# Quadratic voting for participatory budgets

What quadratic voting is, why concentrating points costs more and more, an example with three people and four projects, and when to use it in a budget.

2026-10-11 · Cibernatural · Guides · 5 min read

A participatory budget asks residents to split a limited sum between projects. How they vote changes which projects win: with one tick per person, the project with the most supporters wins; with points to distribute, the one that gathers the most intensity wins. Quadratic voting is a variant of point allocation that makes concentrating points cost more and more. This guide explains how it works, with a worked example, and when it fits.

## What is quadratic voting?

Quadratic voting is a point allocation in which giving *p* points to an option costs *p*² credits from each person's budget.

Every voter gets the same credits (16, say). Giving 1 point costs 1 credit; 2 points cost 4; 3 cost 9; 4 cost 16. Points can be spread across several options, and what counts towards the result are the **points**, not the credits spent. Steven Lalley and Glen Weyl formalised it in 2018, and Weyl popularised it with Eric Posner in *Radical Markets*.

## Why is the cost quadratic?

Because every additional point on the same option costs more than the previous one, so whoever wants to concentrate support has to give up a say on everything else.

With 16 credits, 4 points on a single project use the whole budget; 2 points on each of four projects also cost 16 but add up to 8 points. The rising cost means the number of points someone puts on an option reflects how much it really matters to them, without a small but intense minority sweeping the vote by going all in. That is the difference from linear (cumulative) allocation, where 16 credits are 16 points to place however you like.

## How is it counted?

The points each option receives are added up; the option with the most points wins, and the credits spent only constrain the ballot.

An example with three people, four projects and 16 credits each.

With **linear allocation** (16 points placed freely):

| Person | Park | Library | Street lighting | Bike lane |
|---|---|---|---|---|
| 1 | 8 | 2 | 4 | 2 |
| 2 | 0 | 16 | 0 | 0 |
| 3 | 9 | 0 | 5 | 2 |
| **Total** | **17** | **18** | **9** | **4** |

The library wins, wanted by only one person, because that person put everything there.

With **quadratic voting** (16 credits; each point costs its square):

| Person | Park | Library | Street lighting | Bike lane | Credits |
|---|---|---|---|---|---|
| 1 | 3 | 1 | 2 | 1 | 9 + 1 + 4 + 1 = 15 |
| 2 | 0 | 4 | 0 | 0 | 16 |
| 3 | 3 | 0 | 2 | 1 | 9 + 4 + 1 = 14 |
| **Total** | **6** | **5** | **4** | **2** | |

The park wins: two people back it strongly and the third does not reject it. The library still has very intense support, but the quadratic cost limits how much a single person weighs.

## When does it make sense in a participatory budget?

When there are several small projects and you want broad support to win rather than the best-organised group, and when voters can spend a minute distributing points.

It fits neighbourhood budgets, improvement plans for a residents' association or a club, and prioritising a list of proposals that have already passed a technical filter. It does not fit a single yes-or-no decision, nor an electorate that will not understand the rising cost: the explanation on the ballot matters as much as the method.

## What are its limits?

It requires one vote per person (anyone who votes twice doubles their credits), rewards those who understand it and is vulnerable to groups that coordinate their ballots.

That is why it is usually combined with a verified identity (account, invitation or voter roll) and a clear explanation: "each additional point costs more". Coordination (several people dividing the options between them to dodge the cost) cannot be ruled out entirely, but the larger the turnout, the less it weighs.

## Where has it been used?

The best-known case is the Democratic caucus of the Colorado House of Representatives, which in 2019 used quadratic voting to prioritise the bills it would fund.

Each legislator received 100 credits to spread across more than a hundred proposals; the method made visible which bills had broad support versus those backed only by their sponsor. It has also been used in civic hackathons in Taiwan and in software communities to prioritise requests.

## How do you do it on GloboPoll?

Create a points poll, choose the quadratic method, the credit budget and, if you want, a cap on points per option.

The **points** type is part of the Pro plan and supports both methods: linear sum and quadratic. The budget ranges from 1 to 1000 and is set when the poll is created; it cannot change once there are votes, because a different budget would make ballots incomparable. The ballot shows how many credits remain and what the next point costs; the results show each option's points, its share and how many ballots back it. To enforce one vote per person you can require an account, a verified email or [single-use invitations](https://www.globopoll.com/en/blog/six-poll-types). All nine types are in [Nine poll types](https://www.globopoll.com/en/blog/six-poll-types) and the Pro plan is on the [pricing page](https://www.globopoll.com/en/pricing).

## Sources

- Steven P. Lalley and E. Glen Weyl, "Quadratic Voting: How Mechanism Design Can Radicalize Democracy", *AEA Papers and Proceedings*, vol. 108, 2018, pp. 33-37.
- Eric A. Posner and E. Glen Weyl, *Radical Markets*, Princeton University Press, 2018, chapter 2.
- [Colorado Tried a New Way to Vote: Make People Pay—Quadratically](https://www.wired.com/story/colorado-quadratic-voting-experiment/), *Wired*, 2019.
- [Quadratic voting](https://en.wikipedia.org/wiki/Quadratic_voting), Wikipedia.

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Source: https://www.globopoll.com/en/blog/quadratic-voting-for-participatory-budgets