# Same Ballots, Three Winners

The same nine ballots can elect three winners. Open the box, predict the results and count the votes under three real rules.

Every person, proposal and voting profile is fictional.

## Predict the winner when only rank 1 counts.

| Ballots | Preference order |
|---:|---|
| 3 | Grove → Fountain → Hall → Stage |
| 2 | Stage → Hall → Fountain → Grove |
| 2 | Hall → Grove → Fountain → Stage |
| 2 | Stage → Hall → Grove → Fountain |

## Counting ledger

1. **One vote for rank 1**: One vote for rank 1: Stage 4, Grove 3, Hall 2, Fountain 0. Stage wins.
2. **3–2–1–0 points**: 3–2–1–0 points: Hall 17, Grove 15, Stage 12, Fountain 10. Hall wins.
3. **Eliminate and transfer**: Eliminate and transfer: Fountain and Hall leave; Hall’s two ballots transfer to Grove. Grove wins 5–4.

> The counting rule decides which kind of support becomes victory.

## Sources and limits

The counting methods are real. The square, plans and every ballot were invented for the game so each rule’s effect stays visible. The game does not simulate turnout, campaigning, negotiation, strategic voting or preference changes after a withdrawal. No method is presented as best in every situation.

- [Jean-Charles de Borda’s 1784 memorandum, facsimile and transcription](https://irem.unicaen.fr/IMG/pdf/2012-03-20_-_fascicule_2_stage_irem_probas-stats_n_b_-_def_corr.pdf)
- [Australian Electoral Commission: counting and transferring preferences](https://www.aec.gov.au/voting/counting/hor_count.htm)
- [ACE Electoral Knowledge Network: definition of plurality systems](https://aceproject.org/ace-en/topics/es/esd/esd01/)
- [Nobel Prize: Kenneth Arrow’s framing of the limits of preference aggregation](https://www.nobelprize.org/prizes/economic-sciences/1972/arrow/facts/)

Conceived and edited by Marius Comper; built with Codex assistance.