What system established collective responsibility for maintaining local law and order?

The tithing system established collective responsibility for maintaining local law and order by organizing communities into groups of ten households, known as tithings. Each household was responsible for the behavior of its members and was expected to report any wrongdoing to the authorities, thus creating a system of mutual accountability. This structure helped ensure that conflict and crime could be managed at a local level, fostering a sense of community vigilance and cooperation in upholding the law.

The other options do not pertain to the same concept of collective responsibility for local law and order. The frank pledge system, while also related to local order, is focused on different organizational structures. The patronage and spoils systems primarily refer to political practices involving the distribution of jobs and funds based on political support rather than community responsibility for law enforcement. Thus, while the tithing system effectively addresses the question's intent, the other answers apply to different aspects of government and social organization.