SAV rewards a bullet vote — the two-voter manipulation¶

Generated from sav_strategy_bullet_vote_c5_b2.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: A

Scenario¶

The smallest strategy counterexample in Lackner & Skowron (Proposition A.4). Two voters, five candidates, ONE seat. Voter 1 sincerely approves A, B and C; voter 2 approves D and E.

Satisfaction Approval Voting gives each BALLOT one vote and splits it evenly among that ballot's marks. So voter 1's three marks are worth 1/3 each, while voter 2's two marks are worth 1/2 each. SAV therefore scores D and E at 1/2 against A, B and C at 1/3 - and the single seat goes to D (E ties; the book breaks it lexicographically).

Voter 1 got nothing she approved. Now let her lie: submit {A} alone. Her one vote lands undivided on A, worth 1.0, and A takes the seat. She has moved from a committee containing none of her approved candidates to one containing A, purely by NARROWING her honest ballot. That is a violation of inclusion-strategyproofness (Definition 3.7), and it is why SAV carries a ✗ in that column of Table 3.1 despite passing Pareto efficiency, committee monotonicity, support monotonicity and consistency - the only rule besides AV to pass all four.

Approval Voting - the count in this file - is the control, and its answer is a five-way tie: every candidate has exactly one approval, so AV cannot separate them at all. That contrast IS the mechanism. SAV's power to distinguish these ballots comes from dividing by ballot length, and that same division is what makes shortening a ballot pay.

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.4.

Ballots¶

The ballots as marked — a filled Yes is a 1 in that candidate's column, a filled No a 0:

#	Ballot as marked	A	B	C	D	E
1		1	1	1	0	0
2		0	0	0	1	1

The same ballots as the file records them:

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

A,B,C,D,E
1,1,1,0,0   # voter 1 — sincerely approves A, B, C
0,0,0,1,1   # voter 2 — approves D and E

What the engine says¶

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

--- Approval Voting (single winner) ---
 Tabulating 2 ballots (any non-zero score = approval).

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

   A -- 1 (50%) -- Elected
   B -- 1 (50%)
   C -- 1 (50%)
   D -- 1 (50%)
   E -- 1 (50%)
  Note: A, B, C, D, E each have 1 approval and tie for the last 1 seat.
        Candidate priority order (A > B > C > D > E) broke the tie: A elected, B, C, D, E not elected.

[Approval Distribution] (how many candidates each ballot approved)
   5 approvals across 2 ballots — average 2.5 of 5 (range 2–3).
     approved 2: 1 ballot
     approved 3: 1 ballot

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
      |   A    |   B    |   C    |   D    |   E    |
   -------------------------------------------------
   A  |   --   |  100%  |  100%  |   0%   |   0%   |
   B  |  100%  |   --   |  100%  |   0%   |   0%   |
   C  |  100%  |  100%  |   --   |   0%   |   0%   |
   D  |   0%   |   0%   |   0%   |   --   |  100%  |
   E  |   0%   |   0%   |   0%   |  100%  |   --   |

Winner — Approval Voting (single winner)
  A

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 04_Approval/03_Criteria/cases/sav_strategy_bullet_vote_c5_b2.yaml

SAV rewards a bullet vote — the two-voter manipulation¶

Scenario¶

Ballots¶

What the engine says¶

See also¶