Victory for either of the two frontrunners in the leadership election for Japan’s ruling Liberal Democratic party will make for a standout moment in the political life of the world’s fourth-largest economy. If 44-year-old agriculture minister Shinjiro Koizumi wins on October 4 and is appointed prime minister, he will be the country’s youngest head of government since the great reformer Hirobumi Ito took office back in 1885. If conservative veteran Sanae Takaichi prevails, she will be Japan’s first female premier.

Yet as the short and largely inconsequential tenures of numerous recent Japanese prime ministers suggests, it will not be easy for Koizumi or Takaichi to make a more substantive impact. Japan is in the throes of a tricky transition to persistent inflation and suffering from fiscal strains, demographic decline and geopolitical uncertainty.

Under outgoing Prime Minister Shigeru Ishiba, who lasted barely a year in office, the LDP lost control of both houses of parliament. The long-dominant party is struggling to fend off new populist right-wing rivals. Its loss last October of the lower house majority it previously enjoyed in coalition with junior partner Komeito means the new LDP president will even have to rely on opposition disunity to secure the prime ministership.