Ranking rules so the order settles conflicts

Definition · Arend Lijphart, Democracy in Plural Societies (1977)

In a deeply divided society, each group governs its own internal affairs — its schools, its family law — within its own sphere, instead of everyone living under one uniform rule.

Analysis

Rules come from law, from ethics and from the local culture, and the compositional operations allow one rulebook to be built from another, so a locale can in principle be given its own priority ordering. But no sphere is carved out in which a group's rules simply apply. Every rule, whatever its source, sits in one common order and can be outranked by a rule from elsewhere, so a local norm is decisive only if it happens to rank high enough rather than because it is local.

Definition · Friedrich Carl von Savigny, System of the Modern Roman Law (1849)

When several bodies of rules could govern the same case, an explicit rule decides which one actually does — and states the reason. Without such a rule, "different rules for different groups" has no answer for the cases in between.

Analysis

The pre-order is an explicit, prior and machine-checkable rule for deciding which of several conflicting rules governs an outcome, stated with more precision than anything else in this cell. What it lacks is a connecting factor. Savigny's rule attaches a case to a body of law through some feature of the case, whereas this ranking is fixed in advance and identical whatever the case, so it answers which rule outranks which and never which rulebook a given situation belongs to.

Definition · Arend Lijphart, Democracy in Plural Societies (1977)

Decisions that affect all groups require every group's consent, and representation is proportional to each group's size — so no segment can simply be outvoted on what matters most to it.

Analysis

Priority is assigned by whoever authors the rulebook. No group whose law, ethics or culture contributed a rule consents to its rank or can block a change to it, and nothing is proportional to population, stake or anything else. The constraint-preserving operations protect earlier rules against later edits, which is a guarantee to the specification, not to any segment.

The paper derives which operations on a rulebook may be allowed if constraints introduced earlier are to survive, so a proposed change can be checked against that list before it is admitted rather than argued over afterwards. Legal orders face the same problem and answer it with doctrine on implied repeal and entrenchment, worked out case by case once someone litigates the later rule. Here the question of whether an amendment undoes a prior settlement is settled in the algebra, before the amendment enters the rulebook.