RRV sample as single-winner STAR — three parties (Purple/Orange/Yellow)¶
Generated from rrv_sample_c15_b13_three-parties.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: Orange5
Scenario¶
Ported from BetterVoting.org's "Reweighted Range Voting Sample Election". Three "parties" (Purple, Orange, Yellow), five candidates each; 13 voters mostly loyal to a party (3 Purple, 6 Orange, 4 Yellow). The source table is laid out candidates-as-rows / voters-as-columns; here it is TRANSPOSED so each voter is one ballot row across all 15 candidates.
RRV is a proportional MULTI-winner method; this file instead runs the same ballots through SINGLE-winner STAR to see who one seat would go to. Orange has the most loyal voters (6 of 13), so an Orange candidate is expected to lead.
Scores mapped from the source 0-9 scale to STAR's 0-5 by round(x * 5 / 9): 0->0, 1->1, 2->1, 3->2, 4->2, 5->3, 6->3, 7->4, 8->4, 9->5. Source: https://bettervoting.org (RRV sample election)
TEACHING NOTE: on this 0-5 scale STAR elects Orange5, but on the source 0-9 scale it elects Orange1 — the scale's granularity moves the second finalist. Worked as a 301 lesson in 07_Concepts/scores_and_ranks/scale_granularity_flips_the_winner.md (see also Curriculum 301.9).
Ballots¶
Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).
Purple1,Purple2,Purple3,Purple4,Purple5,Orange1,Orange2,Orange3,Orange4,Orange5,Yellow1,Yellow2,Yellow3,Yellow4,Yellow5
5,4,5,4,5,1,1,1,1,1,0,0,0,0,0
5,4,4,5,5,1,0,1,0,1,0,1,0,1,0
4,5,5,2,4,1,1,1,1,2,1,0,0,1,0
0,0,0,0,0,5,5,4,5,5,0,0,0,0,0
0,0,0,0,0,5,1,4,4,4,0,0,1,0,0
0,0,0,0,0,5,3,4,4,2,0,1,0,0,1
0,0,0,0,0,5,4,4,4,4,0,0,0,0,0
0,0,0,0,0,4,5,5,5,5,0,1,0,0,1
0,0,0,0,0,4,5,5,5,5,0,0,0,0,0
1,1,1,1,1,0,0,0,0,0,5,5,2,5,5
1,1,1,1,0,0,0,0,0,0,4,4,4,4,4
1,1,1,1,1,0,0,0,0,1,5,4,4,5,4
2,0,2,2,1,0,0,0,0,0,5,5,4,4,5
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
[Divergence from STAR]
STAR = Orange5
Choose-One (Plurality) = Orange1 (differs from STAR)
RCV-IRV = Orange1 (differs from STAR)
Approval = Orange1 (differs from STAR)
Note: 13 of 13 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) 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/rrv_sample_c15_b13_three-parties_RCV-IRV_tabulated.txt
[Runoff Reversal]
- Score Round Winner(s) = (Orange1)
- Runoff Round Winner = (Orange5)
Candidate Orange1 earned the highest total score, but
Candidate Orange5 won the automatic runoff — not a malfunction,
STAR working as designed: the runoff elects the finalist preferred
by the majority (of voters with a preference).
--- STAR Voting Method (single winner) ---
[STAR Voting]
Tabulating 13 ballots.
Purple1,Purple2,Purple3,Purple4,Purple5,Orange1,Orange2,Orange3,Orange4,Orange5,Yellow1,Yellow2,Yellow3,Yellow4,Yellow5
5, 4, 5, 4, 5, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0
5, 4, 4, 5, 5, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
4, 5, 5, 2, 4, 1, 1, 1, 1, 2, 1, 0, 0, 1, 0
0, 0, 0, 0, 0, 5, 5, 4, 5, 5, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 5, 1, 4, 4, 4, 0, 0, 1, 0, 0
0, 0, 0, 0, 0, 5, 3, 4, 4, 2, 0, 1, 0, 0, 1
0, 0, 0, 0, 0, 5, 4, 4, 4, 4, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 4, 5, 5, 5, 5, 0, 1, 0, 0, 1
0, 0, 0, 0, 0, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 5, 5, 2, 5, 5
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4
1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 5, 4, 4, 5, 4
2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 5, 5, 4, 4, 5
[STAR Voting: Scoring Round]
The two highest-scoring candidates advance to the next round.
Orange1 -- 31 -- First place
Orange5 -- 30 -- Second place
Orange3 -- 29
Orange4 -- 29
Orange2 -- 25
Yellow2 -- 21
Yellow1 -- 20
Yellow4 -- 20
Yellow5 -- 20
Purple1 -- 19
Purple3 -- 19
Purple5 -- 17
Purple2 -- 16
Purple4 -- 16
Yellow3 -- 15
Orange1 and Orange5 advance.
[STAR Voting: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Orange5 -- 4 -- First place
Orange1 -- 3
Equal Support -- 6
Orange5 wins.
Runoff math:
13 ballots cast
− 6 Equal Support (no preference between the two finalists)
──
7 voters with a preference (majority = 4)
Orange5 4 (57%) · Orange1 3 (43%)
[STAR Voting: Winner — STAR Voting Method (single winner)]
Orange5
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
| Purple1 | Purple2 | Purple3 | Purple4 | Purple5 | * Orange1 | Orange2 | Orange3 | Orange4 | * Orange5 | Yellow1 | Yellow2 | Yellow3 | Yellow4 | Yellow5 |
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Purple1 > | --- | 3 - 9 - 1 | 1 - 11 - 1 | 2 - 11 - 0 | 2 - 11 - 0 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 6 - 1 - 6 | 3 - 6 - 4 | 3 - 4 - 6 | 3 - 5 - 5 | 3 - 6 - 4 | 3 - 4 - 6 |
Purple2 > | 1 - 9 - 3 | --- | 0 - 11 - 2 | 1 - 10 - 2 | 2 - 8 - 3 | 6 - 1 - 6 | 6 - 1 - 6 | 6 - 1 - 6 | 6 - 1 - 6 | 5 - 2 - 6 | 3 - 6 - 4 | 3 - 4 - 6 | 3 - 5 - 5 | 3 - 6 - 4 | 3 - 4 - 6 |
Purple3 > | 1 - 11 - 1 | 2 - 11 - 0 | --- | 2 - 10 - 1 | 3 - 9 - 1 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 6 - 1 - 6 | 3 - 6 - 4 | 3 - 4 - 6 | 3 - 5 - 5 | 3 - 6 - 4 | 3 - 4 - 6 |
Purple4 > | 0 - 11 - 2 | 2 - 10 - 1 | 1 - 10 - 2 | --- | 2 - 9 - 2 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 7 - 0 - 6 | 5 - 2 - 6 | 3 - 6 - 4 | 3 - 4 - 6 | 3 - 5 - 5 | 3 - 6 - 4 | 3 - 4 - 6 |
Purple5 > | 0 - 11 - 2 | 3 - 8 - 2 | 1 - 9 - 3 | 2 - 9 - 2 | --- | 6 - 1 - 6 | 6 - 1 - 6 | 6 - 1 - 6 | 6 - 1 - 6 | 5 - 2 - 6 | 3 - 6 - 4 | 3 - 4 - 6 | 3 - 5 - 5 | 3 - 6 - 4 | 3 - 4 - 6 |
* Orange1 > | 6 - 0 - 7 | 6 - 1 - 6 | 6 - 0 - 7 | 6 - 0 - 7 | 6 - 1 - 6 | --- | 4 - 7 - 2 | 4 - 7 - 2 | 4 - 7 - 2 | 3 - 6 - 4 | 8 - 1 - 4 | 8 - 1 - 4 | 9 - 0 - 4 | 7 - 2 - 4 | 9 - 0 - 4 |
Orange2 > | 6 - 0 - 7 | 6 - 1 - 6 | 6 - 0 - 7 | 6 - 0 - 7 | 6 - 1 - 6 | 2 - 7 - 4 | --- | 1 - 9 - 3 | 0 - 11 - 2 | 1 - 8 - 4 | 7 - 2 - 4 | 8 - 0 - 5 | 7 - 2 - 4 | 7 - 1 - 5 | 8 - 1 - 4 |
Orange3 > | 6 - 0 - 7 | 6 - 1 - 6 | 6 - 0 - 7 | 6 - 0 - 7 | 6 - 1 - 6 | 2 - 7 - 4 | 3 - 9 - 1 | --- | 1 - 11 - 1 | 1 - 9 - 3 | 8 - 1 - 4 | 8 - 1 - 4 | 9 - 0 - 4 | 7 - 2 - 4 | 9 - 0 - 4 |
Orange4 > | 6 - 0 - 7 | 6 - 1 - 6 | 6 - 0 - 7 | 6 - 0 - 7 | 6 - 1 - 6 | 2 - 7 - 4 | 2 - 11 - 0 | 1 - 11 - 1 | --- | 1 - 9 - 3 | 7 - 2 - 4 | 8 - 0 - 5 | 8 - 1 - 4 | 7 - 1 - 5 | 8 - 1 - 4 |
* Orange5 > | 6 - 1 - 6 | 6 - 2 - 5 | 6 - 1 - 6 | 6 - 2 - 5 | 6 - 2 - 5 | 4 - 6 - 3 | 4 - 8 - 1 | 3 - 9 - 1 | 3 - 9 - 1 | --- | 9 - 0 - 4 | 8 - 1 - 4 | 9 - 0 - 4 | 8 - 1 - 4 | 9 - 0 - 4 |
Yellow1 > | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 1 - 8 | 4 - 2 - 7 | 4 - 1 - 8 | 4 - 2 - 7 | 4 - 0 - 9 | --- | 2 - 8 - 3 | 4 - 8 - 1 | 1 - 11 - 1 | 2 - 9 - 2 |
Yellow2 > | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 4 - 1 - 8 | 5 - 0 - 8 | 4 - 1 - 8 | 5 - 0 - 8 | 4 - 1 - 8 | 3 - 8 - 2 | --- | 5 - 7 - 1 | 3 - 8 - 2 | 1 - 12 - 0 |
Yellow3 > | 5 - 5 - 3 | 5 - 5 - 3 | 5 - 5 - 3 | 5 - 5 - 3 | 5 - 5 - 3 | 4 - 0 - 9 | 4 - 2 - 7 | 4 - 0 - 9 | 4 - 1 - 8 | 4 - 0 - 9 | 1 - 8 - 4 | 1 - 7 - 5 | --- | 1 - 8 - 4 | 1 - 8 - 4 |
Yellow4 > | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 6 - 3 | 4 - 2 - 7 | 5 - 1 - 7 | 4 - 2 - 7 | 5 - 1 - 7 | 4 - 1 - 8 | 1 - 11 - 1 | 2 - 8 - 3 | 4 - 8 - 1 | --- | 3 - 7 - 3 |
Yellow5 > | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 6 - 4 - 3 | 4 - 0 - 9 | 4 - 1 - 8 | 4 - 0 - 9 | 4 - 1 - 8 | 4 - 0 - 9 | 2 - 9 - 2 | 0 - 12 - 1 | 4 - 8 - 1 | 3 - 7 - 3 | --- |
[Condorcet Winner]
No strict Condorcet winner; weak Condorcet winner: Orange5 — matches the STAR winner
[Condorcet Loser]
No strict Condorcet loser; weak Condorcet loser: Purple2 (never wins a matchup)
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Purple1 2 1 0 1 3 6 | 19 1.5
Purple2 1 2 0 0 3 7 | 16 1.2
Purple3 2 1 0 1 3 6 | 19 1.5
Purple4 1 1 0 2 3 6 | 16 1.2
Purple5 2 1 0 0 3 7 | 17 1.3
Orange1 4 2 0 0 3 4 | 31 2.4
Orange2 3 1 1 0 3 5 | 25 1.9
Orange3 2 4 0 0 3 4 | 29 2.2
Orange4 3 3 0 0 2 5 | 29 2.2
Orange5 3 2 0 2 3 3 | 30 2.3
Yellow1 3 1 0 0 1 8 | 20 1.5
Yellow2 2 2 0 0 3 6 | 21 1.6
Yellow3 0 3 0 1 1 8 | 15 1.2
Yellow4 2 2 0 0 2 7 | 20 1.5
Yellow5 2 2 0 0 2 7 | 20 1.5
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 03_STAR_PR/02_Examples/cases/rrv_sample_c15_b13_three-parties.yaml
See also¶
More cases in this set: 02a_c5_b63_proportional-allocated-score · 02b_c5_b63_proportional-sss · 02c_c5_b63_proportional-rrv · 03b_star_pr_3seats · bv2130_bvhchj_party_plurality · bv2130_presidential_board_star_pr · lackner_skowron_shadow_star_pr_c7_b12 · lackner_skowron_shadow_star_pr_rrv_c7_b12