(NOTE: This is a British remix of Nicky Case's lovely “To Build a Better Ballot” (2016), which is public domain. Nicky did the hard part — the art, the code, the wisdom. I've just swapped in UK examples, added proportional representation, and updated things for 2026. Enormous thanks, Nicky. <3)


This is not really about the last election, where Labour got 63% of the seats on 34% of the vote. Not just that, anyway.

First, I need to explain a weird glitch in how we vote. Let's say there are two candidates, Steven Square and Tracy Triangle , on a couple of political axes. (For example, “left vs. right” and “more state vs. less state”.) Let's also say there's a voter who simply votes for whose political position is closest. What would that look like?

click & drag
the candidates and the voter:

It's a tough choice. Triangle's got some sharp points, but Square understands more sides! Alas, on a UK ballot paper, you can only put your X next to one name.

Of course, there's more than one voter in a constituency. Let's simulate what an election looks like with 100+ voters.

drag the candidates & voters around.
(to move voters, drag the middle of the crowd)
watch how that changes the election:

Now let's consider a different election. Say Tracy Triangle is already winning, and a third candidate, Henry Hexagon , turns up. (Hexagon's supporters like how he tackles problems from more angles.) Hexagon takes a political position close to Triangle's — they're fishing in the same pond.

Now, you'd think giving voters more of what they want shouldn't make things worse, right? Well...

at first, beats .
drag to just under ,
and see what happens:

That's right. Steven Square, our least popular candidate, now wins! When two similar candidates stand, they “split the vote” between them, and a third candidate most people didn't want sneaks through the middle.

This is called the spoiler effect, and in Britain it is the everyday weather of politics. On the right, Conservative and Reform can split a seat between them. On the left, Labour, the Liberal Democrats and the Greens can split one too. Whichever “side” you're on, the system can punish you for having more than one party you like.

Which is why so many Britons “vote tactically” — not for their actual favourite, but for the least-bad candidate who can realistically win their seat. There are whole websites devoted to telling you how to hold your nose. We even have a phrase for it: the “wasted vote.”

But this is not about any single party.

This is about designing a democracy that people can trust.

Turnout at the 2024 general election was under 60% — one of the lowest since universal suffrage. Millions live in “safe seats” that haven't changed hands in living memory, where a vote for anyone else feels pointless. Trust in politics, by the government's own surveys, is at a record low. That's bigger than any one ballot paper — but the ballot paper is a good place to start.

Fixing it won't be as daunting as fixing party funding, or the Lords, or anything else. It mostly requires changing a piece of paper — and how we count those pieces of paper.

Let's talk about how to build a better ballot.

Now, some of you may have a couple of objections!

First objection: why would the people in power change the system that got them there? Well, the spoiler effect has bitten every big party at some point — ask the Conservatives about Reform, or Labour about the SNP. Getting rid of the glitch could be a win for major and minor parties. And reform isn't unthinkable here: in 2011 the UK actually held a national referendum on changing how we vote. (More on that in a moment.)

Second objection: didn't some clever clogs prove that all voting systems are unfair? You're thinking of Arrow's Impossibility Theorem — but two answers: 1) some systems are still fairer than others, even if none are perfect; and 2) Arrow's proof only applies to systems where you rank candidates. We'll meet systems where you don't rank at all.

But first, let's look at the system we actually use:

FIRST PAST THE POST (“CHOOSE ONE”)

same as before. click & drag
the candidates and voter

How to count: Add up the votes. Whoever gets the most wins. This is what we use for the House of Commons and English council elections.

Simple — but, as you saw, it leads to the spoiler glitch, and pushes people into voting for the lesser of two evils. And ask yourself: how can we expect our politicians to be honest with us, when our voting system won't let us be honest with it?

So, to fix the spoiler effect, people have suggested alternatives. Such as...

THE ALTERNATIVE VOTE (RANK THEM)

again, click & drag

How to count: Instead of one X, you rank the candidates: 1st, 2nd, 3rd. Then:

  1. Count everyone's 1st choices.
  2. If someone has more than 50%, they win! END.
  3. If not, eliminate the last-place candidate.
  4. Their ballots transfer to those voters' next choice.
  5. Repeat until someone has more than 50%.

This is the most famous alternative to First Past the Post. Australia uses it for its lower house; the Republic of Ireland uses it for the presidency. British parties already use it to elect their own leaders. And in 2011, the UK held a referendum on switching the Commons to the Alternative Vote — which was rejected, roughly 68% to 32%.

(One system, several names: what Britain calls the “Alternative Vote” is the exact same thing Americans call “Ranked-Choice Voting” and mathematicians call “Instant-Runoff Voting”. Same ballot, same count — just different labels.)

The Alternative Vote kills the classic spoiler effect — but, as we'll see, it has a glitch of its own. So people have looked at systems where you don't rank at all:

APPROVAL VOTING (“CHOOSE MANY”)

yup, stiiiiill click & drag

How to count: Tick every candidate you'd be happy with — as many as you like. Add up the ticks. The candidate with the most ticks wins.

Wait, picking more than one? Doesn't that break one-person-one-vote? Not really — your vote was never a single X, it was always the whole ballot paper. Here you simply get to say which candidates you approve of, instead of guessing which one is “electable”. Best of all: it'd work with the exact same ballot boxes and pencils-on-strings we already have. The only change is the instruction at the top, from “vote for one” to “vote for as many as you like”. (For the in-depth UK case, see proportional.uk on single-winner approval.)

So that's our shortlist: the system we use, plus two alternatives. But how can we tell if they're actually better? What glitches might they have? Let's simulate them.

Remember that spoiler simulation from earlier? Here it is again — but now you can switch between the three voting systems. See how each one copes with a potential spoiler:

drag to just under to create a spoiler.
then compare the three voting systems:
(note: in the rare case of a tie, a winner is picked at random)

As you can see, both alternatives shrug off the spoiler that breaks First Past the Post. So — job done? Just pick one and go home?

Alas, no. In curing one glitch, the Alternative Vote picks up another. Below, Tracy Triangle is already winning — and you're going to make her even more popular by dragging voters towards her. Obviously, becoming more popular can't make a winner lose... right?

You can probably guess where this is going...

drag the voters slowly up towards :

What happened? Originally, is knocked out first, so faces a weaker and wins. But once you move voters closer to , the order of elimination changes: now is knocked out first, so faces a stronger — and loses.

Under the Alternative Vote, a winning candidate can lose by becoming more popular. Mathematicians call this a failure of “monotonicity”, and estimate it could happen in a meaningful chunk of competitive elections. It's also hard to audit, because councils rarely publish enough detail to re-run the count. Not ideal, in an age when trust is the whole point.

So every single-winner method has its trade-offs. But here's the thing that matters most for Britain — and it's easy to miss:

Every system so far elects just one winner per seat. They argue about how to crown that single MP. But even a “perfect” way of picking one winner per constituency does nothing about the real British problem...

...which is what happens when you add up 650 separate little elections.

At the 2024 general election, Labour won about a third of the votes — and nearly two-thirds of the seats. Reform UK won more than 4 million votes (~14%) and got 5 seats. The Greens won nearly a million votes and got 4. The Liberal Democrats won fewer votes than Reform, but — because their support was geographically concentrated — won 72 seats. The same had happened in reverse before: in 2015 the SNP swept Scotland on a fraction of the UK vote, while UKIP's 3.8 million votes returned a single MP.

This isn't a complaint about any one party — the distortion lands on the right one decade and the left the next. It's a property of the system: First Past the Post rewards votes that are concentrated and throws away votes that are spread out. No amount of cleverness in counting a single seat can fix that.

To make seats match votes, you need a fundamentally different idea. You need proportional representation.

Here's the key move. Instead of carving the country into 650 tiny areas that each elect one MP, you draw bigger areas that each elect several MPs together. Then you share out those seats so the mix of winners reflects the mix of voters.

If a region is 40% one way, 30% another, and 30% a third way, a proportional system returns representatives in roughly those proportions — instead of one side taking everything.

This is not exotic, foreign or untested. The UK already votes proportionally for the Scottish Parliament, the Senedd (Welsh Parliament), the Northern Ireland Assembly, Scottish councils, and the London Assembly. Only Westminster and English councils still cling to choose-one.

And here's the lovely part: each of the three ballots you just met has a proportional big sibling. Same ballot paper in your hand — you just fill several seats at once, and share them out fairly. Let's take them in turn.

PARTY LIST

1. Choose one → Party List. Take the simplest ballot — one X for one party — and instead of giving the whole area to the single biggest party, hand out the seats in proportion to the votes. Win a third of the votes, win about a third of the seats. That's it.

drag the parties & voters around.
watch a 650-seat parliament split up in proportion:

You may have voted this way already: Great Britain used a party-list system for European Parliament elections from 1999 to 2019. And from the 2026 election onward, the Senedd switches to a fully proportional party-list system — 96 members, six per area. The one catch with a closed list is that the party ranks its own candidates, so you trust the party with who actually gets in. Which is exactly what the next method fixes...

SINGLE TRANSFERABLE VOTE

2. Rank them → Single Transferable Vote. Take the ranked ballot from the Alternative Vote, but now several seats are up for grabs. A candidate wins as soon as they reach a quota — the fair share of votes needed for one seat. The clever bit: if your favourite gets more votes than they need, the surplus flows to your next choice; and if your favourite has no hope, your vote flows on too. Your vote keeps looking for somewhere useful to land, so hardly any is wasted.

again: drag things around and change the seats.
the caption shows the quota, and who's elected:

This is the proportional system Britain knows best: it elects the Northern Ireland Assembly, every one of Scotland's councils, and the Dáil in the Republic of Ireland. Because you rank people rather than just parties, you can back a party and pick which of its candidates you actually rate — or rank across party lines entirely. (You'll often see it abbreviated “STV”.)

The counting — quotas, surpluses and transfers — has a lot of moving parts. If you really want to get into the nitty-gritty, this superb deep-dive on the Single Transferable Vote walks through it step by step.

PROPORTIONAL CHOOSE MANY (Proportional Approval)

3. Choose many → Proportional Choose Many. Take the approval ballot — tick everyone you'd be happy with — and fill the seats one at a time. Elect the most-ticked candidate, then turn down the volume on every ballot that already helped elect someone, so the same bloc can't grab every seat in a row. Smaller groups get their fair turn. (The formal name is Proportional Approval Voting; it's the proportional cousin of choose-many.)

same easy tick-box ballot — but now it fills several seats,
and shares them out so every group is heard:

It's the simplest of the three to vote in — the ballot is just ticks — and it needs no parties at all, which makes it a favourite of voting-reform nerds. It isn't yet used for big public elections, but it shows how little you have to change the ballot to get a proportional result. (For the in-depth UK case, see proportional.uk on proportional approval.)

Because it uses a different idea of “useful support,” Proportional Approval can pick a different set of people from STV. STV follows each ranked vote as it transfers through a quota count: elect candidates with enough first-choice support, move surpluses, and eliminate candidates from the bottom. PAV looks at all the candidates each voter ticked, then weakens ballots that have already helped elect someone. So STV is very sensitive to ranking order and transfer paths, while PAV rewards candidates who are broadly approved by voters whose voices have not yet been used much. Both are proportional; they can disagree about which individuals best represent the same proportional mix.

Want to put all three side by side? Here they are on one playground — switch between them and watch the same voters produce three (often similar!) proportional parliaments:

switch between Party List, Single Transferable Vote
and Proportional Choose Many, and change the seats:

None of these is a free lunch, and it's only fair to say so. Proportional parliaments tend to mean coalitions and compromise rather than one party steamrolling everything — grown-up consensus or backroom horse-trading, depending on your mood. Closed party lists hand power to the parties; transferable-vote counts take longer. The honest pitch isn't “proportional representation is perfect.” It's that it keeps a promise the current system simply can't: if a third of people vote for something, they get about a third of the seats.

ahem

DEAR ANDY “KING OF THE NORTH” BURNHAM
(and everyone else in Britain who wants their vote to count)

Thank you for being one of the few big names willing to say it out loud. We've known for a long time that First Past the Post forces voters to be dishonest, manufactures a “lesser of two evils” choice, leaves millions stranded in safe seats, and hands out majorities that the vote totals never justified.

If the only choice on the table is First Past the Post versus the Alternative Vote — the 2011 question — then sure, the Alternative Vote is a small step up. But Britain already said no to it once, and it's still a single-winner system: it tidies up one constituency while leaving the national mismatch between votes and seats completely intact.

The bigger prize is proportionality. And we don't have to imagine it — Scotland, Wales and Northern Ireland already vote proportionally, and the sky has stayed up. Personally, I lean towards Proportional Choose Many (proportional approval): it carries none of the complexity or baggage of the Alternative Vote the country already rejected — the ballot is just ticks. But honestly, which proportional system we pick matters far less than people think: they're all proportional, so every one of them is dramatically fairer than what we have now. Choose whichever you like best, and let's get on with it.

And where we do keep single-winner contests — by-elections, mayors, police commissioners, the odd lone council seat — we should switch them to plain Choose Many approval voting: fair, competitive, spoiler-proof, and (since the country already turned down ranking) about as gentle a change as a ballot paper can take. Better still, it keeps both ballots consistent: tick the candidates you like to fill one seat, tick the candidates you like to fill several. One simple habit, every election.

I won't pretend to know the One True System — partly because the social-choice nerds will descend on me if I do, and partly because we genuinely learn most by trying things. All the more reason for councils, mayors and devolved nations to keep experimenting.

Because keeping that discussion going is what democracy is. Support for democracy itself has wobbled across the West, and ours is no exception. There's no One Weird Trick to fix that. But showing people that the system will actually respond to them — that a vote, any vote, finally counts — is a pretty good place to start.

Because this isn't really about building a better ballot.

It's about building a better democracy.

<3,
~ Felix Sargent, June 2026


P.S. Since you played all the way through, here's a bonus: a full “Sandbox Mode” with every method in this piece — single-winner and proportional — up to 13 candidates, and a save-and-share link. Have a tinker!

SANDBOX MODE! (link to just this)

Pick any method — the single-winner ones (First Past the Post / choose-one, the Alternative Vote, choose-many) or the proportional ones (Party List, the Single Transferable Vote, Proportional Choose Many) — add candidates, drag voters into clusters, change the number of seats, and watch what each system does. Hit save for a link you can share.

PUBLIC DOMAIN
Zero rights reserved. Like the original, this remix is free for everyone — teachers, mathematicians, hobbyists, campaigners, and policy wonks. Use it, copy it, rip it apart, make it better.
WITH ENORMOUS THANKS TO
NICKY CASE

This entire thing — the words, the art, the playful little draggable voters, the whole “explorable explanation” format — is built on Nicky Case's “To Build a Better Ballot” (2016). Nicky released it into the public domain so that people exactly like us could remix it for our own countries and our own times. So: thank you, Nicky, for the generosity and the genius. Go and explore the rest of Nicky's work — it's wonderful.

ON THE SHOULDERS OF GIANTS

The proportional methods here were inspired by the Smart Voting Simulator by Paretoman, another remix of Nicky's original that dives deep into proportional representation. And Nicky's original was itself inspired by Ka-Ping Yee's voting visualisations (2005) and Bret Victor's “Ladder of Abstraction” (2011). You can learn more about Explorable Explanations here.

“BUT WHAT CAN I DO?”

If you're in the UK and this got you fired up, these folks campaign for fairer votes (they don't always agree on which system is best, but they all want to fix the one we've got): the Electoral Reform Society, Make Votes Matter, Unlock Democracy, Fairvote UK, and Open Britain. You can also just write to your MP — they do read it.

If you're a teacher: this is public domain — use it freely in class. If you're a coder: remix it. If you're neither: share it with someone who needs convincing.

MADE IN BRITAIN,
STANDING ON NICKY'S

betterballot.uk — a public-domain remix.

The maths of voting is universal.
The examples here are British,
and current as of 2026.

Spotted a mistake, or have a better example?
Brilliant — it's public domain, so go and fix it.

sharing is caring!