====================================================================== SOURCE FILE: burlington_2009_ranked_robin.yaml TABULATED FILE: burlington_2009_ranked_robin_tabulated.txt ====================================================================== election_title: "Burlington 2009 mayor — Ranked Robin: Montroll, a perfect 5-0 Condorcet winner" scenario_description: |- The same real ballots counted round-robin: Montroll beats Kiss 4063-3476, Wright 4596-3663, Smith 4569-2996, Simpson 6261-591, and Write-In 6656-100 — five wins, zero losses. The candidate a majority preferred to every single rival is the one RCV-IRV eliminated in the semifinal. Lesson page: README.md in this folder. Real ballots: PrefLib dataset 00005 (00005-00000002.toi, 8,980 ballots, 384 unique orders; from Burlington's published election records). 6 ballots (0.07%) carrying equal-rank overvotes are not representable in this ranked syntax and are excluded — 8,974 tabulated; every official figure reproduces within +/-1 and every margin is hundreds of votes. voting_method: RankedRobin num_winners: 1 ballots: |- 840:Wright 355:Kiss>Montroll 326:Kiss 271:Wright>Smith 256:Wright>Montroll 234:Kiss>Montroll>Smith 200:Montroll>Kiss 178:Montroll 147:Wright>Montroll>Smith 145:Montroll>Kiss>Smith 139:Montroll>Smith 125:Kiss>Smith 124:Smith 123:Kiss>Montroll>Smith>Wright>Simpson 122:Wright>Smith>Montroll 121:Kiss>Smith>Montroll 120:Kiss>Montroll>Smith>Simpson>Wright 104:Wright>Montroll>Smith>Simpson>Kiss 103:Kiss>Montroll>Simpson>Smith>Wright 102:Wright>Montroll>Smith>Kiss>Simpson 101:Wright>Smith>Montroll>Kiss>Simpson 94:Montroll>Wright 93:Montroll>Smith>Kiss 93:Smith>Wright 90:Wright>Smith>Montroll>Simpson>Kiss 90:Smith>Montroll 88:Smith>Kiss>Montroll 83:Smith>Montroll>Kiss 80:Kiss>Smith>Montroll>Simpson>Wright 80:Wright>Kiss 76:Wright>Smith>Simpson>Montroll>Kiss 72:Montroll>Kiss>Smith>Wright>Simpson 71:Kiss>Montroll>Wright>Smith>Simpson 69:Wright>Montroll>Kiss>Smith>Simpson 69:Montroll>Smith>Kiss>Wright>Simpson 66:Kiss>Wright 62:Montroll>Smith>Wright 61:Montroll>Kiss>Smith>Simpson>Wright 60:Montroll>Wright>Smith>Kiss>Simpson 60:Kiss>Montroll>Smith>Wright 58:Smith>Kiss>Montroll>Simpson>Wright 57:Montroll>Wright>Smith 56:Montroll>Wright>Kiss>Smith>Simpson 55:Kiss>Smith>Montroll>Wright>Simpson 54:Wright>Montroll>Smith>Kiss 53:Montroll>Smith>Kiss>Simpson>Wright 52:Smith>Wright>Montroll>Kiss>Simpson 52:Wright>Smith>Kiss>Montroll>Simpson 52:Montroll>Smith>Wright>Kiss>Simpson 52:Kiss>Montroll>Simpson 51:Smith>Kiss 50:Montroll>Kiss>Wright>Smith>Simpson 50:Wright>Kiss>Montroll>Smith>Simpson 50:Smith>Wright>Montroll 48:Kiss>Montroll>Wright 46:Montroll>Kiss>Wright 46:Wright>Montroll>Kiss 45:Wright>Kiss>Smith>Montroll>Simpson 45:Wright>Smith>Montroll>Kiss 43:Smith>Montroll>Kiss>Wright>Simpson 42:Kiss>Montroll>Smith>Simpson 41:Kiss>Montroll>Simpson>Smith 41:Montroll>Smith>Kiss>Wright 39:Kiss>Wright>Montroll>Smith>Simpson 39:Montroll>Wright>Smith>Simpson>Kiss 38:Smith>Montroll>Kiss>Simpson>Wright 38:Montroll>Kiss>Smith>Wright 37:Montroll>Wright>Smith>Kiss 37:Smith>Montroll>Wright 34:Montroll>Wright>Kiss 32:Smith>Kiss>Montroll>Wright>Simpson 32:Montroll>Smith>Wright>Kiss 31:Smith>Montroll>Wright>Kiss>Simpson 31:Kiss>Wright>Montroll 30:Wright>Smith>Kiss 29:Kiss>Smith>Montroll>Wright 28:Smith>Wright>Montroll>Simpson>Kiss 27:Montroll>Kiss>Simpson>Smith>Wright 27:Montroll>Smith>Simpson>Kiss>Wright 27:Smith>Wright>Kiss>Montroll>Simpson 27:Smith>Kiss>Montroll>Wright 27:Smith>Montroll>Wright>Kiss 26:Kiss>Smith>Wright>Montroll>Simpson 26:Smith>Montroll>Kiss>Wright 25:Wright>Simpson 24:Kiss>Simpson>Montroll>Smith>Wright 24:Montroll>Kiss>Wright>Smith 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1:Simpson>Kiss>Montroll>Smith>Wright 1:Smith>Simpson>WriteIn>Montroll>Kiss 1:Wright>Smith>Kiss>Montroll>WriteIn 1:Smith>Montroll>Kiss>Simpson>WriteIn 1:Simpson>Smith>Montroll>Kiss>Wright 1:WriteIn>Wright>Smith>Simpson>Montroll 1:Wright>Montroll>Smith>Kiss>WriteIn 1:Simpson>Montroll>Wright>Kiss>WriteIn 1:Smith>Kiss>Montroll>Simpson>WriteIn 1:Montroll>Kiss>Simpson>Smith>WriteIn 1:Wright>Smith>WriteIn>Montroll>Simpson 1:Smith>Simpson>Wright>Kiss>Montroll 1:Kiss>WriteIn>Smith>Montroll>Simpson 1:Simpson>Wright>Kiss>Smith>Montroll 1:Wright>WriteIn>Montroll>Smith>Simpson 1:Smith>Montroll>Wright>WriteIn>Simpson 1:Kiss>Simpson>WriteIn>Montroll>Wright 1:Montroll>Wright>Simpson>Kiss>Smith 1:WriteIn>Smith>Kiss>Wright>Montroll 1:Smith>Simpson>Montroll>WriteIn>Kiss 1:Montroll>Kiss>Smith>WriteIn>Wright 1:Montroll>Wright>WriteIn>Simpson>Kiss 1:Kiss>WriteIn>Wright>Smith>Simpson 1:Smith>Kiss>Wright>Simpson>WriteIn 1:Kiss>Smith>Simpson>WriteIn>Montroll 1:Wright>WriteIn>Smith>Montroll>Simpson 1:Simpson>Kiss>Wright>Montroll>Smith 1:Simpson>Montroll>Wright>Smith>Kiss 1:Montroll>Kiss>Simpson>WriteIn>Smith 1:Montroll>Smith>Simpson>Wright>WriteIn 1:Simpson>Kiss>Montroll>Wright>WriteIn 1:Kiss>Simpson>Smith>WriteIn>Wright 1:Simpson>Smith>Wright>Montroll>Kiss 1:Montroll>Kiss>WriteIn>Wright>Simpson 1:Kiss>Smith>Montroll>WriteIn>Wright 1:Kiss>Montroll>Smith>Wright>WriteIn 1:Wright>Montroll>Kiss>Smith>WriteIn 1:WriteIn>Wright>Simpson>Montroll>Kiss 1:Wright>Kiss>Simpson>Montroll>Smith 1:Kiss>Simpson>Montroll>Wright>WriteIn 1:Smith>Wright>Kiss>Montroll>WriteIn 1:Kiss>Simpson>Montroll>Smith>WriteIn 1:WriteIn>Montroll>Kiss>Smith>Simpson 1:Wright>Montroll>WriteIn>Smith>Kiss 1:Smith>Montroll>Simpson>Kiss>WriteIn 1:Smith>Simpson>Montroll>Wright>Kiss 1:Kiss>Wright>Simpson>Montroll>WriteIn 1:Wright>Simpson>Kiss>Smith>Montroll 1:Montroll>Simpson>WriteIn>Smith>Kiss 1:Wright>Smith>Montroll>WriteIn>Kiss 1:Wright>Smith>Montroll>WriteIn>Simpson 1:Simpson>Montroll>Smith>Wright>Kiss 1:Simpson>Kiss>Smith>Montroll>WriteIn 1:Kiss>Montroll>Simpson>Wright 1:Wright>Montroll>Simpson>Smith 1:Kiss>Wright>Simpson>Montroll 1:Kiss>Simpson>Smith>WriteIn 1:Montroll>Kiss>WriteIn>Wright 1:Simpson>Kiss>Montroll>Smith 1:Kiss>Smith>Montroll>WriteIn 1:WriteIn>Kiss>Wright>Montroll 1:Montroll>Simpson>Smith>Kiss 1:Simpson>Kiss>Smith>Wright 1:Simpson>Kiss>Smith>Montroll 1:Smith>Simpson>Kiss>Wright 1:Smith>Kiss>Simpson>Wright 1:Montroll>Kiss>Simpson>Wright 1:Kiss>WriteIn>Montroll>Smith 1:Wright>Simpson>Montroll>Smith 1:Montroll>Simpson>Wright>Kiss 1:Kiss>Smith>Wright>Simpson 1:Kiss>Montroll>Smith>WriteIn 1:Wright>Smith>WriteIn>Montroll 1:Wright>Smith>WriteIn>Simpson 1:Smith>Simpson>Montroll>Wright 1:Montroll>WriteIn>Simpson>Smith 1:Montroll>Smith>Simpson>Wright 1:Wright>Montroll>Kiss>Simpson 1:Smith>Montroll>Wright>Simpson 1:Wright>Kiss>Simpson>Montroll 1:Smith>Kiss>Wright>Simpson 1:Montroll>Wright>Smith>WriteIn 1:Smith>Simpson>Montroll>Kiss 1:WriteIn>Montroll>Kiss>Wright 1:Montroll>Wright>WriteIn 1:Wright>Simpson>Montroll 1:Wright>Simpson>Kiss 1:WriteIn>Kiss>Montroll 1:Smith>Simpson>WriteIn 1:Simpson>Smith>Montroll 1:Simpson>Smith>Kiss 1:Simpson>Smith>Wright 1:Kiss>Simpson>WriteIn 1:Simpson>Montroll>Smith 1:Montroll>WriteIn>Simpson 1:Wright>WriteIn>Montroll 1:Wright>WriteIn>Simpson 1:Wright>WriteIn>Kiss 1:Kiss>WriteIn>Montroll 1:Kiss>WriteIn>Wright 1:Simpson>WriteIn 1:Smith>WriteIn 1:WriteIn>Smith expected_winners: - Montroll # file: burlington_2009_ranked_robin.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 8974 ballots (ranked ballots). Ballots: 840 × Wright 355 × Kiss > Montroll 326 × Kiss 271 × Wright > Smith 256 × Wright > Montroll 234 × Kiss > Montroll > Smith 200 × Montroll > Kiss 178 × Montroll 147 × Wright > Montroll > Smith 145 × Montroll > Kiss > Smith 139 × Montroll > Smith 125 × Kiss > Smith 124 × Smith 123 × Kiss > Montroll > Smith > Wright > Simpson 122 × Wright > Smith > Montroll 121 × Kiss > Smith > Montroll 120 × Kiss > Montroll > Smith > Simpson > Wright 104 × Wright > Montroll > Smith > Simpson > Kiss 103 × Kiss > Montroll > Simpson > Smith > Wright 102 × Wright > Montroll > Smith > Kiss > Simpson 101 × Wright > Smith > Montroll > Kiss > Simpson 94 × Montroll > Wright 93 × Montroll > Smith > Kiss 93 × Smith > Wright 90 × Wright > Smith > Montroll > Simpson > Kiss 90 × Smith > Montroll 88 × Smith > Kiss > Montroll 83 × Smith > Montroll > Kiss 80 × Kiss > Smith > Montroll > Simpson > Wright 80 × Wright > Kiss 76 × Wright > Smith > Simpson > Montroll > Kiss 72 × Montroll > Kiss > Smith > Wright > Simpson 71 × Kiss > Montroll > Wright > Smith > Simpson 69 × Wright > Montroll > Kiss > Smith > Simpson 69 × Montroll > Smith > Kiss > Wright > Simpson 66 × Kiss > Wright 62 × Montroll > Smith > Wright 61 × Montroll > Kiss > Smith > Simpson > Wright 60 × Montroll > Wright > Smith > Kiss > Simpson 60 × Kiss > Montroll > Smith > Wright 58 × Smith > Kiss > Montroll > Simpson > Wright 57 × Montroll > Wright > Smith 56 × Montroll > Wright > Kiss > Smith > Simpson 55 × Kiss > Smith > Montroll > Wright > Simpson 54 × Wright > Montroll > Smith > Kiss 53 × Montroll > Smith > Kiss > Simpson > Wright 52 × Smith > Wright > Montroll > Kiss > Simpson 52 × Wright > Smith > Kiss > Montroll > Simpson 52 × Montroll > Smith > Wright > Kiss > Simpson 52 × Kiss > Montroll > Simpson 51 × Smith > Kiss 50 × Montroll > Kiss > Wright > Smith > Simpson 50 × Wright > Kiss > Montroll > Smith > Simpson 50 × Smith > Wright > Montroll 48 × Kiss > Montroll > Wright 46 × Montroll > Kiss > Wright 46 × Wright > Montroll 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WriteIn 1 × Smith > WriteIn 1 × WriteIn > Smith Round-Robin — every pair, head-to-head (For – Against): Kiss beats Wright 4313 – 4059 Montroll beats Wright 4596 – 3663 Wright beats Smith 3970 – 3792 Wright beats Simpson 5269 – 1309 Wright beats WriteIn 6061 – 162 Montroll beats Kiss 4063 – 3476 Kiss beats Smith 3944 – 3574 Kiss beats Simpson 5514 – 843 Kiss beats WriteIn 6147 – 113 Montroll beats Smith 4569 – 2996 Montroll beats Simpson 6261 – 591 Montroll beats WriteIn 6656 – 100 Smith beats Simpson 5568 – 721 Smith beats WriteIn 6055 – 113 Simpson beats WriteIn 3337 – 161 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Wright | Kiss | Montroll | Smith | Simpson | WriteIn | --------------------------------------------------------------------------------------------------------------------------------------- Wright > | --- |4059 - 602 - 4313 |3663 - 715 - 4596 |3970 - 1212 - 3792 |5269 - 2396 - 1309 |6061 - 2751 - 162 | Kiss > | 4313 - 602 - 4059 | --- |3476 - 1435 - 4063 |3944 - 1456 - 3574 |5514 - 2617 - 843 |6147 - 2714 - 113 | Montroll > | 4596 - 715 - 3663 |4063 - 1435 - 3476 | --- |4569 - 1409 - 2996 |6261 - 2122 - 591 |6656 - 2218 - 100 | Smith > | 3792 - 1212 - 3970 |3574 - 1456 - 3944 |2996 - 1409 - 4569 | --- |5568 - 2685 - 721 |6055 - 2806 - 113 | Simpson > | 1309 - 2396 - 5269 | 843 - 2617 - 5514 | 591 - 2122 - 6261 | 721 - 2685 - 5568 | --- |3337 - 5476 - 161 | WriteIn > | 162 - 2751 - 6061 | 113 - 2714 - 6147 | 100 - 2218 - 6656 | 113 - 2806 - 6055 | 161 - 5476 - 3337 | --- | Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order): # Candidate W–L–T Copeland Margin Beats 1 Montroll 5–0–0 5 +15319 Kiss, Wright, Smith, Simpson, WriteIn 2 Kiss 4–1–0 4 +10742 Wright, Smith, Simpson, WriteIn 3 Wright 3–2–0 3 +8850 Smith, Simpson, WriteIn 4 Smith 2–3–0 2 +8668 Simpson, WriteIn 5 Simpson 1–4–0 1 -15972 WriteIn 6 WriteIn 0–5–0 0 -27607 — Winner — Ranked Robin (RCV-RR): Montroll beats every opponent head-to-head — the Condorcet winner. --- Smith Set (the generalized Condorcet winner) --- The smallest group whose every member beats every candidate outside it — the honest answer to "who is even in contention?". Smith set (1 of 6): Montroll Outside (5): Wright, Kiss, Smith, Simpson, WriteIn One member ⇒ Montroll is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner Montroll is INSIDE the Smith set. ✓ Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of the set outscores every outsider, so the top of the win–loss table is always inside the set, however the tie among them is then broken. More: 07_Concepts/topics/smith_set.md