Exercise 11 — Recruit a spoiler¶
You manage Brett's campaign, and the polling is grim: Alba leads the two-way race 5–4 and every voter is locked in. Then an intern slides a memo across the table: "We can't flip a single voter — so let's add a candidate. Recruit Axl, who's practically Alba with a different haircut. Alba's five voters will split, our four hold, we win." Your job: game out the memo under three counting rules before deciding whether the trick is worth it.
▶ Live on BetterVoting: base race vote · results ↗ · clone added vote · results ↗ (elections ggg7hd / 93gjx6, Test IDs BV2197–98; the clone election runs all four methods — watch Choose-One fall for it live while RCV-IRV, STAR, and Ranked Robin hold).
You practice: the spoiler effect as a design property — predicting which ballot designs a vote-splitting attack actually works against — and reading an Equal-Support runoff line. (Concept home: vote-splitting; glossary: clone independence.)
Work each part on paper before opening its solution. Both YAMLs are runnable; their expected_winners keys are regression-tested, and the _tabulated mirrors are the full audit reports. (Axl shares Alba's initial on purpose — they're clones; the distinct-initials naming rule yields to the lesson.)
The ballots¶
Base race — nine voters, two candidates: Alba's camp of five scores (Alba 5, Brett 0); Brett's camp of four scores (Alba 0, Brett 5).
After the memo — same nine voters, three names. Alba's camp splits its first preferences over the clones but scores both high; Brett's camp is unchanged:
| ×3 Alba camp | ×2 Alba camp | ×4 Brett camp | |
|---|---|---|---|
| Alba | 5 | 4 | 0 |
| Axl | 4 | 5 | 0 |
| Brett | 0 | 0 | 5 |
Your task¶
- (a) Confirm the base race: who wins under Choose-One, Score, and STAR?
- (b) The memo assumes Choose-One counting. Does the trick work there? Show the count.
- (c) Now the town uses STAR. Predict, then tabulate: who reaches the runoff, what does the runoff line say, who wins? Where exactly does the memo's logic die?
- (d) Try it under RCV-IRV. Does the spoiler work there? (Careful — the answer may not flatter your favorite talking point.)
- (e) Write the one-paragraph reply you'd send back with the memo, as a matter of ballot design rather than ethics.
Solutions¶
(a) The base race — Alba, everywhere
Choose-One: 5–4 Alba. Score: 25–20 Alba. STAR: finalists by necessity, runoff **Alba 5–4**. When there are only two names, every reasonable method is the same method: majority rule.(b) Under Choose-One, the memo works
First choices after Axl enters: **Alba 3, Axl 2, Brett 4 — Brett wins** with the *same nine opinions* that preferred Alba's camp 5–4. No voter changed their mind; the ballot design simply cannot hear "either clone over Brett." That's the spoiler effect in its purest form — the attack Choose-One invites, and the reason this repo's [split-voting set](../../method_comparisons/split_voting/README.md) exists.(c) Under STAR, the memo dies in the scoring round
[Divergence from STAR]
STAR = Alba
Choose-One (Plurality) = Brett (differs from STAR)
--- STAR Voting Method (single winner) ---
[STAR Voting]
Tabulating 9 ballots.
Count × Alba,Axl,Brett
4 × 0, 0, 5
3 × 5, 4, 0
2 × 4, 5, 0
[STAR Voting: Scoring Round]
The two highest-scoring candidates advance to the next round.
Alba -- 23 -- First place
Axl -- 22 -- Second place
Brett -- 20
Alba and Axl advance.
[STAR Voting: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Alba -- 3 -- First place
Axl -- 2
Equal Support -- 4
Alba wins.
Runoff math:
9 ballots cast
− 4 Equal Support (no preference between the two finalists)
─
5 voters with a preference (majority = 3)
Alba 3 (60%) · Axl 2 (40%)
[STAR Voting: Winner — STAR Voting Method (single winner)]
Alba
(d) Under RCV-IRV, the memo also fails — credit where due
First choices: Alba 3, Axl 2, Brett 4. **Axl is eliminated first**, and both of his ballots transfer straight back to Alba (she's ranked next on them): final round **Alba 5, Brett 4**. Pure-clone *crowding* is the vote-splitting variant RCV-IRV genuinely handles — its transfers exist for exactly this case, and the honest scorecard says so (the glossary's [clone-independence entry](../../07_Concepts/GLOSSARY.md) gives IRV this point). IRV's spoiler trouble is the *non-clone* case — a competitive third candidate who squeezes the middle ([exercise 5](ex05_center_squeeze.md)) — not this one.(e) The reply memo
"The plan only works if the town counts Choose-One ballots — the one design where a voter's support for Axl is *subtracted* from Alba. Under STAR the clones pool rather than split (both finalist slots go to their camp and we finish third); under RCV-IRV the transfers just reassemble Alba's five. And if anyone audits *why* we recruited a candidate we hope loses, we've handed the story to the opposition. Recommend we spend the budget persuading an actual voter — under every ballot here, that's worth strictly more than a fake candidate." — The general lesson, minus the intrigue: *how much a spoiler can extract is a property of the ballot*, which is why [the Equal Vote criterion](../01_Learn/properties_and_limits/equally_weighted_vote.md) centers on it.Reading this fairly¶
A strategic construction, flagged as such per the four-part test — and run symmetrically: the attack succeeds against Choose-One, and fails against both STAR and RCV-IRV, each for its own structural reason. Real clone politics is messier than two candidates with interchangeable haircuts (imperfect clones leak preferences — the fuller story is the split-voting set and the glossary's teaming-vs-crowding distinction).
Run it yourself¶
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 01_STAR/05_Practice/cases/ex11_two_way_base.yaml
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 01_STAR/05_Practice/cases/ex11_spoiler_added.yaml
Sources: ex11_two_way_base.yaml · ex11_spoiler_added.yaml. Full audit reports: base · spoiler added.
Where this comes from. Original to this repo (ballots, cast, and the intern). Concept homes: the spoiler effect, the split-voting set, and the equally weighted vote.
Back to the exercises set · curriculum home: Voting 301