[Quarkboy]

The prevailing opinion in my physics department is that the LDP will lose the majority in the lower house after the election, however they will still be the largest fraction and will be forced into a power sharing agreement with the coalition of oppositions parties (or perhaps one or two of the opposition parties that are currently allied to oppose the LDP but will most likely split up if there will be a power sharing agreement).

This has happened once before (in the 70s, I think?) in modern japanese political history but no one knows exactly what sort of ruling coalition will come out of it. It depends a lot on just how poorly the LDP does... if they just lose the majority by a bit than they will be able to mostly control things in a ruling coalition, however if they are severely weakened then they may have to make large number of concessions, e.g. let the prime minister be from another party, etc.

As a progress thing goes this is actually a good thing, since hopefully whatever coalition is formed will then have a majority in both houses and progress can be made by compromise within the coalition.