The issue where the well-informed see greatest hope for change is the church’s ban on communion for divorced, remarried Catholics. Univision’s survey found overwhelming majorities in favour of ending it, not only in Europe and North America, but in Latin America, too. Conservatives raise two objections: one theological and one pragmatic. How can someone in what the church sees as an invalid marriage be a worthy recipient of the Eucharist, which Catholics believe is the body of Christ? And how can the Vatican appear to undermine marriage at a time when the church is engaged in what it sees as a desperate battle to defend the institution against same-sex marriage in many countries, and rising divorce and cohabitation rates almost everywhere?

In recent weeks Pope Francis has nevertheless appeared to be edging towards a shift. Last month he chose Cardinal Walter Kasper, a liberal who has argued against the ban, to address cardinals meeting to discuss questions about the family. And on February 28th, during his daily mass in Casa Santa Marta, he called on priests to “accompany” those whose marriages had failed. “Do not condemn,” he said. “Walk with them and don’t practise casuistry on their situation.”

Liberal Catholics are also hoping that the pope will reconsider the role of women in the church. “For me, this is the litmus test,” says a former senior Vatican official. “If he does not do something radical for women, then I think we can assume he will not make any substantial reforms.” One possibility is that he might place a woman, perhaps the head of a religious order, in charge of a Vatican department. Some theologians have argued that only the ordained can exercise power in the name of the pope. But on March 3rd Cardinal Kasper, perhaps acting as a stalking horse, said there was no reason why women could not run some of the Pontifical Councils, second-class Vatican “ministries”, which have briefs that include the laity, the family, culture and the media.