Based on the provided data, I've constructed a process flow that reflects the various paths and frequencies for declaration handling. Here's a description of the process underlying this data:

1. **Employee submits a Declaration** (Frequency: High, as it appears in all pathways)
   - This is the starting point for all processes.

2. **Declaration Approval/Rejection by Various Roles**
   - **Pre_Approver**, **Administration**, and **Supervisor** can approve or reject declarations.
   - **Employee** can also resubmit declarations after rejections.

3. **Final Approval**
   - Once a declaration is approved by all relevant roles, it reaches the final approval stage, often handled by the **Supervisor**.

4. **Payment Handling**
   - After final approval, payment handling occurs, indicating the successful completion of the process.

Here are the main pathways and their frequencies:

- **Pathway 1** (Frequency = 7): Employee -> Pre_Approver -> Supervisor (Final Approval) -> Payment Handled
  - This is the most common pathway, with an average performance (assumed to be payment amount) of approximately $4.9M.

- **Pathway 2** (Frequency = 6): Employee -> Administration -> Supervisor (Final Approval) -> Payment Handled
  - This pathway occurs six times on average, with varying performance values ($2.9M, $2M, and $0.75M).

- **Pathway 3** (Frequency = 6): Employee -> Administration -> Budget Owner -> Supervisor (Final Approval) -> Payment Handled
  - Another pathway occurring six times, with an average performance of around $1.4M.

- **Pathway 4** (Frequency = 6): Employee -> Supervisor (Rejection) loop involving the employee and supervisor.
  - This pathway shows multiple rejections without final approval or payment handling, suggesting issues or disagreements between the employee and supervisor.

- **Pathway 5** (Frequency = 5): Employee -> Administration (Rejection)
  - This pathway involves only one role (Administration), with a high frequency of rejection. The average performance is around $1.4M.

- **Pathway 6** (Frequency = 5): Employee -> Pre_Approver loop involving the employee and pre_approver, then Supervisor (Final Approval) -> Payment Handled
  - This pathway shows multiple rejections between the employee and pre_approver before final approval. The average performance is around $2.2M.

- **Pathway 7** (Frequency = 4): Employee -> Administration (Rejection/Re-submission loop), then Supervisor (Final Approval) -> Payment Handled
  - This pathway involves multiple rejections and resubmissions between the employee and administration before final approval, with an average performance of around $3.5M.

- **Pathway 8** (Frequency = 4): Employee -> Administration -> Budget Owner loop involving the employee and budget owner, then Supervisor (Final Approval) -> Payment Handled
  - This pathway shows multiple rejections and resubmissions between the employee and budget owner before final approval, with an average performance of around $1.5M.

From these pathways, it's clear that there are varying levels of efficiency in the declaration handling process, with some declarations requiring multiple rejections and resubmissions before final approval. The most efficient pathway (Pathway 1) occurs most frequently but is not necessarily the highest performing in terms of payment amount.