The following post is by Professor Michael Thies of UCLA. [Corrected since initial posting.]
One weirdness of MMP is what to do when a party wins more seats in single-seat districts than its PR vote share would have earned. A few “overhang seats” are easy enough to deal with, but I wondered how last month’s Japanese election results would have looked under MMP (with the dubious assumption that nothing else changes).
If we simplify and assume nationwide PR, and use the PR vote shares that each party actually earned in the 16 December election (1st column of the table below) for all 480 seats, the 2nd column shows the seats “earned.”
If this were Germany, with overhang seats, the LDP would get to keep all 237 SMD seats (not 294 combined total that it actually received, because it would get no PR seats), and the legislature would have to grow to 584 seats. Of course, if overhangs were not part of the rule, the LDP would have 27.6 percent of the seats instead of the 61.3% they do have. This way, LDP-Kom would be well short of a majority (133+57)/480 = 39.6% w/o overhangs, and with a slim majority with overhangs: (237+57)/584 = 50.3%.