Skip to content

Same opinions, every method — the line-up

The clearest way to see what a voting method is for: hold the voters' honest opinions fixed, change only the counting rule, and watch where each one lands. Nobody changes their mind; the only variable is how much of the ballot the method reads. Line the results up, and the virtues show themselves.

→ Its ballot-side twin — the same voter on three ballot styles: one voter, three ballots. The core distinction underneath both: scores vs. ranks.


One electorate, honest opinions

Five coworkers pick the team lunch — Sushi, Tacos, or Pizza. Everyone scores each option 0–5, honestly (this is the repo's canonical lunch vote, runnable · live on BetterVoting ↗):

Voter Sushi Tacos Pizza
Sofia 5 0 3
Sam 5 0 3
Tara 0 5 3
Theo 0 5 3
Pat 3 1 5

Read it and the shape is plain: two love Sushi, two love Tacos, and everybody is happy with Pizza — nobody scores it below 3. Pizza is the option the whole table can live with; Sushi and Tacos each split the room in half.

The same opinions, as each ballot

Those honest scores contain every other ballot inside them. The voters didn't change — only what the ballot lets them say:

Voter Choose-One (top pick) Ranking (their order) Approval (all they're OK with) Score
Sofia Sushi Sushi › Pizza › Tacos Sushi, Pizza 5·0·3
Sam Sushi Sushi › Pizza › Tacos Sushi, Pizza 5·0·3
Tara Tacos Tacos › Pizza › Sushi Tacos, Pizza 0·5·3
Theo Tacos Tacos › Pizza › Sushi Tacos, Pizza 0·5·3
Pat Pizza Pizza › Sushi › Tacos Sushi, Tacos, Pizza 3·1·5

First choices alone: Sushi 2, Tacos 2, Pizza 1. Notice Pizza looks weakest by first choices — precisely because it's everyone's happy second, not their passion.

The line-up — who wins under each method

Now count the same five ballots every way. (Every winner here is engine-verified on the runnable file above.)

Method What it reads Winner
Choose-One (Plurality) first choices only Sushi
RCV-IRV (Hare) first choices, then eliminate the lowest Sushi
Approval how many are OK with each 🍕 Pizza
Ranked Robin every head-to-head matchup 🍕 Pizza
STAR total scores, then an automatic runoff 🍕 Pizza

What the line-up shows

Three different whole-ballot methods — Approval, Ranked Robin, STAR — independently land on Pizza, the choice the whole table is happy with. The two methods that look only at first choices pick Sushi, which two of the five coworkers rated a flat 0.

Nobody voted strategically. Nobody changed their opinion. The entire difference is how much of the ballot the method reads:

  • Choose-One and IRV decide on first choices, so the broadly-liked compromise — nobody's #1 — never gets its due, and the winner is an option half the room rejected.
  • Approval, Ranked Robin, and STAR read the whole ballot — approval thresholds, every head-to-head, or scores plus a runoff — and each finds the candidate with real, broad support.

That's the case for expressive ballots and whole-ballot counts, in one lunch order: give voters room to say what they think, then count all of it, and the winner is the one a majority is genuinely glad about. STAR and Ranked Robin are two roads to that same destination.


Use this view anywhere

The line-up is a reusable lens, not a one-off. Any election in this library can be run through it — the point is always the same: hold the opinions fixed, vary the count, and let the method reveal itself. Bigger, real-world line-ups: