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Teach vote splitting — a plan for 101, 201 and 301

Level: 101 → 301 · for presenters

Everything on this page is presenter-facing: what to say, what to show, what the room will ask back. The learner-facing version of the same material is Vote splitting & the spoiler effect.

→ Companion presenter pages: Teaching STAR Voting · Run a paper-ballot demo · Count a STAR election by hand

The one rule that determines everything else

Open in Choose-One. Every time.

Vote splitting is a failure of choose-one voting. STAR cannot demonstrate it, because under STAR nothing splits by force — so a lesson that opens with STAR is describing a problem the room has never felt, and teaching the cure as a feature rather than as a repair. Let the split happen to your audience first. Then fix it.

And when you fix it, the sentence is not "STAR counts better." It is:

Choose-One did not miscount those votes. It never asked the question whose answer would have changed the result.

That reframes every reform on the table from a better calculator to a better question — which is both more accurate and much harder to argue with.

The three live elections you will use

All three are real BetterVoting elections. Put the results link on screen; the room can follow along on their phones.

Election Size The number Level
BV2296 The smallest spoiler ↗ · vote 3 cand × 7 Vanilla wins on 43% 101
BV2293 Seven apples and a banana ↗ · vote 8 cand × 9 Banana wins on 22% 201
BV2295 Fizzy or sweet? ↗ · vote 7 cand × 7 Two same-size groups, opposite verdicts 301

Every race is cross-checked: BetterVoting and the LH engine agree on all twelve, and both Ranked Robin results are confirmed a third time by pref_voting's independent Copeland implementation.

101 — feel the split, then fix it

Objective: the room can explain, in their own words, why a group that agrees can lose to a group that is smaller.

Level: 101 · for voters

# Rung Use What they should feel
1 Two candidates — nothing can split 07a Majority rule. Every method agrees. This is the baseline.
2 The smallest spoiler 08a · BV ↗ Vanilla wins on 43% — and every chocolate lover had it last
3 The same seven friends, scoring 08b Vanilla finishes last of three and never reaches the runoff — the information was there all along; the ballot just never collected it
4 The majority Choose-One threw away 08c Either chocolate beats Vanilla head-to-head 4–3

They can now do: spot the shape (several similar options, one distinct one) on a real ballot, and say why the winner's percentage matters.

Do not yet introduce: Condorcet winners, center squeeze, IIA, or any method beyond Choose-One and STAR. Rung 3 is the payoff; stop there.

201 — when does it actually bite?

Objective: the room can tell a spoiled election from a merely sub-majority one — and knows that the difference cannot be read off the result sheet.

Level: 201 · deep dive

This level is the one most explanations skip, and skipping it is what makes the whole argument fragile.

# Rung Use The point
1 Six names: the vote splits and costs nothing 07b Gala wins on 33%, apple vote divided five ways, and nothing went wrong. Splitting ≠ spoiled.
2 Eight names: now it costs everything 07c Banana on 22% while 78% wanted an apple
3 Name the spoilers same Pink Lady and McIntosh got one vote each. Neither could win. Both changed who did. That is the definition.
4 The same nine voters, expressively 07d STAR · 07e Approval · 07f RCV-IRV · 07g Ranked Robin All four elect Gala. Under STAR, Banana finishes last of eight
4b The answer key 07g Gala is 7–0 head-to-head and Banana is 0–7 — Choose-One elected the Condorcet loser
5 The control 06 A 41% winner that nothing spoiled — same warning signs, opposite verdict
6 STAR's own limit 05a → 05b A faction that bullet-votes can still split itself. The cure is in the voters' hands

They can now do: look at "winner took 34%" in a news report and say "that's a screening flag, not a finding — you'd need the preference data to know."

The fairness beat, and do not skip it: rung 4 shows RCV-IRV fixing this spoiler. It does. Ending the classic spoiler is what instant-runoff was built for. Its own well-known failure is center squeeze — a different thing — and this election is not an example of it. A room that catches you overselling stops believing the parts that are true.

301 — you cannot read a spoiler off a candidate list

Objective: the room can explain why a clone set is defined by voters rather than by categories, and why that makes spoilers unpredictable in advance.

Level: 301 · for debaters

# Rung Use The point
1 Two groupings, same size 09a · BV ↗ Fizzy 4/7, sugar 4/7 — Choose-One elects Diet Cola on 29%
2 The same ballots, grouped the other way 09b Identical election, opposite verdict. A category is not a clone set
3 Spoiler ≠ IIA ≠ center squeeze spoiler effect Three distinct things routinely conflated in argument — in both directions
4 Deliberate splitting ex11 — recruit a spoiler Run it as a strategy problem: which ballot designs is the attack worth mounting against?
5 How often, honestly the 2022 count 11.9% of US primaries had the setup. That is not a count of spoiled elections

They can now do: argue the case without overclaiming — including conceding the cases where nothing was spoiled.

The ten-minute demo, beat by beat

No slides needed. A whiteboard and seven imaginary friends.

0:00 — Set it up. "Seven of us are splitting a tub of ice cream. Three flavours: milk chocolate, dark chocolate, vanilla. Everybody gets one vote. Fair?" Wait for the nods. Everyone agrees this is fair, and you want that on the record.

1:00 — Show the room, not the ballot. Write the seven people's actual opinions on the board:

2 friends:  milk chocolate first, dark chocolate a close second, no vanilla
2 friends:  dark chocolate first, milk chocolate a close second, no vanilla
3 friends:  vanilla, and they don't much like chocolate

Ask: "Before we vote — what does this group want?" Let someone say "chocolate." Four of the seven want chocolate. Say the number out loud.

2:30 — Vote. One mark each. Write the tally as it comes:

Vanilla          3
Milk Chocolate   2
Dark Chocolate   2

3:30 — The pause. Do not explain yet. Ask: "Who won?" Then: "Who did this room want?" Let the gap sit there for a beat. Someone will say it before you do.

4:30 — Name it. "Four of you wanted chocolate. All four ranked vanilla last. Vanilla won with three. Nobody cheated, nobody miscounted, nobody voted strategically. The chocolate four were simply not allowed to say they'd take either one."

5:00 — Let them invent the workarounds. (cut this beat first if you are short) Ask: "You're one of the chocolate four. What do you do next year?" Collect answers, and name each one as you write it:

They say You write
"hold a chocolate-only vote first" that's a primary
"one of the chocolates should drop out" that's the get-out-of-the-race phone call
"agree in advance which chocolate we back" that's a party machine

"Every fix you just invented is something you've seen on the news. We have built an entire industry of workarounds for one property of this ballot."

6:00 — The key sentence. "Choose-One didn't count your votes wrong. It never asked the question whose answer would have changed the result."

6:30 — Fix it. Same seven friends, score every flavour 0–5:

Milk Chocolate  20      Dark Chocolate  18      Vanilla  15

Point at Vanilla's 15. "Vanilla just came last. The flavour that won the first election is now bottom of three — and it doesn't even make the runoff. The two chocolates take both finalist slots."

7:00 — The runoff. "STAR's second step: the top two scorers go to an automatic runoff, and every ballot counts for whichever finalist it scored higher. No second trip to the polls."

Runoff:  Milk Chocolate 4  ·  Dark Chocolate 2  ·  Equal Support 1

"Same people. Same opinions. Nothing added except the ability to say 'I'd take either.'"

Do not say "the four chocolate lovers reunited." They didn't — they split 2–2 between the two chocolates, because they genuinely disagree about chocolate. The margin comes from two vanilla voters leaning mildly toward milk. The score ballot didn't end their disagreement; it stopped their disagreement costing them the election. If someone asks "so which chocolate did the four want?", that's the honest answer, and it's a better one.

8:00 — Land it. "Now imagine that's not ice cream." Stop. Do not name a party or a candidate — the room will do it themselves, and it lands far harder when they do.

9:00 — Take questions. See the objections list below.

The two ways this demo fails, and the recoveries

Failure 1 — the sting doesn't land. You reveal that four of seven wanted chocolate, and instead of wincing the room shrugs: "So what? Most votes wins. Three beats two. That's how voting works." If the sting misses, everything after it is a solution to a problem nobody has.

Recovery: don't argue, count. Say: "Fair enough. Let's make it simpler — forget the three flavours. Chocolate or vanilla, that's the whole ballot. Which do these seven friends pick?" Walk the seven on your fingers — four chocolate, three vanilla — and write it:

head-to-head:   chocolate 4  ·  vanilla 3

"So on the simplest possible vote — the one where 'most votes wins' works perfectly — chocolate wins. Now put one more chocolate on the menu, and chocolate loses. The menu changed the winner. That's the bug."

This recovery is stronger than the beat that failed, because the objector's own rule delivers the verdict.

Failure 2 — someone attacks the ballot. "But those two chocolates are basically the same thing — of course that's a stupid ballot."

They are right, and it is the best thing that can happen to you. Do not defend the ballot. Say:

"Exactly — and that's the whole problem. Under choose-one voting, offering people more of what they want is a disadvantage. That's why parties spend so much effort clearing their own primary field, and why a good candidate gets told not to run. The ballot punishes the side with more choices."

That turns the objection into your strongest point. Have it ready; you will get it most times you run this.

The forty-five minute workshop

The design problem to plan for, because it decides the whole session: your room's own vote is not guaranteed to split. A healthy room may simply agree. So run two exhibits — the room's live election, which teaches whatever it teaches, and the frozen ladder, which must split because it was built to. Say this out loud when you get there: "your election may not have split; about one in eight real primaries did; here is one that has to." That sentence is itself the 201 lesson — exposure is not the same as a flipped outcome — so teach it rather than apologising for it.

The three BV links below are read-only exhibits. They are frozen cases whose numbers the repo's pages quote. Send the room to your election to vote; send them to these only to look.

Materials: printed ballots (see Run a paper-ballot demo for the generator), a whiteboard, the three BV links on screen.

Time What
0–10 The ten-minute demo above, run live with the room's own votes on paper
10–20 Hand-count it together. Choose-One first (stacks of paper), then the scoring round, then the runoff pile-sort — three piles: prefers A, prefers B, Equal Support. The pile-sort is the fastest way to make the runoff physical
20–30 The ladder, on screen: BV2293 ↗. Two names → six names → eight names. Ask them to predict the winner at each step before you reveal it. Most rooms get rung 2 wrong — they expect the split to bite immediately, and it doesn't
30–38 What each method does with the same nine ballots — STAR, Approval, RCV-IRV, Ranked Robin, all electing Gala. Say plainly that RCV-IRV fixes this one
38–45 The honest half: the control case (a 41% winner nothing spoiled) and STAR's residual split. Close on what splitting does before anyone votes

If you only have 20 minutes: demo + hand-count. Drop the ladder. If you only have 5: rungs 2 and 3 of 101. The tally and the fix. Nothing else.

What splitting does before anyone votes

The arithmetic is the setup. The damage is behavioural, and it is worth two minutes at the end of any session:

  1. Voters abandon their favourite. "Don't waste your vote" is not cynicism — under choose-one it is correct advice, which is what makes it corrosive. (→ favorite betrayal)
  2. Parties ration candidates. Clearing the field, pressuring people out of primaries, endorsing early — all of it is rational defence against splitting, and all of it narrows what voters get to choose from.
  3. Good candidates never run at all. The deepest harm, and the only one that leaves no trace in any result sheet. Say so honestly: it cannot be measured, which is exactly why it goes unmentioned.

Point (3) is the strongest closing line available and the easiest to overclaim. State it as what it is — a structural incentive whose effects are invisible by construction — not as a statistic.

Objections, and fair answers

Concede the true part first, every time. A defensive answer loses the room faster than the objection did.

"You rigged the ballot — two chocolates and one vanilla." Yes. And under choose-one that rigging is real and permanent: the side offering more options is at a disadvantage. That is the finding, not a trick in the setup.

"That's just independence of irrelevant alternatives, a theoretical criterion." IIA and the spoiler effect are genuinely different things and it is fair to insist on the distinction. But the distinction cuts both ways: what happened here is not a theoretical axiom violation, it is four people who wanted chocolate getting vanilla. Whether a criterion is "theoretical" is decided by whether it changes real outcomes, and this one did.

"RCV already fixes this." For this election, it does — and our own ranked count elects Gala. Say so. Instant-runoff was built to end the classic spoiler and it ends it. The open question is a different failure (center squeeze), plus what happens to ballots that stop counting. Do not blur the two to win a point.

"So STAR is immune to vote splitting?" No, and the honest version is better: STAR removes forced splitting — you are never made to choose between allies. A faction that bullet-votes can still split itself (05a). The cure is in the voters' hands, which is a real difference from choose-one, where it isn't.

"This never happens in real elections." About 11.9% of 2022 US primaries had a multi-candidate field and a sub-majority winner — the setup. That is not a count of spoiled elections, and anyone quoting it as one is overreaching. The honest reading.

"The winner got 34%, so that election was spoiled." Not necessarily, and this is where the argument is usually lost. A sub-majority winner may be exactly who the majority preferred — see the control case. Telling the two apart needs preference data that a one-mark ballot never collects.

"Just hold a runoff / a primary." A top-two runoff fixes it only if the right two make the top two — and vote splitting is precisely what decides who does. A primary moves the split earlier rather than removing it; that is why parties work so hard to manage their own.

"Wouldn't people just coordinate?" They do, constantly — that is the coordination cost. Endorsements, withdrawals, "electability" arguments and lesser-evil voting are all the system working as designed. The question is whether that work should be forced on voters and parties, or done by the ballot.

"Isn't this just about third parties?" No — it is about any two similar candidates, which is most often two candidates of the same party in a primary. Framing it as a third-party problem understates it.

Checks for understanding

101 — 1. Four of seven wanted chocolate. Who won, and why? · 2. Did anyone vote dishonestly? · 3. What could the chocolate voters not say on the choose-one ballot? · 4. What changed between the two counts — the people, or the ballot? · 5. Why can't this happen with only two candidates?

201 — 1. At rung 2 the winner had 33% and the vote was split five ways. Was that election spoiled? (No — the apple side still won.) · 2. Which two candidates spoiled rung 3, and how many votes did each get? (Pink Lady and McIntosh, one each.) · 3. Banana won under Choose-One and finished last of eight under STAR. Is that a contradiction? (No — different questions.) · 4. Does RCV-IRV fix this election? (Yes.) · 5. Name one thing that would make you say a sub-majority winner was not spoiled. · 6. How could a STAR election still split a faction? (Bullet-voting.)

301 — 1. Fizzy and sugar both hold 4 of 7 first choices. Why is only one a clone set? · 2. Could you have predicted the spoiler from the candidate list alone? (No — you need the ballots.) · 3. Give a case that is a spoiler but not a center squeeze, and one that is the reverse. · 4. Someone says "the fizzy vote will split three ways." What do you ask for? (The ballots.) · 5. Why is "STAR is immune to vote splitting" wrong, and what is the accurate claim?

The question that separates memorisation from understanding is 201.1 and 201.5. A learner who answers "yes, spoiled" to a 33% winner has learned a slogan. A learner who asks for the preference data has learned the concept.

The rest of the library — every splitting case, and its job

The three levels above use one cast each. These are everything else the repo has on the subject, so you can swap a scenario to fit your audience without rebuilding the lesson.

How big can the field get? The largest is the pineapple progression — a pizza menu grown from 3 toppings to 11, where the Choose-One winner's mandate shrinks from 34% to 11% while Cheese, everybody's easy second, wins every whole-ballot count at every rung. Three live BV elections, one per rung. That is the large-field demo; the fruit basket (8 candidates on 9 ballots) is the small-ballot one. Use pineapple when you want the shrinking-mandate curve, the fruit basket when you want every voter visible on one slide.

Case Field The job
Pineapple progression 3 → 4 → 11 The large field. The winner's mandate shrinks to 11% as the menu grows; the whole-ballot winner never changes
Crowded field 3 → 5 → 7 65 voters who never change their minds; at seven candidates four different methods elect four different people
Minority winner 3 The canonical 34%-wins case, 100 voters so the count is the percent
00 Plurality vs majority 3 "Most votes" and "over half" are different bars — where the gap comes from
01 Political left split 4 The political version: a 66% coalition splits three ways, a 34% Conservative wins
02 Ice cream chocolate split 4 The 100-voter chocolate/vanilla version — percentages rather than headcounts
03 Lunch: veggie vs meat 4 A 70% veggie majority loses to a single burger
04 Star Wars 3 Skywalker and Leia split the Rebel vote; the one you actually preferred wins under STAR
06 Sub-majority, not spoiled 3 The control. A 41% winner nothing spoiled — mandatory at 201
05a → 05b 3 STAR's residual split, and its cure
Food-truck row 5, 2 seats The multi-seat version: a 57% majority splits three ways and takes zero of two seats under SNTV
SNTV village council multi-seat Why SNTV jurisdictions develop candidate-rationing machine politics
ex11 — Recruit a spoiler 2 → 3 The attack, run as a strategy exercise across three counting rules
Scenario 1 / 2 / 3 3 Spoiler · bloc-leader-wins-anyway · outsider-truly-wins — the three outcomes side by side
Residual vote splitting — The concept page behind 05a/05b

A caution on reuse: two chocolate-vs-vanilla elections now exist — the 100-voter 02 and the 7-friend 08a. Under the house one-election-per-page rule they must never appear on the same page. Lead with 08a (smaller, BV-backed, and the 101 set-piece); 02 is the one to reach for when you specifically want percentages out of 100.

Three different things are called "vote splitting" — say which one you mean

This trips up more reading than any other thing on the topic, and a room that has googled the term beforehand may arrive with the wrong one. All three are real, all three are called vote splitting in print, and only the first is what this page teaches.

The name What it actually is Where you meet it
1 Vote splitting / the spoiler effect Similar candidates dividing one pool of supporters under a one-mark ballot This page. Election-reform writing
2 Split-ticket voting One voter choosing different parties in concurrent races — the German two-vote ballot, mixed-member systems Political-science literature: Pappi & Thurner, Gschwend, Bochsler, Plescia, Bugarin
3 Splitting electoral votes A state allocating its electoral votes by district instead of winner-take-all Nebraska and Maine (Nebraska Public Media)

Sense 2 has a large, serious empirical literature — ecological inference, coalition insurance, strategic ticket-splitting in mixed systems — and none of it is about spoilers. A reader who follows a citation trail from this page into that literature will end up somewhere entirely different and think they have found the academic treatment of our topic. If you cite academic work on vote splitting, check which sense it uses first.

Where to send people next

Sourced by tier, with the lean stated — house rule: match the source to the claim, and disclose the advocacy where it exists.

Best on-ramps for someone who has never thought about this

  • CGP Grey — Why Your Vote Doesn't Count — the animal-kingdom framing. Using animals instead of politicians sidesteps partisan defensiveness entirely, which is why it remains the single best cold-open for a general audience.
  • Teach With TVW — Ever heard of 'Vote Splitting'? — sixty seconds, from a public-affairs broadcaster rather than a reform group. The only non-advocacy video on this list, which makes it the safest thing to hand a skeptical audience.
  • Nicky Case — To Build a Better Ballot — an interactive explorable with draggable voters and candidates on a 2-D ideological plane, simulating Choose-One, Approval, Borda, RCV-IRV and Score. The gold standard of the genre, and the closest thing to letting someone play with a spoiler.
  • Ka-Ping Yee's voting simulations — the "Yee diagrams": 2-D win-zone maps showing how a centrist is crushed under plurality and preserved under Condorcet and score methods. (The original host is currently down — Wayback link. The repo's own spatial voting model page covers the same ground.)

Reference — neutral or definitional

Advocacy sources — useful, lean stated

Two definitions worth borrowing — with one correction

The Equal Vote / STAR Voting glossary wording is clean and worth reusing:

Vote splitting — like-minded voters end up split between two or more similar candidates, often causing both to lose to a candidate less preferred than either.

Spoiler effect — a losing candidate draws votes away from one who would otherwise have won; the election is "spoiled" if it elects someone less preferred, or opposed by a majority.

Both are good. But the glossary continues that STAR and Approval are "immune to vote-splitting", and that is stronger than this repo's own evidence supports. Use this instead:

STAR and Approval remove forced vote splitting — a voter is never made to choose between allies. A faction can still split itself by bullet-voting, as 05a shows and 05b cures. The difference from choose-one is that the remedy is in the voters' hands.

Saying "immune" wins the sentence and loses the argument the first time someone finds 05a. Our own case file is the reason to say the narrower thing — and being the people who volunteer the limit is worth more than the adjective.

The FairVote claim-check — what to concede and what to correct

If someone brings FairVote's spoiler article to the discussion, concede three things immediately, because all three are correct:

  • Don't blame the third-party candidate — "the problem isn't with the candidate, it's with our elections." This repo agrees completely.
  • Spoiler ≠ IIA. They are genuinely different, and reform advocates do conflate them.
  • RCV-IRV does prevent the classic vote-splitting spoiler. Our own ranked race in BV2293 ↗ elects Gala.

Then the one claim that does not hold: "Palin did not spoil the race for Begich, because she did not split the Republican vote." Alaska 2022's own cast vote record says otherwise (Clelland et al., arXiv:2303.00108) — Begich beat Peltola head-to-head 87,859 to 79,451, and was eliminated anyway for holding too few first choices while the Republican-leaning vote was divided with Palin. That is vote splitting deciding an elimination order, which is FairVote's own definition applied to their own example. The article's rebuttal — that many Begich voters ranked Peltola second — shows the electorate was not cleanly partisan, which is true and does not rescue the claim.

The deeper move to name, politely: the article defines "spoiler" narrowly enough ("votes in a majority bloc splintered between several candidates") that no real electorate, which is never cleanly blocked, can ever qualify. A definition that cannot be satisfied by any actual election is not a definition worth defending. The repo's worked count is Alaska 2022; the standing pattern for this kind of response is FairVote's Condorcet article, counted.