This is the entire system:

Let V be the total group of voters and C be the group of certified candidates in a departmental election where S seats are to be filled.

(a) Ballot Format

Each voter assigns a Support Rating (R) from the set [0, 1, 2, 3, 4, 5] to each candidate. If a voter does not rate a candidate, that rating equals 0. Rating any candidate is independent of ratings given to any other candidate.

(b) Voting Budget

Prior to tallying, every voter is allocated an initial Voting Budget. This starting budget is calculated as the total number of seats (S) divided by the total number of valid ballots cast (V).

(c) Seat Cost

Each seat to be filled carries a constant cost of exactly 1 unit, using the same units as the Voting Budget.

(d) Sequential Allocation

Seats are filled iteratively, one at a time, until all seats are filled or no remaining candidate is Fundable under subsection (e).

(e) Fundability and Support Rate

Let "b" represent a voter's remaining Voting Budget at the current step. An unelected candidate is "Fundable" if there is a "Support Rate" (a multiplier value greater than or equal to 0) that makes the total contributions from all voters equal to or greater than the seat cost of 1.

Mathematically, for a candidate to be Fundable, the sum across all voters of the smaller of these two numbers must be equal to or greater than 1:

1. The voter's remaining budget (b)
2. The voter's rating for that candidate (R) multiplied by the Support Rate.
   The actual Support Rate for a candidate is defined as the absolute lowest possible multiplier that allows that sum to reach exactly 1.

(f) Selection (Cheapest Candidate)

Among all Fundable candidates, the candidate elected to the next available seat is the one requiring the lowest Support Rate. This is the "cheapest" candidate to fund because it requires the smallest multiplier applied to voter ratings to reach the seat cost.

If multiple candidates share the exact same minimum Support Rate, the tie is resolved by a public, audited lot conducted by the Anti-Corruption Bureau.

(g) Budget Deduction

For each voter, their remaining budget is updated after a candidate is elected. The amount a voter contributes toward the elected candidate's seat is the smaller of these two numbers:

1. The voter's remaining budget (b)
2. The voter's rating for the winning candidate (R) multiplied by the winning candidate's Support Rate.
   The voter's new remaining budget is their old budget minus this contribution amount. Voters who gave the winning candidate a rating of 0 contribute nothing and retain their full remaining budget.

(h) Exhaustion Fallback

If seats remain unfilled and no candidates are Fundable, the remaining seats are filled sequentially by the unelected candidates with the highest total sum of Support Ratings across all voters, ignoring remaining budgets completely.

(i) None of the Above

"None of the Above" (NOTA) is evaluated as a candidate on the ballot under subsection (a). The election is voided if NOTA satisfies either of the following conditions:

1. NOTA is Fundable at a strictly lower Support Rate than any elected candidate.
2. NOTA receives a higher total sum of Support Ratings than the lowest-ranked elected candidate.
   If voided, no candidate on the original ballot may stand in the resulting special election

The day before an election a candidate who did not gain enough signatures to make it on the ballot but enough to be in the top X number of candidates is randomly chosen to be included on the ballot

The signatures is just one of many examples a voting system can use but the main philosophy is that the shock cant be unrightfully removing someone/something it must be adding someone/something that at least partially “deserves” what it has been added

I dont know how the category system works I am new here please explain