1. The eight methods, tested one by one
Each method's rule in one sentence — then click a row or "Details" for a slightly longer explanation of how it works.
You place a single cross next to one name. Whoever collects the most crosses wins — even with just one voter in four behind them. The gesture is unbeatably simple, but everything hinges on that one choice: there's no way to say "I prefer X, but if X can't win, I prefer Y" — that's the trap of tactical voting.
A single cross, on a single name. Nothing else to do.
① First-past-the-post (one round)
10/20✅ Maximum simplicity and robustness: one cross, one pile, one count.
⚠️ Flattens all nuance: spoiler effect, tactical voting, a winner possible with 25% support.
This is the current system. If no candidate clears 50% in the first round, only the top two face off in a second. The final head-to-head gives the winner clear legitimacy, but your favourite can be eliminated as early as round one because of a "spoiler effect" — a similar candidate splitting the vote.
If no one passes 50% in the first round, the top two run again, alone.
② Two-round runoff — the current French system
11/20✅ The legitimacy of the final head-to-head.
⚠️ Non-monotonic (voting more for a candidate can make them lose) and the majority's favorite can be eliminated in the first round.
You rank the candidates in order of preference. At the count, the last-place candidate is eliminated, and every ballot that ranked them first transfers to the next candidate on that ballot — and so on until someone clears 50%. You can vote sincerely for a minor candidate without "wasting" your vote: it will transfer. The flip side: every elimination means picking the ballots back up, which makes counting locally, station by station, essentially impossible — it has to be centralized.
A full ranking: 1st, 2nd, 3rd choice… If the last is eliminated, the vote moves to the next name down.
③ Instant-runoff voting
9/20✅ Independent of clones, removes tactical voting on the first choice.
⚠️ Non-monotonic and not summable per station: every elimination requires a centralized recount.
You rank the candidates. Each rank is worth a decreasing number of points (1st gets the most, last gets the least), and it's all added up. Unlike instant-runoff, a single pass is enough: the points add up directly, station by station. In exchange, the method is easy to game: ranking your most dangerous rival dead last, even insincerely, hands points to everyone but them.
The same ranking, but each rank is worth points that get added up directly.
④ Borda
9/20✅ Simple to count, favors consensus candidates.
⚠️ The most manipulable: complaisant clones and strategic "burying" of rivals.
You rate each candidate independently of the others, like reviewing dishes at a restaurant. Two candidates can get the same score, or none can get the top score — rating isn't ranking. Simple to count (it's all addition), but the optimal strategy — giving everyone either 0 or 5, never anything in between — drowns out more nuanced voters.
An independent rating for each — two candidates can get the same score.
⑤ Score
13/20✅ Expressive; scores escape Arrow's framework.
⚠️ Rewards 0/5 escalation: the sincere voter counts for less than the strategist.
You check every candidate you approve of, with no limit on how many. Whoever gets the most checks wins. Just as simple to count as a single-round election, and with no spoiler effect: approving one more candidate takes nothing away from the others. The limit: a plain yes/no expresses no intensity — there's no way to say you slightly prefer X over Y if you approve of both.
Tick as many candidates as you like — approving one takes nothing away from another.
⑥ Approval
15/20✅ Simple, robust to the spoiler effect and to clones.
⚠️ Binary: ignores the intensity and order of preferences; the first choice of 51% can lose.
You give each candidate a grade, from "Excellent" to "To reject" — like a school report card. The winner is whoever's middle grade (the median) is best, not the average. More robust than an average against isolated extreme opinions, but a coordinated bloc of voters grading everything "Excellent" or "To reject" can, at scale, shift that median.
A grade, like a school report — from "Excellent" to "Reject".
⑦ Majority judgment
14/20✅ Expressive: mentions convey the perceived quality of each candidate, not just an order.
⚠️ Heavier tally by grade; at scale, a polarised bloc grading everything Excellent/To reject can shift the median.
You rank your 5 favourite candidates. The count compares every pair of candidates like a series of small duels: between X and Y, who was placed ahead by more voters? Whoever beats every other candidate in a head-to-head wins — the method most faithful to the collective preference. The cap at 5 candidates (instead of 12) serves both the voter (ranking 5 favourites is reasonable, ordering 12 candidates one by one is a much heavier cognitive load) and the count (fewer ranks to mark means fewer marks to read and check) — without changing the way the matchup matrices add up, just as easily at 12 as at 5.
Your 5 favourites, in order. The count deduces every head-to-head duel from that.
⑧ Top 5 method (Condorcet-Schulze)
17/20✅ The only one guaranteed to elect the Condorcet winner; the relative ranking removes tactical voting (ranking your true favourite costs nothing); matrices published, summable, re-checkable by all.
⚠️ A more demanding ballot than a single cross; when there's a cycle (rare), Schulze's tie-break has to be explained.
2. Which voting system is best? (the comparison)
Each method is scored on 10 simple criteria, 0, 1 or 2 points each — a total out of 20. A starting point for debate, not a verdict: challenge it.
🧭 The comparison method
Ten criteria, 0 to 2 points each (0 = a clear-cut flaw, 2 = the method genuinely does well), a total out of 20. Hover any score in the table to read its justification case by case — nothing is given without an explanation.
The ballot is filled in without mistakes.
The share of opinion the ballot captures.
Countable by hand, in public.
Local results add up into a verifiable national total.
Does an added mark leave a trace?
Elects, when one exists, the candidate who beats every other in a matchup.
A minor candidate doesn't flip the front-runners' matchup.
Two near-identical candidacies don't sabotage each other or cheat as a team.
Voting sincerely for your favourite must not help your worst adversary.
Ranking a candidate higher can't make them lose.
| Method | ✍️ | 🗣️ | 🤲 | ➕ | 🛡️ | 🏛️ | 🎭 | 👥 | 🗽 | 📈 | /20 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| ① First-past-the-post (one round) | 2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | 10 |
| ② Two-round runoff — the current French system | 2 | 0 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 0 | 11 |
| ③ Instant-runoff voting | 1 | 2 | 0 | 0 | 1 | 1 | 1 | 2 | 1 | 0 | 9 |
| ④ Borda | 1 | 2 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 2 | 9 |
| ⑤ Score | 1 | 2 | 1 | 2 | 1 | 0 | 2 | 2 | 0 | 2 | 13 |
| ⑥ Approval | 2 | 1 | 2 | 2 | 1 | 0 | 2 | 2 | 1 | 2 | 15 |
| ⑦ Majority judgment | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 14 |
| ⑧ Top 5 method (Condorcet-Schulze) | 1 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 17 |
👆 Hover or tap a score to read its justification.
🏛️ Why no voting method scores 20/20
It is mathematically proven (Arrow's theorem, 1951): with three or more candidates, no voting method can tick every box at once. Choosing a voting method means knowingly choosing which flaws you accept — the scale below shows which ones.
🎯 Why does only method ⑧ cap the ranking at 5 candidates out of 12?
See how each method treats the 12 candidates:
| Method | How many candidates does it rank? | Why |
|---|---|---|
| ① First-past-the-post | A single cross | The number of candidates in the race doesn't change the gesture. |
| ③ Instant-runoff voting | All 12, in full | One elimination round at a time: ranking 12 or 5 changes nothing to the mechanics, only the effort asked of the voter grows. |
| ④ Borda | All 12, in full | Each rank is worth a point that decreases down to 1: over 12 ranks, the scale simply runs from 12 down to 1 instead of 5 down to 1. |
| ⑧ Top 5 method | 5 out of 12, by choice | Ranking 5 favourites fits in the voting booth, in a few seconds; ordering 12 candidates, one by one, is a much heavier cognitive load. |
The cap at 5 also serves the count, not just the booth: fewer ranks to mark means fewer marks to read and check for the counting officer — which limits reading errors during the count. What doesn't change: the number of passes (still a single one, like 6 of the other 7 methods — detail just below, in "Hand-counting") and the way the matrix adds up, cell by cell, whether the ballot carries 5 or 12 ranks.
🖐️ Hand-counting: what actually costs time
The real hand-counting challenge isn't the number of methods: it's how many times the same ballot has to be picked back up, and how long it takes the counting officer to read a mark without a mistake. This is the same "🤲 Manual count" score from the table above, with the same colour code — no need to invent a new one:
| Method | In the booth | At the count, per ballot | Passes | Complexity |
|---|---|---|---|---|
| ① One round | One cross | One mark | A single one | 2 |
| ② Two rounds | One cross, twice | One mark, twice | One per round | 2 |
| ③ Instant-runoff | A full ranking | Up to 12 marks, read progressively | Several — one per elimination round | 0 |
| ④ Borda | A full ranking | Up to 12 marks converted to points | A single one | 1 |
| ⑤ Score | Twelve scores | Up to 12 scores added up | A single one | 1 |
| ⑥ Approval | Unlimited crosses | Up to k crosses | A single one | 2 |
| ⑦ Majority judgment | Twelve grades | 12 grades counted | A single one | 1 |
| ⑧ Top-5 method | A ranking of 5 | 45 duels inferred, in one matrix | A single one | 1 |
👆 Hover or touch a complexity score to read its justification.
The strengths and limits of each method play out in practice, step by step.