Page "Prime Minister of Japan" Paragraph 3

The Prime Minister is designated by both houses of the Diet, before the conduct of any other business.

For that purpose, each conducts a ballot under the run-off system.

If the two houses choose different individuals, then a joint committee of both houses is appointed to agree on a common candidate.

Ultimately, however, if the two houses do not agree within ten days, the decision of the House of Representatives is deemed to be that of the Diet.

Therefore, the House of Representatives can theoretically ensure the appointment of any Prime Minister it wishes.

The candidate is then formally appointed to office by the Emperor.