The McNamara Cascade Protocol

Proportionality Without Compromise, Representation Without Waste.

Mathematical Specification & Count Mechanics

The Mathematics of The McNamara Cascade Protocol (MCP)

The McNamara Cascade Protocol is a bounded, 3-Stage discrete apportionment algorithm. It resolves the vote-wasting lower-tail truncation of traditional divisor methods (like d'Hondt and Sainte-Laguë) while strictly enforcing a 1-seat maximum capacity on individual independent candidates and guaranteeing deterministic chamber fill.

Step 1: Effective Quota & Independent Surplus Discounting

A registered party list possesses multi-seat capacity, but an individual independent candidate has a statutory capacity of maximum 1 seat. To prevent surplus votes from artificially inflating or deflating the quota for competing party slates, independent surplus votes are discounted:

1. Base Quota (Q₀) = Total Valid Ballots (V_raw) / Total Chamber Seats (S)
2. Independent Surplus (if Votes > Q₀) = Votes − Q₀
3. Usable Active Votes (V_eff) = V_raw − ∑(Independent Surplus)
4. Effective Working Quota (Q) = V_eff / S
5. Quota Vote Share = (100 / S)% (e.g., 0.77519% for 129 seats)

Step 2: Stage 1 Integer Quota Allocation

Every qualifying entrant's vote tally is divided by the Effective Quota (Votes / Q) to determine whole guaranteed seats:

For Registered Party Lists:
• Stage 1 Seats (S₁) = ⌊Votes / Q⌋ (e.g., 35.09 quotas = 35 guaranteed seats)
• Fractional Quota Remainder = Votes − (S₁ × Q) [Logged for Stage 3]

For Individual Candidates:
• Stage 1 Seats = 1 Seat if Votes ≥ Q; 0 Seats otherwise

Cascade Pool Formed (R):
• R = Total Chamber Seats (S) − Sum of All Stage 1 Seats

Step 3: Stage 2 Unrepresented Cohort Cascade

Rather than immediately returning unused seats to large parties, Stage 2 diverts the Cascade Pool directly to unseated minority and independent movements:

  1. Filter Unrepresented Entrants: Compile all parties and independents where Stage 1 Seats = 0 and Valid Votes > 0.
  2. Rank by Raw Votes: Sort the unrepresented list strictly from highest to lowest raw vote count.
  3. Sequential Award: Award 1 seat each down the leaderboard until either the Cascade Pool (R) is exhausted or all qualifying unrepresented entrants have received a seat.
  4. Zero-Vote Exclusion: Entrants receiving zero valid votes are strictly barred from receiving seats.

Step 4: Stage 3 Surplus Remainder Resolution (Fail-Safe)

In scenarios where the number of unrepresented entrants is smaller than the available Cascade Pool, the remaining seats are filled using exact largest-remainder mathematics:

  1. Rank Stage 1 Parties by Remainder: Gather all registered party lists that achieved seats in Stage 1, ordered in descending order of their unused vote remainders.
  2. Exhaustive Fill: Allocate remaining seats one-by-one down this remainder list until 100% of the chamber seats (S) are filled.
  3. Deterministic Tie-Break: If two party remainders are identical, priority passes to the party with the higher total raw vote volume.

Core Mathematical Guarantees

Property Mathematical Guarantee & Mechanism
100% Chamber Fill Law Stage 1 + Stage 2 + Stage 3 ≡ S. Guarantees a fully populated assembly without arbitrary deadlocks.
Strict Individual Human Bound For all independent candidates: Final Seats ≤ 1. Prevents individual multi-seat distortions while preserving full party proportionality.
Wasted Vote Minimization Lowers effective entry thresholds from ~6.0%–8.5% (AMS) down to ~0.098%, achieving an ultra-low Gallagher Index (LSq ≈ 1.02%).
Axiomatic Monotonicity Satisfies the Lower Quota Rule, House Size Monotonicity (immune to the Alabama Paradox), and Clone Subadditivity.