Exercise 15a, second look — the same Yes/No ballots read pairwise¶

Generated from ex15_approval_pairwise.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: Blair

▶ Live on BetterVoting: vote · results ↗ (election d4v2dh · test BV2258).

Scenario¶

The SAME 35 ballots as ex15_approval_yes_no.yaml, with each approval written as a 5 and each non-approval as a 0, so the engine prints the pairwise matrix and names the Condorcet winner. The magnitudes carry no information here — every head-to-head count depends only on the two-class order (approved above not-approved), which is what makes this a DICHOTOMOUS PROFILE.

The payoff: the head-to-head order reproduces the approval order exactly. Blair beats Cosmo 13-7 (15 voters approved both, so they express no preference) and beats Ada 20-7; Cosmo beats Ada 15-8. Blair > Cosmo > Ada, the same ranking as the approval totals 28 > 22 > 15.

That is guaranteed, not luck. On a dichotomous profile "more voters strictly prefer x to y" reduces to "more voters approve x than y", so a Condorcet winner always exists and approval voting agrees with every Condorcet method. The caveat lives one folder over: real approval ballots are compressed from richer opinions, and the Condorcet winner of the uncompressed opinions can be someone else — see method_comparisons/black_curtain/condorcet_compression.md.

Exercise page: ../ex15_read_the_ballot.md Live results: https://bettervoting.com/d4v2dh/results (BV2258, race 2 of 2 — the same 35 ballots as race 1, cast as 5/0 scores; BV's STAR count agrees: Blair. The frozen export sits beside the sibling yaml, ex15_approval_yes_no_bv_export.json — one export covers both races.)

Ballots¶

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

#	Ada	Blair	Cosmo
1	0	5	5
2	5	5	0
3	5	0	5
4	0	5	0

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).

Count:Ada,Blair,Cosmo
15:0,5,5
8:5,5,0
7:5,0,5
5:0,5,0

What the engine says¶

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

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

[STAR Voting]
 Tabulating 35 ballots.
Count × Ada,Blair,Cosmo
   15 ×   0,    5,    5
    8 ×   5,    5,    0
    7 ×   5,    0,    5
    5 ×   0,    5,    0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Blair         -- 140 -- First place
   Cosmo         -- 110 -- Second place
   Ada           --  75
 Blair and Cosmo advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Blair         -- 13 -- First place
   Cosmo         --  7
   Equal Support -- 15
 Blair wins.
   Runoff math:
     35  ballots cast
   − 15  Equal Support (no preference between the two finalists)
     ──
     20  voters with a preference  (majority = 11)
           Blair 13 (65%)  ·  Cosmo 7 (35%)

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

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
                 |      Ada     |  * Blair    |  * Cosmo    |
-------------------------------------------------------------
           Ada > |     ---      | 7 -  8 - 20 | 8 - 12 - 15 |
       * Blair > | 20 -  8 -  7 |    ---      |13 - 15 -  7 |
       * Cosmo > | 15 - 12 -  8 | 7 - 15 - 13 |    ---      |

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

[Condorcet Loser]
  Condorcet Loser: Ada — 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
Ada        15   0   0   0   0  20  |    75   2.1
Blair      28   0   0   0   0   7  |   140   4.0
Cosmo      22   0   0   0   0  13  |   110   3.1

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/ex15_approval_pairwise.yaml

Exercise 15a, second look — the same Yes/No ballots read pairwise¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶