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Allocated Score — the recommended STAR-PR tabulation

Seat the highest scorer, then mark one quota's worth of that winner's strongest supporters as represented and set them aside. Repeat until the seats are full. It is the Equal Vote Coalition's recommended Proportional STAR, the method BetterVoting runs as STAR_PR, and the one this library exercises most.

→ Family: the three STAR-PR methods · the theory underneath: the math behind proportional STAR · what a quota does and doesn't promise: what "proportional" actually means · the majoritarian contrast: Bloc STAR

Level: 301 · deep dive

How it counts

Three moves, repeated once per seat:

  1. Winner selection — elect the highest-scoring remaining candidate.
  2. Allocating voters — mark one quota's worth of that winner's strongest supporters as represented. Supporters are sorted into groups by the score they gave the winner: the 5-star group is allocated first, then 4-star, and so on until the quota is filled.
  3. Fractional surplus — the last group added is usually a little larger than the quota needs. The extra is returned to that group and shared evenly, so those voters keep partial influence over later seats.

Subsequent rounds include everyone not yet fully represented. Partial representation is real here, and it is the point of a scored ballot: it records not just whether a voter is represented but to what degree.

Fractional surplus is what makes step 3 fair rather than arbitrary. Voters who gave the winner the same score are treated identically, instead of an alphabetical or random cut deciding which of them gets used up. (electowiki adds that it preserves independence of irrelevant alternatives and monotonicity, though that claim carries a citation needed there — treat it as unverified.)

voting_method: allocated plus num_winners: k.

Watch it count

63 ballots, 5 candidates, 3 seats. 39 voters back Alice/Ben/Cara, 24 back Dan/Eve — watch both fractional-surplus reweights, and the third seat going to the minority that Bloc STAR would have shut out:

[Divergence from STAR]
  STAR                   = Ben
  Choose-One (Plurality) = Alice   (differs from STAR)
  Approval               = Alice   (differs from STAR)

--- Allocated Score Voting Method (3 winners) ---

[Allocated Score Voting]
 Tabulating 63 ballots to fill 3 seats.
Count × Alice,Ben,Cara,Dan,Eve
   18 ×     5,  4,   3,  0,  0
   15 ×     0,  0,   0,  5,  4
   12 ×     4,  5,   3,  0,  0
    9 ×     3,  4,   5,  0,  0
    9 ×     0,  0,   0,  4,  5

[Allocated Score Voting: Round 1]
 The highest-scoring candidate wins a seat.
   Ben           -- 168 -- First place
   Alice         -- 165
   Cara          -- 135
   Dan           -- 111
   Eve           -- 105
 Ben wins a seat.

[Allocated Score Voting: Round 1: Ballot allocation round]
 Allocating 21 ballots.

[Allocated Score Voting: Round 1: Ballot allocation round: Round 1]
 Allocating 12 ballots at score 5.

[Allocated Score Voting: Round 1: Ballot allocation round: Round 2]
 Remaining allocation quota is 9.
 Allocating 27 ballots at score 4.
 This allocation overfills the remaining quota.  Returning fractional surplus.
 Allocating only 33.33% of these ballots.
 Keeping these ballots, but multiplying their weights by 2/3.
 27 ballots reweighted from 1 to 2/3.

[Allocated Score Voting: Round 2]
 Tabulating 51 remaining ballots.
Count × Alice,Ben,Cara,Dan,Eve
   18 ×     5,  4,   3,  0,  0
   15 ×     0,  0,   0,  5,  4
   12 ×     4,  5,   3,  0,  0
    9 ×     3,  4,   5,  0,  0
    9 ×     0,  0,   0,  4,  5

[Allocated Score Voting: Round 2: Ballot allocation round]
 Allocating 21 ballots.

[Allocated Score Voting: Round 2: Ballot allocation round: Round 1]
 Allocating 15 ballots at score 5.

[Allocated Score Voting: Round 2: Ballot allocation round: Round 2]
 Remaining allocation quota is 6.
 Allocating 9 ballots at score 4.
 This allocation overfills the remaining quota.  Returning fractional surplus.
 Allocating only 66.67% of these ballots.
 Keeping these ballots, but multiplying their weights by 1/3.
 9 ballots reweighted from 1 to 1/3.

[Allocated Score Voting: Round 3]
 Tabulating 36 remaining ballots.
Count × Alice,Ben,Cara,Dan,Eve
   18 ×     5,  4,   3,  0,  0
   15 ×     0,  0,   0,  5,  4
   12 ×     4,  5,   3,  0,  0
    9 ×     3,  4,   5,  0,  0
    9 ×     0,  0,   0,  4,  5

[Allocated Score Voting: Winners — Allocated Score Voting Method (3 winners)]
 Alice
 Ben
 Dan

Where it stands, honestly

It is a quota method, and it buys its guarantee from the family with the monotonicity problems. Allocated Score passes the Hare Quota Criterion — a cohesive quota-sized faction can force a seat. Classical apportionment theory says that guarantee has a price: quota methods are not house-size monotone, which is the door the Alabama paradox comes through.

That is not hypothetical here. This library asked the question and answered it: Allocated Score has the Alabama paradox. Five gardeners, four candidates — a two-seat committee elects Basil and Dahlia, a three-seat committee elects Aster, Basil and Clover. Dahlia was on the smaller committee and is off the bigger one, with no ballot changed. The trade against a divisor method like RRV is a genuine Balinski–Young one, not a winner.

It is also the STAR-PR method most exposed to free riding, and that is the same trade wearing a different hat. Because the quota is spent one score group at a time, highest first, a ballot's exposure is a step function of the score it gave — so withholding one star from a candidate who is winning anyway can take a ballot out of the charge entirely. In this library's case a bloc flips the second seat by scoring a landslide winner 4 rather than 5, while she still wins 92 to 48. RRV resists that same move because a divisor method has no score groups to step between. The strategy has real limits — it needs a read on how other factions scored, and it backfires when pushed — but it is cheaper here than the usual "modest incentive" framing allows.

Provenance, with the lean stated. Allocated Score is the consensus method of the Equal Vote 0–5 STAR Proportional Representation Research Committee, which spent roughly two years from 2018 comparing options at each stage of the tabulation (credited to Parker Friedland, Keith Edmonds, Jameson Quinn, Sara Wolk and others). That is an advocacy body selecting among methods it favors — what makes it checkable here regardless is that the procedure is precisely specified and independently reimplementable.

Three named variants you will meet in the same discussions:

  • Droop-quota Allocated Score — swapping Hare for Droop is said to mitigate free riding while biasing toward larger factions. That claim is inherited from the STV literature and is untested here — the engine is Hare-only, so there is no Droop run to check it against. A smaller quota cuts both ways: it charges fewer ballots, but it also exhausts the top score group sooner.
  • Sequential Monroe — Allocated Score with a different selection rule (highest-scoring quota rather than highest-scoring candidate). One of the committee's three finalists; the LH engine does not implement it, so a third of the recommended shortlist has no runnable case in this library.
  • Allocated STAR — adds a runoff on the final seat, so the last seat is decided the way single-winner STAR decides one.

Scenarios in this library

Allocated Score is the STAR-PR method with real coverage here — 26 case files across 12 folders, against eight for SSS and six for RRV. Gathered:

Scenario What it shows Read · run
The 63-ballot baseline The count above — two coalitions, three seats, both surplus reweights. page · yaml
The Alabama paradox Add a seat, someone loses one. The monotonicity price of a quota method, at 2 and 3 seats. lesson
Free riding Score a landslide winner 4 instead of 5 and the quota never reaches your ballot — the second seat flips. Plus the two ways the strategy fails, and the same ballots under all three methods. lesson · count
Fractional surplus, isolated The step-3 remainder handled on its own, cross-checked against BetterVoting. lesson · count
Shadow — Lackner & Skowron The academic running example from the multi-winner literature; seats A, B, C, D. Compare with RRV on the identical ballots, which seats F instead of D. page · yaml
A presidential board A realistic multi-seat board election, BV-backed. lesson · count
Two seats, one neighborhood The same ten ballots that Bloc STAR sweeps — counted proportionally instead. The clearest bloc-vs-PR pair in the library. exercise 12 · count
Quota circus Six candidates, 29 ballots, two seats — quota behavior under an awkward field. page
Herb council, 3 seats The ballot-style lab's PR half, beside its bloc twin. page
Food-Truck Row One electorate, five counts; this is its proportional share. set · count
Pets governance Six methods on one electorate — the proportional committee. set · count
Bloc vs PR, minimal The smallest possible pair: same ballots, both counts. set · count