The Allocated Score engine with every number on the table — tier-by-tier accounting,
coalition weight, and fractional surplus, round by round.
This document is a companion to Proportional STAR — The Basics. That article walks through a simplified three-seat election and introduces the key ideas — selection, accounting, the two windows, the gauge. This article uses a larger, more politically complex election and shows every calculation. If you haven't read the companion first, start there. If you have, this is where we open the hood.
The formula is Allocated Score. Each round, it does two things at two windows: Window 1 selects the candidate with the most weighted support and awards the seat. Window 2 processes the charge — the quota is deducted from the voters who backed the winner, starting with the strongest supporters. The math below shows exactly how that charge is calculated, tier by tier, every round.
Seven candidates are running for five seats. Scan the Party Endorsements column — the endorsement web tells the political story before a single vote is cast.
| Candidate | Party Registration | Party Endorsements | Rating |
|---|---|---|---|
| Martinez | Democratic | Democratic, Working Families | ⓪①②③④⑤ |
| Rivera | Democratic | Democratic | ⓪①②③④⑤ |
| Torres | Democratic | Democratic | ⓪①②③④⑤ |
| Chen | Republican | Republican, Forward | ⓪①②③④⑤ |
| Walsh | Republican | none | ⓪①②③④⑤ |
| Olson | Independent | Forward, Green | ⓪①②③④⑤ |
| Patel | Green | Green | ⓪①②③④⑤ |
District 7 is a competitive multimember district electing five representatives. Democrats are the largest bloc and are expected to win at least two of the five seats — the question is whether they can take a third. Republicans should secure one seat through Chen, their endorsed standard-bearer, who also carries the Forward Party endorsement — but Walsh, running without any party endorsement and drawing support only from the district's far-right voters, faces long odds. The real drama is in the middle and on the left flank. Olson, an Independent with endorsements from both Forward and Green, is drawing from two different voter pools. Patel, the Green Party's own candidate, is a wild card: Green endorsed Olson as well, so the question is whether Green voters will have enough influence left after supporting Olson to carry their own candidate. Analysts expect the major parties to take their seats. It's the remaining seats that are up for grabs.
100 ballots are cast across five voter groups. The quota — the price of one seat — is 100 ÷ 5 = 20. Each group scores all seven candidates identically. Scores range from 0 (no support) to 5 (maximum). Cross-scores — giving stars to candidates outside your own party — are driven by endorsements. Here are the groups and how they scored:
All ballot weights begin at 1.00. Each round, Window 1 identifies the candidate with the highest weighted total and awards the seat. Window 2 then charges the quota, tier by tier, starting with the strongest supporters. The gauge panel after each round shows where every group stands.
2 Democratic · 1 Republican · 1 Independent (Forward + Green) · 1 Green. Five seats reflecting the distribution of voter support. Forward voters backed two winners (Chen and Olson) and were fully allocated by Seat 3. Green's strategic 4★ for Olson preserved enough weight for Patel to win the final seat. Walsh's isolation — no endorsements, no coalition — left them stranded.
The Allocated Score formula counted weighted support, selected the leader, charged the quota, and repeated — five times, blind to everything except the scores on the ballots. The groups that formed around each winner were not declared or registered. They emerged from the scores. The proportionality of the outcome was not determined by a thumb on the scale or a backroom deal. It was a consequence of the arithmetic. Equal price, equal treatment, repeated until every seat is filled. That's how Proportional STAR counts every vote and makes every vote count.