It should have been a bad week for Shinzo Abe, Japanese prime minister, and a better one for Renho Murata, his chief opponent.

Over two days of testimony in parliament, Mr Abe contradicted himself about his memory of a cronyism scandal, even as a key figure in a different scandal linked to the prime minister was hauled in for questioning by prosecutors over fraud allegations. Yet with her foe on the ropes, it was opposition leader Ms Murata who on Thursday chose to resign.

Mr Abe’s approval rating has in just a few months plunged from a comfortable 60 per cent to 33 per cent — perilously close to levels that have done for previous Japanese prime ministers. But Ms Murata’s exit over the dismal poll ratings of her own Democratic party shows why most political observers expect Mr Abe to survive: there is simply no viable alternative.