Exercise 3 — One electorate, five verdicts (the snack vote)¶

Generated from ex03_five_verdicts.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: Cherry

▶ Live on BetterVoting: vote · results ↗ (election ywqhq4 · test BV2191).

Scenario¶

Nine voters pick the office snack. Choose-One elects Apple (4 first choices) — who loses head-to-head to BOTH rivals (the Condorcet loser). RCV-IRV eliminates Cherry first (2 first choices) and elects Banana. Approval (approve = score 3+) gives Cherry 9 of 9. Score gives Cherry 34 of a possible 45. STAR advances Cherry and Apple and Cherry wins the runoff 5-4. And Ranked Robin confirms Cherry as the Condorcet winner. One electorate, five different verdicts from five tabulations — the ballot-vs-method lesson of the exercise ex03_five_verdicts.md. Structure inspired by the worked comparisons in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5; ballots and cast are this repo's own. Live on BetterVoting (Test ID BV2191): https://bettervoting.com/ywqhq4/results — one election, five races (Choose-One, RCV-IRV, Approval, STAR, Ranked Robin), all five verdicts live; BV agrees with LH on every race.

Ballots¶

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

Apple,Banana,Cherry
5,0,3 # 4 voters: Apple fans, Cherry a solid second
5,0,3
5,0,3
5,0,3
0,5,4 # 3 voters: Banana fans, Cherry nearly as good
0,5,4
0,5,4
0,1,5 # 2 voters: Cherry fans, cool on both others
0,1,5

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Cherry
  Choose-One (Plurality) = Apple   (differs from STAR)
  RCV-IRV                = Banana   (differs from STAR)
  Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
        method difference, not a tie-breaking artifact.
  Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
        outlier — the classic center-squeeze signature.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/ex03_five_verdicts_RCV-IRV_tabulated.txt

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

[STAR Voting]
 Tabulating 9 ballots.
Count × Apple,Banana,Cherry
    4 ×     5,     0,     3
    3 ×     0,     5,     4
    2 ×     0,     1,     5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Cherry        -- 34 -- First place
   Apple         -- 20 -- Second place
   Banana        -- 17
 Cherry and Apple advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Cherry        -- 5 -- First place
   Apple         -- 4
   Equal Support -- 0
 Cherry wins.
   Runoff math:
     9  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     9  voters with a preference  (majority = 5)
           Cherry 5 (56%)  ·  Apple 4 (44%)

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

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
               |  * Apple   |   Banana  | * Cherry  |
-----------------------------------------------------
     * Apple > |    ---     |4 - 0 - 5  |4 - 0 - 5  |
      Banana > | 5 - 0 - 4  |   ---     |3 - 0 - 6  |
    * Cherry > | 5 - 0 - 4  |6 - 0 - 3  |   ---     |

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

[Condorcet Loser]
  Condorcet Loser: Apple — loses every head-to-head matchup — elected by Choose-One (Plurality)!

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Apple      4  0  0  0  0  5  |    20   2.2
Banana     3  0  0  0  2  4  |    17   1.9
Cherry     2  3  4  0  0  0  |    34   3.8

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/ex03_five_verdicts.yaml

Exercise 3 — One electorate, five verdicts (the snack vote)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶