They include a woman who could become Japan’s first female prime minister, the son of a former prime minister and a veteran moderate. Whoever becomes the LDP leader must also gain cooperation from main opposition parties or risk a cycle of short-lived leadership. Sanae Takaichi, 64, admires former British Prime Minister Margaret Thatcher and is a protégée of former Prime Minister Shinzo Abe. Shinjiro Koizumi, 44, is the son of a popular former prime minister, Junichiro Koizumi, and seeks to be the youngest prime minister in Japan’s modern history. Koizumi has approached Ishin and in August visited Osaka Expo, where he was escorted by party leader and Osaka Gov.