The smallest divergence — Bloc STAR¶

Generated from min_bloc_c3_b2.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Bloc STAR (multi-winner, majoritarian) · 2 seats · Expected winners: Ana, Ben

Scenario¶

Two voters, three candidates, two seats — the smallest election in which Bloc STAR and Proportional STAR (Allocated Score) fill the council differently. Identical ballots to min_pr_c3_b2.yaml; only the count differs. Both methods agree that Ben takes the first seat. They disagree about the second, and the reason is the whole difference between the two methods: Bloc lets the voter who already got Ben pick the second seat too, while Proportional STAR considers that voter represented and hands the second seat to the voter who has nobody yet.

Ballots¶

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

Ana,Ben,Cleo
0,0,1   # Voter 1 — likes only Cleo, and only mildly
2,3,0   # Voter 2 — prefers Ben, then Ana

What the engine says¶

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

--- Bloc STAR Voting Method (2 winners) ---

[Bloc STAR]
 Tabulating 2 ballots to fill 2 seats.
Ana,Ben,Cleo
  0,  0,   1
  2,  3,   0

[Bloc STAR: Round 1: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Ben           -- 3 -- First place
   Ana           -- 2 -- Second place
   Cleo          -- 1
 Ben and Ana advance.

[Bloc STAR: Round 1: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Ben           -- 1 -- First place
   Ana           -- 0
   Equal Support -- 1
 Ben wins.
   Runoff math:
     2  ballots cast
   − 1  Equal Support (no preference between the two finalists)
     ─
     1  voters with a preference  (majority = 1)
           Ben 1 (100%)  ·  Ana 0 (0%)

──────────────────────────────────────────────────

[Bloc STAR: Round 2: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Ana           -- 2 -- First place
   Cleo          -- 1 -- Second place
 Ana and Cleo advance.

[Bloc STAR: Round 2: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Ana           -- 1 -- Tied for first place
   Cleo          -- 1 -- Tied for first place
   Equal Support -- 0
 There's a two-way tie for first.

[Bloc STAR: Round 2: Automatic Runoff Round: First tiebreaker]
 The highest-scoring candidate wins.
   Ana           -- 2 -- First place
   Cleo          -- 1
 Ana wins.

[Bloc STAR: Winners — Bloc STAR Voting Method (2 winners)]
 Ben
 Ana

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.
               |     Ana    |    Ben    |    Cleo   |
-----------------------------------------------------
         Ana > |    ---     |0 - 1 - 1  |1 - 0 - 1  |
         Ben > | 1 - 1 - 0  |   ---     |1 - 0 - 1  |
        Cleo > | 1 - 0 - 1  |1 - 0 - 1  |   ---     |

[Condorcet Winner]
  No strict Condorcet winner; unbeaten candidates: Ben, Cleo (pairwise ties)

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

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Ana        0  0  0  1  0  1  |     2   1.0
Ben        0  0  1  0  0  1  |     3   1.5
Cleo       0  0  0  0  1  1  |     1   0.5

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 method_comparisons/bloc_vs_pr/cases/min_bloc_c3_b2.yaml

The smallest divergence — Bloc STAR¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶