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Same mean, different spread — the consensus candidate and the polarizing one

Generated from same_mean_different_spread_c2_b5.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: Blake

Scenario

Two candidates, five voters, and an exact tie in the Scoring Round: Alice 15, Blake 15, both averaging 3.0. Every difference between them is SPREAD. Alice is a flat 3 on all five ballots; Blake is three 5s and two 0s. The Score Distribution block is the whole lesson — same mean, variance 0.0 vs 6.0 — and 6.0 is the LARGEST variance arithmetically possible at a mean of 3.0 on a 0-5 scale, so Blake is exactly as divisive as this ballot allows. Because the totals tie, pure Score cannot separate them at all; the divergence block's Approval reading (approve = 3+ stars) picks Alice 5-3; STAR's Automatic Runoff hands the seat to Blake 3-2. "Polarizing" is not a mood — it is variance, and only the second round reads it.

Ballots

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

# Ballot as marked Alice Blake
1 A 0–5 STAR ballot — Blake is my champion; Alice is fine: Alice 3, Blake 5. 3 5
2 A 0–5 STAR ballot — Blake is my champion; Alice is fine: Alice 3, Blake 5. 3 5
3 A 0–5 STAR ballot — Blake is my champion; Alice is fine: Alice 3, Blake 5. 3 5
4 A 0–5 STAR ballot — Alice is fine; Blake, absolutely not: Alice 3, Blake 0. 3 0
5 A 0–5 STAR ballot — Alice is fine; Blake, absolutely not: Alice 3, Blake 0. 3 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).

Alice,Blake
3,5 # Blake is my champion; Alice is fine
3,5 # Blake is my champion; Alice is fine
3,5 # Blake is my champion; Alice is fine
3,0 # Alice is fine; Blake, absolutely not
3,0 # Alice is fine; Blake, absolutely not

What the engine says

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

[Divergence from STAR]
  STAR     = Blake
  Approval = Alice   (differs from STAR)

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

[STAR Voting]
 Tabulating 5 ballots.
Count × Alice,Blake
    3 ×     3,    5
    2 ×     3,    0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Alice         -- 15 -- First place
   Blake         -- 15 -- Second place
 Alice and Blake advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Blake         -- 3 -- First place
   Alice         -- 2
   Equal Support -- 0
 Blake wins.
   Runoff math:
     5  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     5  voters with a preference  (majority = 3)
           Blake 3 (60%)  ·  Alice 2 (40%)

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

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
               |  * Alice   | * Blake   |
-----------------------------------------
     * Alice > |    ---     |2 - 0 - 3  |
     * Blake > | 3 - 0 - 2  |   ---     |

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

[Condorcet Loser]
  Condorcet Loser: Alice — 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
Alice      0  0  5  0  0  0  |    15   3.0
Blake      3  0  0  0  0  2  |    15   3.0

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/02_Examples/cases/same_mean_different_spread_c2_b5.yaml

See also

More cases in this set: 02a_c3_b1_three-candidates · 02b_c3_b2_three-candidates · 03a_c3_b3_style-bullet-vote · 03b_c3_b3_1_style-protest-vote · 03b_c3_b3_2_expand_style-protest-vote · 03c_c6_b8_style-gallery · 03d_c5_b5_style-gallery-five-more · 04b_c4_b3_display-options-all · 05a_c5_b3_unanimous-ballots · 06a_c9_b3_large-field-equal-support · 06b_c9_runoff-overturns-leader · 09_c4_b100_tennessee-capital · abstentions · bv2182_tg4779_faq_runoff_reversal · bv2184_fyy886_lunch_vote · bv2187_qrw6wb_ann-bob-cal · bv2256_c8h3tb_traditional_style · bv2263_xw23m9_over_50_percent · csv_ambiguity_ex1_c4_b8 · display_options_demo · equal_support_runoff_demo · quorum_demo_c3_b6 · quorum_fail_demo_c3_b6 · star_ala_approval · three_winners_cw_score_runoff · vote_splitting · vote_splitting2 · vote_splitting3 · vote_splitting_scenario1_spoiler · vote_splitting_scenario2_bloc_leads · vote_splitting_scenario3_outsider_wins