Weighted vote swings
List every coalition and identify members whose departure changes a winning total into a losing one.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 1–4 cooperatively
- Time
- 15–25 minutes
- Materials
- Voter labels A2, B1, C1; eight coalition rows
Prepare
Give A weight 2, B weight 1 and C weight 1. A coalition wins with total at least 3. Empty coalitions and singletons must be listed too; no participant casts a real classroom vote.
Play
Enumerate the eight subsets of A,B,C exactly once. Add the weights in each. For each winning subset, remove one member temporarily and recalculate. Mark that member critical only if the remaining total is below 3. Restore the member before the next test.
Worked example
AB and AC each total 3; both members are critical in each pair. ABC totals 4: removing A leaves 2, so A is critical; removing B or C leaves 3, so neither is critical there.
Finish and check
Count critical occurrences across all winning coalitions. A has 3, B1, C1: five in total. Shares are 3/5,1/5,1/5. This definition counts coalitions equally; it does not predict real political influence or a person’s worth.
Adaptation and limits
Partners exchange tables and check empty, A, B, C, AB, AC, BC, ABC. Finish when every row and every critical mark agrees. Change the quota only after completing this table, keeping that new result separate.
Purpose, observation and provenance
Within this activity: List every coalition and identify members whose departure changes a winning total into a losing one.
Ask the group to remove each member of ABC separately and explain why only A is critical there.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Stanford CS106B: Voting Power — The reference defines critical coalition members. Our three-voter example, prompts and table are original; no assignment code is reproduced.
Secondary practice: Cooperation and explaining a check.
For a class of 30, use ten groups of three. Prepare one player-material set per group and keep the host key with the adult. Rotate operator, recorder and checker after each worked example; a reader or scribe may help without choosing answers. Avoid public ranking or diagnostic labels.
Age bands are planning suggestions. Background references may address older learners and do not validate suitability for this age band. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Rules to keep beside the materials
- Give A weight 2, B weight 1 and C weight 1. A coalition wins with total at least 3. Empty coalitions and singletons must be listed too; no participant casts a real classroom vote.
- Enumerate the eight subsets of A,B,C exactly once. Add the weights in each. For each winning subset, remove one member temporarily and recalculate. Mark that member critical only if the remaining total is below 3. Restore the member before the next test.
- AB and AC each total 3; both members are critical in each pair. ABC totals 4: removing A leaves 2, so A is critical; removing B or C leaves 3, so neither is critical there.
- Count critical occurrences across all winning coalitions. A has 3, B1, C1: five in total. Shares are 3/5,1/5,1/5. This definition counts coalitions equally; it does not predict real political influence or a person’s worth.
- Partners exchange tables and check empty, A, B, C, AB, AC, BC, ABC. Finish when every row and every critical mark agrees. Change the quota only after completing this table, keeping that new result separate.
Weighted vote swings — play materials
| Coalition | Total | Wins ≥3? | Critical members |
|---|---|---|---|
| ∅ | |||
| A | |||
| B | |||
| C | |||
| AB | |||
| AC | |||
| BC | |||
| ABC |
Host check — keep private until finished
Winning AB, AC, ABC; critical totals A3/B1/C1; shares 60%/20%/20%.
These are model answers or legal examples, not records of an experiment or learner outcomes.