====================================================================== SOURCE FILE: alabama_3seats.yaml TABULATED FILE: alabama_3seats_tabulated.txt ====================================================================== election_title: The Alabama paradox — 3 seats scenario_description: > Five gardeners scoring four candidates for a community-garden committee. These are the SAME five ballots as the other file in this folder; the only difference is how many seats are up. At two seats Proportional STAR seats Basil and Dahlia. At three seats it seats Aster, Basil and Clover — Dahlia has LOST her seat because the committee grew. That is the Alabama paradox, a failure of house-size monotonicity, and it is a known property of quota methods rather than a bug in this file. voting_method: allocated num_winners: 3 ballots: |- Aster,Basil,Clover,Dahlia 3,3,2,4 5,4,0,2 1,0,4,3 0,5,5,3 5,5,0,0 # file: alabama_3seats.yaml ====================================================================== TABULATION RESULTS ====================================================================== === The Alabama paradox — 3 seats === Five gardeners scoring four candidates for a community-garden committee. These are the SAME five ballots as the other file in this folder; the only difference is how many seats are up. At two seats Proportional STAR seats Basil and Dahlia. At three seats it seats Aster, Basil and Clover — Dahlia has LOST her seat because the committee grew. That is the Alabama paradox, a failure of house-size monotonicity, and it is a known property of quota methods rather than a bug in this file. --- Preference Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against Informational only — not part of the 3-winner count below, so no Top-2 finalists are marked. | Aster | Basil | Clover | Dahlia | ----------------------------------------------------------------- Aster > | --- |2 - 2 - 1 |3 - 0 - 2 |2 - 0 - 3 | Basil > | 1 - 2 - 2 | --- |3 - 1 - 1 |3 - 0 - 2 | Clover > | 2 - 0 - 3 |1 - 1 - 3 | --- |2 - 1 - 2 | Dahlia > | 3 - 0 - 2 |2 - 0 - 3 |2 - 1 - 2 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: Aster > Basil > Dahlia > Aster) [Condorcet Loser] No strict Condorcet loser; weak Condorcet loser: Clover (never wins a matchup) [Divergence from STAR] STAR = Aster RCV-IRV = Dahlia (differs from STAR) Approval = Basil (differs from STAR) RCV-RR = Basil (differs from STAR) Note: 3 of 5 ballots (60%) 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. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/alabama_3seats_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/alabama_3seats_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Basil) - Runoff Round Winner = (Aster) Candidate Basil earned the highest total score, but Candidate Aster 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). --- Allocated Score Voting Method (3 winners) --- [Allocated Score Voting] Tabulating 5 ballots to fill 3 seats. Aster,Basil,Clover,Dahlia 3, 3, 2, 4 5, 4, 0, 2 1, 0, 4, 3 0, 5, 5, 3 5, 5, 0, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Aster 2 0 1 0 1 1 | 14 2.8 Basil 2 1 1 0 0 1 | 17 3.4 Clover 1 1 0 1 0 2 | 11 2.2 Dahlia 0 1 2 1 0 1 | 12 2.4 Hare quota is 5/3. [Allocated Score Voting: Round 1] The highest-scoring candidate wins a seat. Basil -- 17 -- First place Aster -- 14 Dahlia -- 12 Clover -- 11 Basil wins a seat. [Allocated Score Voting: Round 1: Ballot allocation round] Allocating 1+2/3 ballots. [Allocated Score Voting: Round 1: Ballot allocation round: Round 1] Allocating 2 ballots at score 5. This allocation overfills the quota. Returning fractional surplus. Allocating only 83.33% of these ballots. Keeping these ballots, but multiplying their weights by 1/6. 2 ballots reweighted from 1 to 1/6. [Allocated Score Voting: Round 2] The highest-scoring candidate wins a seat. Aster -- 9+5/6 -- First place Dahlia -- 9+1/2 Clover -- 6+5/6 Aster wins a seat. [Allocated Score Voting: Round 2: Ballot allocation round] Allocating 1+2/3 ballots. [Allocated Score Voting: Round 2: Ballot allocation round: Round 1] Allocating 1 ballot at score 5. [Allocated Score Voting: Round 2: Ballot allocation round: Round 2] Remaining allocation quota is 2/3. Allocating 1 ballot at score 3. This allocation overfills the remaining quota. Returning fractional surplus. Allocating only 66.67% of this ballot. Keeping this ballot, but multiplying its weight by 1/3. 1 ballot reweighted from 1 to 1/3. [Allocated Score Voting: Round 3] Tabulating 4 remaining ballots. Aster,Basil,Clover,Dahlia 3, 3, 2, 4 5, 4, 0, 2 1, 0, 4, 3 0, 5, 5, 3 5, 5, 0, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Aster 2 0 1 0 1 1 | 14 2.8 Basil 2 1 1 0 0 1 | 17 3.4 Clover 1 1 0 1 0 2 | 11 2.2 Dahlia 0 1 2 1 0 1 | 12 2.4 The highest-scoring candidate wins a seat. Clover -- 5+1/2 -- First place Dahlia -- 4+5/6 Clover wins a seat. [Allocated Score Voting: Winners — Allocated Score Voting Method (3 winners)] Aster Basil Clover