Committee monotonicity (1 of 2) — one seat, and the consensus candidate takes it¶

Generated from abc_committee_monotonicity_1seat_c3_b10.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Approval Voting · 1 seat · Expected winner: C

Scenario¶

Half of a matched pair. The SAME ten ballots are counted twice, once for one seat and once for two: this file is the one-seat count, its companion abc_committee_monotonicity_2seats_c3_b10.yaml is the two-seat count.

Ten voters, three candidates: two approve only A, three approve A and C, three approve B and C, two approve only B. Approval counts: C 6, A 5, B 5.

For ONE seat, eleven of the thirteen rules in Lackner & Skowron's Table 3.1 elect the consensus candidate C - Approval Voting, CC, PAV, seq-PAV, seq-CC, Monroe, Greedy Monroe, seq-Phragmen, leximax-Phragmen, the Method of Equal Shares and MAV. C is the only candidate a majority approves, and she is nobody's enemy. (SAV and rev-seq-PAV instead pick A or B here, because SAV divides each ballot's vote among its marks: A and B score 3.5 to C's 3.)

The interesting half is the companion file. Committee monotonicity (Definition 3.2) says that growing the committee from k to k+1 should ADD a member, never reshuffle: the one-seat winner should still be seated when there are two seats. Approval Voting and the sequential rules honour that. Chamberlin-Courant, PAV, Monroe, leximax-Phragmen and MAV all elect {A,B} for two seats and drop C entirely - the candidate who won outright when there was a single seat is not even on the committee once a seat is ADDED. That is Proposition A.2 in the book, and it is the ✗ in Table 3.1's committee monotonicity column.

Reproduce it: python 06_Other/abcvoting_tabulation_engine/abc_axiom_check.py

Source: Lackner, M. & Skowron, P. (2023), "Multi-Winner Voting with Approval Preferences", SpringerBriefs, doi:10.1007/978-3-031-09016-5, Proposition A.2.

Ballots¶

Row 1 = candidate names; each later row is one voter's approvals (1 = approve, 0/blank = not approved).

A,B,C
1,0,0   # 2 voters — approve A only
1,0,0
1,0,1   # 3 voters — approve A and C
1,0,1
1,0,1
0,1,1   # 3 voters — approve B and C
0,1,1
0,1,1
0,1,0   # 2 voters — approve B only
0,1,0

What the engine says¶

Full report from the _tabulated mirror (regenerated on every run; every analysis forced on):

--- Approval Voting (single winner) ---
 Tabulating 10 ballots (any non-zero score = approval).

Ballots:
   columns = A, B, C      (1 = approve; 0 = not approved)
     2 × 1,0,0
     3 × 1,0,1
     3 × 0,1,1
     2 × 0,1,0

   C -- 6 (60%) -- Elected
   A -- 5 (50%)
   B -- 5 (50%)

[Approval Distribution] (how many candidates each ballot approved)
   16 approvals across 10 ballots — average 1.6 of 3 (range 1–2).
     approved 1: 4 ballots
     approved 2: 6 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
      |   C    |   A    |   B    |
   -------------------------------
   C  |   --   |  50%   |  50%   |
   A  |  60%   |   --   |   0%   |
   B  |  60%   |   0%   |   --   |

Winner — Approval Voting (single winner)
  C

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 04_Approval/03_Criteria/cases/abc_committee_monotonicity_1seat_c3_b10.yaml

Committee monotonicity (1 of 2) — one seat, and the consensus candidate takes it¶

Scenario¶

Ballots¶

What the engine says¶

See also¶