Exercise 2 — The tenth ballot: the nine counted ballots¶

Generated from ex02_nine_ballots.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: Alex

Scenario¶

The base case: nine club ballots, five candidates. Scoring round: Alex 27, Bella 25, Chris 24, Eli 22, Dana 20 — Alex and Bella advance, and Alex wins the runoff 6-3. The exercise (ex02_tenth_ballot.md) then perturbs this election twice: a forgotten tenth ballot whose FAVORITE is Alex flips the win to Chris (a participation failure), and Bella withdrawing flips it to Chris too (a runoff-slot spoiler). Ballots adapted from a RangeVoting.org example, posed as an exercise in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5.

Ballots¶

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

Alex,Bella,Chris,Dana,Eli
3,2,4,5,0 # 4 voters: Dana first, Chris close second
3,2,4,5,0
3,2,4,5,0
3,2,4,5,0
3,5,0,0,4 # 3 voters: Bella first, Eli second
3,5,0,0,4
3,5,0,0,4
3,1,4,0,5 # 2 voters: Eli first, Chris second
3,1,4,0,5

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Alex
  Choose-One (Plurality) = Dana   (differs from STAR)
  RCV-IRV                = Bella   (differs from STAR)
  RCV-RR                 = Eli   (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.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/ex02_nine_ballots_RCV-IRV_tabulated.txt
  RCV-RR round-robin: cases_tabulated/ex02_nine_ballots_RCV-RR_tabulated.txt

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

[STAR Voting]
 Tabulating 9 ballots.
Count × Alex,Bella,Chris,Dana,Eli
    4 ×    3,    2,    4,   5,  0
    3 ×    3,    5,    0,   0,  4
    2 ×    3,    1,    4,   0,  5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Alex          -- 27 -- First place
   Bella         -- 25 -- Second place
   Chris         -- 24
   Eli           -- 22
   Dana          -- 20
 Alex and Bella advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Alex          -- 6 -- First place
   Bella         -- 3
   Equal Support -- 0
 Alex wins.
   Runoff math:
     9  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     9  voters with a preference  (majority = 5)
           Alex 6 (67%)  ·  Bella 3 (33%)

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

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
               |   * Alex   | * Bella   |   Chris   |    Dana   |    Eli    |
-----------------------------------------------------------------------------
      * Alex > |    ---     |6 - 0 - 3  |3 - 0 - 6  |5 - 0 - 4  |4 - 0 - 5  |
     * Bella > | 3 - 0 - 6  |   ---     |3 - 0 - 6  |5 - 0 - 4  |7 - 0 - 2  |
       Chris > | 6 - 0 - 3  |6 - 0 - 3  |   ---     |2 - 3 - 4  |4 - 0 - 5  |
        Dana > | 4 - 0 - 5  |4 - 0 - 5  |4 - 3 - 2  |   ---     |4 - 0 - 5  |
         Eli > | 5 - 0 - 4  |2 - 0 - 7  |5 - 0 - 4  |5 - 0 - 4  |   ---     |

[Condorcet Winner]
  No Condorcet winner (majority cycle: Alex > Bella > Dana > Chris > Alex)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Alex       0  0  9  0  0  0  |    27   3.0
Bella      3  0  0  4  2  0  |    25   2.8
Chris      0  6  0  0  0  3  |    24   2.7
Dana       4  0  0  0  0  5  |    20   2.2
Eli        2  3  0  0  0  4  |    22   2.4

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/ex02_nine_ballots.yaml

Exercise 2 — The tenth ballot: the nine counted ballots¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶