Scratch just a bit under the hope generated by the coming electoral changes in Washington, Jerusalem, and maybe Ramallah, and you discover deep despair about the possibility of an Israeli-Palestinian peace deal.

The roads taken in the last 15 years in pursuit of a deal – the negotiations since Oslo, the unilateralism of the Gaza disengagement, and even the violence since the (second) Intifada – all failed.

The opponents of an agreement did not waste that time, however: The number of Israeli settlers grew almost threefold since the early days of the peace process, making a territorial compromise even more difficult.

Political leadership on both sides offers little hope for reconciliation. The Palestinian national movement is weak and deeply divided. The coming Israeli elections will most likely bring about a more hawkish Israeli Parliament, if not a more conservative prime minister.

A sense of hopelessness has reached even the most committed peace activists. The Palestinian activist Sari Nusseibeh, for example, wondered publicly if territorial compromise is still an option. And Israel's Yossi Beilin recently announced that he will retire from politics altogether.

Israelis and Palestinians need a new vision. They need a vision that will include a powerful incentive not only to get the train of negotiations back on track, but will also outline a final destination for its journey. With the lessons of the failed Oslo process before us, it is clear now that a future peace agreement needs to respond to the deepest grievances and darkest fears of both sides.

To find a path forward, we need to go back to the origins of it all. It was Europe's violent rejection of Jews in the past that begat modern Zionism and paradoxically contributed to its success. Once the problem, Europe may now be the solution. To both encourage and reward a territorial and security agreement between the Israelis and Palestinians, it should offer a clear path for their membership in the European Union.

It could help the parties fashion a settlement. The prospect of joining the richest union of states on earth is an enormous incentive for reaching a deal. The union's organization and values offer the frame for a peace agreement.

In fact, the dual identity of a supranational entity comprised of peaceful national states holds the answer for both sides' most profound concerns. For Israelis, EU membership offers physical security and permanent legitimacy. For Palestinians, membership means a territorial settlement, including a return, of sorts, of their lands through the new joint European source of security and authority over them.

Such an arrangement also holds significant benefits for Europe. It would contribute to political stability on its eastern and southern flank. If successful, it might even open a path for EU members to certain North African states, thus limiting the frustrations of millions of would-be immigrants to leave their instable region and go to Europe.

If European capital moves to areas of abundant nearby labor, labor has less reason to migrate to areas of capital abundance. Perhaps more important, it will expand the geographical borders of Europe, as well as the confines of its current identity, in a manner that will make the conversation with Turkey far easier.

Of course, there will be challenges. Israelis are haunted by the potential flood of Palestinian refugees from the open borders that Europe espouses (though the Schengen agreement has been applied differentially). Palestinians are still angered by the result of European colonialism, and Europeans may not want to proceed beyond admitting the nearby Island of Cyprus. Europe might be hesitate to broker such a deal, but the possibility of their succeeding with a Palestinian settlement, which had eluded the US for 40 years, would be a strong incentive to proceed. All these are weighty issues, but solvable ones.

The possibility of a day in which the descendants of the ancient foes – Christendom, Islamic civilization and Judaism – come together to resolve the century-long conflict over the Holy Land, finally acknowledging their common ancestor, Abraham, is not far afield. By using entrance to the European Union as an incentive for peace, Europe would not only free the region from a seriously destabilizing quarrel, but may also finally put to rest a millennia-long rivalry.

• Richard N. Rosecrance is a professor at Harvard Kennedy School's Belfer Center and was a member of the policy Planning Council at the Department of State. Ehud Eiran is a research fellow at the Belfer Center and served in the prime minister's office in Israel.