Why do you need to know how the voting works? In order not to put too much weight on the particular person who happens to occupy the Prime Minister's office, that's why.
Mr. Abe has debts to his peers in office and to the groups who worked to give him a party majority in the lower house. He has to work within the parameters of (a) rule by the elected legislators in both houses, (b) his coalition partners' policies, and (c) public opinion. Add to this pressures exerted by foreign governments.
Therefore, it is not wise for newspapers (I'm thinking of the NY Times on Monday) to announce that because Mr. Abe is Prime Minister, Japan will do thus and so.
Japan has had some wonderful historical experiences with wise and powerful leaders (for instance, the Gentlemen of Japan in the Meiji Era and the shogun from Odawara Hojo Houn before that) and some truly awful ones with the foolish and strong. So, the brilliant leaders test their mettle against heavy checks and balances, and the borderline ones are held on the rails by those same checks and balances.
It works for us.