Exercise 1 — Two districts, one mayor: WEST district¶

Generated from ex01_district_west.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: Avery

▶ Live on BetterVoting: vote · results ↗ (election d3b9wc · test BV2188).

Scenario¶

West District's nine ballots, tallied on their own. Scoring round: Avery 35, Blake 33, Carmen 32, Elena 25, Diego 0 — Avery and Blake advance. Eight of the nine ballots score the two finalists identically (Equal Support), and the one decided voter prefers Avery. West's winner: Avery. Part 1 of 3 of the consistency exercise (ex01_two_districts.md): East also elects Avery, yet the combined city elects Carmen. 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. Live on BetterVoting (Test ID BV2188): https://bettervoting.com/d3b9wc/results — the election carries a second, Ranked Robin race on the same opinions (equal ranks allowed): Elena, the district's Condorcet winner, wins it 4-0.

Ballots¶

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

Avery,Blake,Carmen,Diego,Elena
3,3,4,0,5 # 5 West voters: Elena first, Carmen second, Avery = Blake
3,3,4,0,5
3,3,4,0,5
3,3,4,0,5
3,3,4,0,5
5,5,3,0,0 # 3 West voters: Avery = Blake at the top, Carmen third
5,5,3,0,0
5,5,3,0,0
5,3,3,0,0 # 1 West voter: Avery OVER Blake — the only decided runoff vote

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Avery
  Choose-One (Plurality) = Elena   (differs from STAR)
  RCV-IRV                = Elena   (differs from STAR)
  RCV-RR (Condorcet)     = Elena   (differs from STAR)
  Note: 9 of 9 ballots (100%) had equal non-zero scores, so their ranks were
        decided by candidate priority order. The RCV-IRV result may be an
        artifact of score-to-rank tie-breaking rather than a deep
        difference.
  Note: Ranked Robin (RCV-RR) sides with RCV-IRV, so STAR is the outlier
        here — STAR need not elect the Condorcet candidate.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/ex01_district_west_RCV-IRV_tabulated.txt
  RCV-RR round-robin: cases_tabulated/ex01_district_west_RCV-RR_tabulated.txt

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

[STAR Voting]
 Tabulating 9 ballots.
Count × Avery,Blake,Carmen,Diego,Elena
    5 ×     3,    3,     4,    0,    5
    3 ×     5,    5,     3,    0,    0
    1 ×     5,    3,     3,    0,    0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Avery         -- 35 -- First place
   Blake         -- 33 -- Second place
   Carmen        -- 32
   Elena         -- 25
   Diego         --  0
 Avery and Blake advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Avery         -- 1 -- First place
   Blake         -- 0
   Equal Support -- 8
 Avery wins.
   Runoff math:
     9  ballots cast
   − 8  Equal Support (no preference between the two finalists)
     ─
     1  voters with a preference  (majority = 1)
           Avery 1 (100%)  ·  Blake 0 (0%)

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

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
               |  * Avery   | * Blake   |   Carmen  |   Diego   |   Elena   |
-----------------------------------------------------------------------------
     * Avery > |    ---     |1 - 8 - 0  |4 - 0 - 5  |9 - 0 - 0  |4 - 0 - 5  |
     * Blake > | 0 - 8 - 1  |   ---     |3 - 1 - 5  |9 - 0 - 0  |4 - 0 - 5  |
      Carmen > | 5 - 0 - 4  |5 - 1 - 3  |   ---     |9 - 0 - 0  |4 - 0 - 5  |
       Diego > | 0 - 0 - 9  |0 - 0 - 9  |0 - 0 - 9  |   ---     |0 - 4 - 5  |
       Elena > | 5 - 0 - 4  |5 - 0 - 4  |5 - 0 - 4  |5 - 4 - 0  |   ---     |

[Condorcet Winner]
  Condorcet Winner: Elena — STAR elected Avery instead (Elena was eliminated in the scoring round)

[Condorcet Loser]
  Condorcet Loser: Diego — loses every head-to-head matchup

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Avery      4  0  5  0  0  0  |    35   3.9
Blake      3  0  6  0  0  0  |    33   3.7
Carmen     0  5  4  0  0  0  |    32   3.6
Diego      0  0  0  0  0  9  |     0   0.0
Elena      5  0  0  0  0  4  |    25   2.8

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/ex01_district_west.yaml

Exercise 1 — Two districts, one mayor: WEST district¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶