Exercise 8 — a smallest runoff reversal (sample solution, two candidates)¶

Generated from ex08_minimal_reversal_2c.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: STAR (single winner) · 1 seat · Expected winner: A

Scenario¶

A sample solution to the construction exercise ex08_build_a_reversal.md: the smallest election this repo knows where the score leader loses the automatic runoff. Three voters, two candidates. B piles up points from two friendly-but-not-first ballots (B 13, A 10) — yet a 2-1 majority scores A above B, so A wins the runoff. Score voting and majority rule disagree in the purest possible form; STAR sides with the majority. (With only two candidates the finalist matrix is trivial, so show_matrix is off per house style.)

Ballots¶

The ballots as marked — the filled bubble is the score given, and the score is the number in its column:

#	A	B
1	5	4
2	5	4
3	0	5

The same ballots as the file records them:

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

A,B
5,4 # two voters: A first, B a friendly 4
5,4
0,5 # one voter: B only

What the engine says¶

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

[Divergence from STAR]
  STAR     = A
  Approval = B   (differs from STAR)

[Runoff Reversal]
 - Score Round Winner(s) = (B)
 - Runoff Round Winner   = (A)
  Candidate B earned the highest total score, but
  Candidate A won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 3 ballots.
Count × A,B
    2 × 5,4
    1 × 0,5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   B             -- 13 -- First place
   A             -- 10 -- Second place
 B and A advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   A             -- 2 -- First place
   B             -- 1
   Equal Support -- 0
 A wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           A 2 (67%)  ·  B 1 (33%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 A

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

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |    * A     |   * B     |
-----------------------------------------
         * A > |    ---     |2 - 0 - 1  |
         * B > | 1 - 0 - 2  |   ---     |

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

[Condorcet Loser]
  Condorcet Loser: B — loses every head-to-head matchup — elected by Approval!

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
A          2  0  0  0  0  1  |    10   3.3
B          1  2  0  0  0  0  |    13   4.3

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 01_STAR/05_Practice/cases/ex08_minimal_reversal_2c.yaml

Exercise 8 — a smallest runoff reversal (sample solution, two candidates)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶