The Alabama paradox — 3 seats¶
Generated from alabama_3seats.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: Allocated Score (proportional STAR) · 3 seats
Scenario¶
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.
Ballots¶
Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical 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
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
[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
[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
[Allocated Score Voting: Winners — Allocated Score Voting Method (3 winners)]
Aster
Basil
Clover
Full audit — preference matrix, Condorcet, and score distribution¶
--- 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)
[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.
[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.
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/03_Criteria/alabama_paradox/cases/alabama_3seats.yaml
See also¶
More cases in this set: alabama_2seats