Two officers, three candidates — Allocated Score¶

Generated from two_officers_allocated.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Allocated Score (proportional STAR) · 2 seats · Expected winners: Dana, Finn

Scenario¶

The companion to "three neighbors": the smallest election that splits the DIVISOR method off from the two QUOTA methods. Three voters, three candidates, two seats. Dana leads on score (9, against Eli 8 and Finn 7) and takes seat 1 under every method. Seat 2 is the argument.

Voters 1 and 2 both gave Dana 4 stars; voter 3 gave her only 1. Everything turns on how hard those two big backers are charged for the seat they won -- and the three methods form a clean ladder from harshest to gentlest:

Allocated Score charges them down to 1/4. The 1.5-voter quota is overfilled by the two 4-star ballots, so fractional surplus leaves them at a quarter. Voter 3 is never reached by the score tiers at all and keeps FULL weight. -> Eli 4+1/4, Finn 4+3/4 -> Dana, Finn
SSS charges them down to 1/3, against a SCORE quota (total 9, Hare score quota 7+1/2) rather than a ballot quota. Voter 3 pays too, landing at 5/6. -> Eli 4+1/6, Finn 4+1/3 -> Dana, Finn
RRV computes no quota at all and merely DIVIDES: weight becomes 1 / (1 + score_given_to_winners / max_score), so the two land at 5/9 -- dampened, not spent. They keep enough to carry their shared second choice. -> Eli 5+5/18, Finn 5 -> Dana, Eli

1/4, 1/3, 5/9. As the charge gets gentler the partly-satisfied voters keep more say, and at the last rung their second choice overtakes. Found by exhaustive smallest-first search, verified stable across five tiebreaker seeds, so no lot is involved.

Ballots¶

Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).

Dana,Eli,Finn
4,3,1      # Voter 1 — Dana first, Eli a solid second
4,2,2      # Voter 2 — Dana first, Eli and Finn equal behind
1,3,4      # Voter 3 — Finn first, barely backs Dana

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

--- Allocated Score Voting Method (2 winners) ---

[Allocated Score Voting]
 Tabulating 3 ballots to fill 2 seats.
Dana,Eli,Finn
   4,  3,   1
   4,  2,   2
   1,  3,   4

[Allocated Score Voting: Round 1]
 The highest-scoring candidate wins a seat.
   Dana          -- 9 -- First place
   Eli           -- 8
   Finn          -- 7
 Dana wins a seat.

[Allocated Score Voting: Round 1: Ballot allocation round]
 Allocating 1+1/2 ballots.

[Allocated Score Voting: Round 1: Ballot allocation round: Round 1]
 Allocating 2 ballots at score 4.
 This allocation overfills the quota.  Returning fractional surplus.
 Allocating only 75.00% of these ballots.
 Keeping these ballots, but multiplying their weights by 1/4.
 2 ballots reweighted from 1 to 1/4.

[Allocated Score Voting: Round 2]
 The highest-scoring candidate wins a seat.
   Finn          -- 4+3/4 -- First place
   Eli           -- 4+1/4
 Finn wins a seat.

[Allocated Score Voting: Winners — Allocated Score Voting Method (2 winners)]
 Dana
 Finn

Full audit — preference matrix, Condorcet, and score distribution¶

--- Preference Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        Informational only — not part of the 2-winner count below,
        so no Top-2 finalists are marked.
               |     Dana   |    Eli    |    Finn   |
-----------------------------------------------------
        Dana > |    ---     |2 - 0 - 1  |2 - 0 - 1  |
         Eli > | 1 - 0 - 2  |   ---     |1 - 1 - 1  |
        Finn > | 1 - 0 - 2  |1 - 1 - 1  |   ---     |

[Condorcet Winner]
  Condorcet Winner: Dana — matches the STAR winner

[Condorcet Loser]
  No strict Condorcet loser; jointly weak Condorcet losers: Eli, Finn (winless — pairwise ties)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Dana       0  2  0  0  1  0  |     9   3.0
Eli        0  0  2  1  0  0  |     8   2.7
Finn       0  1  0  1  1  0  |     7   2.3
 Hare quota is 3/2.

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 03_STAR_PR/02_Examples/method_divergences/cases/two_officers_allocated.yaml

Two officers, three candidates — Allocated Score¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶