The term "Tosai-gogisei " refers to the way of decision-making in an organization. It adopts the same procedure as those of the collegial system in which an agenda is considered at a collegial body of more than one member, but it is an independent system in which the power of final decision-making is given to one person. This was the way that had been often used under the legal code system and basically adopted for decision-making in Japanese politics before recent times.
For example, in a conference of Imperial Court during the Heian period, participants of a collegial body each gave opinions and discussed them and later they voted. After that, the contents of discussion were reported to the Emperor, who was the person to make the final decision (or his substitute, that is, a regent or a chief adviser to the Emperor), and the odd man made a final decision on policies based on it.
Therefore, the actual situation had varied a great deal depending on the power relationship between 'participants of collegial body' and 'the final odd man.'
Basically, it was desirable to value the conclusion of the collegial body the same as the collegial system, and mostly the final decision was made based on it, but if that the odd man had absolute or nearly absolute power, it sometimes became similar to the independent system or despotism.
According to the "Shoyuki (Diary of FUJIWARA no Sanesuke)" in the Heian period, there was a case where the major opinion in the conference of the Imperial court was denied by the opposition of FUJIWARA no Yorimichi, a chief adviser to the Emperor, and another minor opinion supported by Yorimichi was implemented, and in another case more recently, amnesty for Nichiren, which was opposed by all hyojoshu (chamber of government affairs and justice) in the Kamakura bakufu (Japanese feudal government headed by a shogun), was implemented by Tokimune HOJO, a regent to the shogunate, who was the odd man. In addition, in the Takeda clan of Kai province during the Sengoku Period (Period of Warring States) the final decision was also made by the family head of the Takeda family after a consensual decision made by the vassals.
This way of decision-making, in which the highest man of power had the authority of the final decision while suppressing complaints of under class people using the form of adopting their opinions, had been kept as a 'traditional' and 'fundamental' way until the Edo period. And even recently, this way had been continued in conferences while in the presence of the emperor and so on.