Haruo Tsukamoto, 74, is facing what he calls the hardest political choice of his life: who he should vote for to become Japan’s next prime minister, and whether he should keep backing the party he has supported for decades.

The sixth-generation rice farmer in Ibaraki Prefecture is one of nearly a million rank-and-file members of the ruling Liberal Democratic Party eligible to vote in a leadership race on Saturday. The party has dominated Japanese politics for most of the postwar era, and its leader almost always becomes prime minister.

That hold is slipping.