TO JUDGE by this week, the race to succeed François Hollande as president in 2017 has begun. One by one, rival politicians are carving out positions. On the left Manuel Valls, the Socialist prime minister, sounds ever more like a rival to his own boss. On the right, two former prime ministers are in the running, and a third contender is likely to declare: Nicolas Sarkozy. The former president is expected this weekend to announce his candidacy for the centre-right UMP party leadership, a prelude to a presidential bid.The start of the week belonged to Mr Valls, who put his government on the line on September 16th in a parliamentary vote of confidence after his eviction of three anti-austerity rebels last month. He narrowly won, ensuring the government’s survival. But 31 of his own deputies abstained, up from 11 at a previous vote in April, in protest at what they consider to be a betrayal of the socialist policies which Mr Hollande was elected to put in place.The ambitious Mr Valls is now treading a difficult line between loyalty to the unpopular Mr Hollande and a muscular desire to show that his more reformist, business-friendly politics can be an alternative to tax-and-spend socialism. It is a perilous strategy. Mr Valls’s poll ratings are tumbling as he becomes linked with Mr Hollande, whose popularity is at a record low of 13%. Damaging revelations by Valérie Trierweiler…