The LDP has an election date

Aso Taro has resigned his post as party president and the LDP has scheduled its party leadership for four weeks from today, 28 September. The campaign for the party presidency will officially begin ten days earlier, on 18 September, giving the candidates just over two weeks to make their intentions known and then begin traveling the country to make their appeals to the party's chapters.

Safe to say, the race is wide open. Given that Masuzoe Yoichi is just about the most popular politician in Japan and the only LDP politician candidates wanted to be seen with, he probably has the upper hand in the race for the 141 votes wielded by the LDP's prefectural chapters — if he decides to run. His position may be weaker, however, among the party's Diet members, who now number 202 betweens the two houses. The list of names in the LDP field could be lengthy, and the race chaotic. Masuzoe has said that he is a blank slate as to whether to run, and in the meantime plans to focus on his work as a cabinet minister. Tanigaki Sadakazu might run once again.

Given that the race won't officially begin until 18 September, it is likely that the party will be choosing its leader after Hatoyama Yukio is officially elected as prime minister, which will presumably occur a few days earlier.