Appendix E: Initiative ranking
This appendix defines the deterministic ranking of registered initiatives used by the GK whenever initiatives must be compared, including conflict resolution and the algorithm for determining inactive initiatives.
Every initiative \(i\) has a normative level, represented by an integer \(\mathrm{level}(i)\), determined by the Legal Domain upon which it acts:
\[ \mathrm{level}(i) = \begin{cases} 3, & \text{if } i \text{ acts upon the Constitution;} \\[4pt] 2, & \text{if } i \text{ acts upon the Law;} \\[4pt] 1, & \text{if } i \text{ acts upon a Public Service Contract.} \end{cases} \]For any initiative \(i\), define:
- \(\mathrm{service}(i)\): the service created or modified by \(i\), if any;
- \(S_{\mathrm{svc}}(s)\): the total score of service \(s\), defined in Article XI: Democracy;
- \(S_{\mathrm{init}}(i)\): the total score of initiative \(i\) at the moment of its registration, defined in Article XI: Democracy;
- \(\mathrm{seq}(i)\): the sequence number assigned to \(i\) in the GK, according to the strict total order of registration.
Define the service‑score component of an initiative \(i\) as:
\[ S_{\mathrm{svc}}^{\mathrm{act}}(i) = \begin{cases} S_{\mathrm{svc}}(\mathrm{service}(i)), & \text{if } i \text{ acts upon a service;} \\[4pt] 0, & \text{otherwise.} \end{cases} \]The ranking vector of an initiative \(i\) is:
\[ R(i) = \bigl(\mathrm{level}(i),\; S_{\mathrm{svc}}^{\mathrm{act}}(i),\; S_{\mathrm{init}}(i),\; \mathrm{seq}(i)\bigr). \]The lexicographic order on initiatives is defined by:
\[ i \succ j \quad\text{iff}\quad R(i) >_{\mathrm{lex}} R(j). \]For a fixed evaluation time and fixed voting scores, this ordering is total and deterministic. It ensures that:
- initiatives with higher normative levels always outrank those with lower normative levels;
- among initiatives that act upon services, the service’s total score dominates the initiative’s own score;
- initiatives concerning the same service are ordered by their initiative scores;
- ties are resolved by the sequence number assigned by the GK.
\(S_{\mathrm{svc}}(s)\) may change over time, because voting on services remains open indefinitely. This dynamism is intentional: it ensures that, in the lexicographic ranking, the current popularity of a service dominates the popularity of the initiative that created or modified it.