of the deaf.