Same election · Same voters · Different winners

The voting-method simulator

The same voters, the same preferences… and yet, depending on the counting method, the winner changes. That’s neither a glitch nor a trick: it’s a mathematical property of voting. Which is exactly why it deserves a debate — so we can choose our method together. That’s reform #3 of the PACTE.

1. The classroom election

An imaginary village elects its town hall. Five candidacies, deliberately neutral — no connection to any real party. 100 voters, whose preferences we know perfectly: this is our laboratory.

Ms. Blue

restore the fountain

Mr. Green

plant an orchard

Ms. Yellow

open a kiosk

Mr. Purple

expand the market hall

Ms. Pink

start a community garden

🧪 The electorate is fully visible. Each line is a “profile”: a group of voters who rank the candidates in the same order. Move the sliders: the whole page recalculates live — every method, every count, every winner. The total always stays at 100 voters: when one profile goes up, the surplus is taken from the profiles below it, one at a time (the last row draws from the first). Profiles above don't move — your settings stay put.

2. The eight methods, tested one by one

For each method: the rule in one sentence, then the step-by-step count on the electorate above, the winner, and an honest review of its strengths and limits. None of them is “the right one”: the simulator shows, the debate will decide.

🗂️ The same electorate, eight different ballots

Each voter profile above is a list of preferences — from favorite candidate to least liked. For each method, the simulator derives the matching ballot. In short:

Method	What your ranking becomes
① One round	Only your 1^st choice is kept — the rest is ignored.
② Two rounds	Your 1^st choice in round one; in round two, your preferred of the two finalists.
③ Instant runoff	Your full ranking, read top to bottom for the vote transfers.
④ Borda	Your full ranking, converted into points: 4, 3, 2, 1, 0.
⑤ Score	Your rank becomes a score: 1^st = 5/5, then 4, 3, 2, last = 1/5.
⑥ Approval	You approve your top k choices (k is adjustable in the tab).
⑦ Majority judgment	Your rank becomes a grade: 1^st = “Very Good” … last = “To Reject.”
⑧ Condorcet	Your full ranking, compared matchup by matchup (who comes first?).

⚠️ This is a deliberate simplification: in real life, a voter may approve or grade differently from what their ranking suggests. The simulator compares counting methods, not voting psychologies.

3. One election, five winners

The same electorate, eight counts — and here is who wins. This table recalculates when you move the sliders.

None of these results is “rigged”: each method honestly applies its rule to the same ballots. So the question isn’t “who cheated?” but “which rule do we want?” — and that question deserves a public debate, then a vote.

4. The known problems — and their answers

Every method has blind spots, documented for two centuries by the mathematicians of voting. Knowing them is already knowing how to answer them.

🎯 Tactical voting and the “spoiler” effect

Under first-past-the-post, voting for your true favorite can hand victory to your worst choice: two similar candidates split their votes, and a third one wins. So many people vote “tactically” rather than sincerely.

Answers: every method that reads the ballot beyond the 1^st choice (rankings, grades, approvals) sharply reduces this problem: you can back your favorite without “wasting” your vote.

🔁 The Condorcet paradox

Sometimes the head-to-head matchups go in circles. Mini-example, 100 voters and 3 projects:

35 rank Fountain > Kiosk > Orchard
33 rank Kiosk > Orchard > Fountain
32 rank Orchard > Fountain > Kiosk

Fountain beats Kiosk (67–33), Kiosk beats Orchard (68–32)… but Orchard beats Fountain (65–35). A cycle: nobody beats everybody.

Answer: a tie-breaking rule, set in advance. Here, the minimax rule: the project whose worst defeat is the smallest wins — Fountain (beaten by 30, versus 34 and 36 for the others). These cycles are rare; what matters is that the rule is known before the vote.

🎭 Strategic manipulation

No method fully escapes calculated voting:

Majority judgment: grading your own side “Very Good” and everyone else “To Reject,” to pull the medians.
Borda: “burying” the most dangerous rival by ranking them last, even if you respect them.
Approval: calculating how far to extend your approvals.

Answers: these strategies require massive coordination to work, and some methods resist them better (Condorcet-style rankings are among the hardest to manipulate). It’s a criterion for the choice to put into the debate, not a reason to give up.

📐 Arrow’s theorem, in two sentences

The mathematician Kenneth Arrow proved that no voting system can be perfect on every desirable criterion at once. Every voting method is therefore a trade-off between qualities that sometimes contradict one another.

That is not a reason to keep the status quo — which is itself a trade-off, and one the citizens never chose. It is, on the contrary, the reason to debate and decide with eyes open: exactly the PACTE’s method.

Answer: since every system is a trade-off, let the people choose theirs — after one month of public debate, by referendum.

🤲 “What about counting by hand?”

All these methods can still be counted by hand, in every polling station, in front of the voters — the transparency of the ballot box is non-negotiable. Some simply call for a little more care:

First-past-the-post (1 or 2 rounds): one pile per candidate — the simplest there is.
Approval: counting check marks, plain additions — as simple as first-past-the-post.
Score voting: adding up scores per candidate — simple, just longer.
Borda: converting each rank into points, then adding — meticulous but mechanical.
Majority judgment: counting the grades per candidate in each polling station; the tables then add up at the national level.
Instant runoff: vote transfers round by round — longer, but done by hand in Australia and Ireland for a century.
Condorcet: each polling station fills in the matchup matrix (10 matchups for 5 candidates); the matrices simply add up.

In every case: paper ballots, poll workers, public results per polling station, verifiable by anyone.

🎲 “What about sortition? And liquid democracy?”

Two other big ideas circulate in debates about democracy. They are not counting methods (they don’t say how to tally ballots), but they deserve to be understood:

Sortition (“lottocracy”): instead of electing representatives, you draw them by lot among citizens, like a criminal-court jury. Strengths: impossible to buy, perfectly representative, open to everyone. Limits: no platform to choose, and legitimacy is built differently. In France, criminal juries have proven for two centuries that randomly selected citizens can settle serious matters. Within the PACTE, this idea is already alive: the citizens’ chamber selected by lot appears among the debate options (organizing RICs, appointing the watchdog authorities).
Liquid democracy: everyone can vote directly or delegate their voice to someone they trust, topic by topic, and take the delegation back at any time. Strength: a flexible dial between direct and representative democracy. Limits: still experimental, and concentrated delegations can recreate notables. A lead for the future, not a prerequisite.

The simulator compares ways of counting votes. These two ideas ask a different question: who decides. The two questions complement each other.

Your turn

You’ve just seen why the voting method is not a technical detail: it is the rule of the democratic game. Reform #3 of the PACTE proposes a month of debate on it, then a decision — by referendum, where the people decide.

📜 Reform #3 and its options 🗳️ Vote on the specimen ballot 🗳️ Create your own vote with these methods ✍️ Support the PACTE