Regarding the relationship between popularity and outcome, I too would appreciate any research on that-as long as it is legible to this non-statistician. In the meantime, I think that we should be clear as to what we mean by outcome. Ellis Krauss in his 2012/02/22 comments is obviously writing about the number of seats won by the respective parties. But the specific features of the Japanese electoral system and shifting political alliances complicate the connection.
Specifically, under the current lower house electoral system, the LDP won 239 (47.8%) of the 500 seats available in 1996 under Hashimoto, 233 (48.5%%) of 480 in 2000 under Mori, and 237 (49.4%) of 480 under Koizumi. However, the LDP's percentages of proportional district votes in those three elections were 32.76%, 28.31%, and 34.96% respectively. The voting numbers appear to better reflect, at least ordinally, the general perception of the relative popularity of the three LDP leaders. Of course to paraphrase Paul Mitford's in his 2012/02/21 comments, ideas matter.
Likewise, the state of the economy, perceived threats, etc. etc., and I don't know how academics manage to control for all that, particularly since we've only had three lower house elections under the current system and three political parties surviving that process in more or less the same shape if not in size. Good luck, y'all.