Israel, which turns 60 this May, is a pure representative democracy. Virtually every social group has its own political party, if not several. This means that none of the country's many ethnic and religious subsets is disenfranchised. But as a result all governments are unstable multi-party coalitions subject to perverse incentives that have more to do with politicians' careers than with the wishes of the electorate at large.Though they say "Israel could give itself is a new political system" they don't explicitly say what that should be. The other extreme is the two-party system in the US, but there are proportional representative systems elsewhere that lie in the comfortable middle. But I think there is a better and more important change worth trying first, though maybe harder to enact.
It wouldn't solve the problem of Israel's terribly unstable governments, but it could mean that such unstable governments couldn't hold peace hostage. The quote above is not inaccurate, but it is simplistic to say that none of Israel's minority groups are disenfranchised. The multiple Arab parties, which could be a counterweight to the right-wing Shas, the single party most responsible for pushing governing coalitions to the right, are not invited into coalitions. Because Shas is the largest party outside a center that lies between Labour and Likud it has an exaggerated role in determining the stability of governing coalitions -and an outsized ego.
As it is, center-left coalitions can count on the votes of the Arab parties for most issues related to peace, but the failure to include the Arab parties in formal coalitions probably, I would think, makes it harder to bargain for votes on other issues to form a more stable government around a genuine center-left coalition.