Diverse voters casting ballots with multiple checkmarks, symbolizing the power of approval voting.

Beyond First Past the Post: Can Approval Voting Fix Our Broken Elections?

Rhea Morgan in Politics & Policy June 2025 • 3 min read.

"Explore Eneström and Phragmén's method and discover how it could revolutionize parliamentary elections by allowing voters to approve multiple candidates, fostering fairer representation and potentially curbing political polarization."

For decades, the 'first past the post' system has dominated parliamentary elections, often resulting in strategic voting where individuals feel compelled to pick the 'lesser evil' rather than their preferred candidate. This can lead to skewed representation, political polarization, and voter apathy as people feel their voices aren't truly heard.

But what if there was a better way? What if voters could express their support for multiple candidates, ensuring that elected officials truly reflect the diverse preferences of the electorate? This is the promise of approval voting, and at the forefront of this movement are the methods of two Swedish mathematicians from the early 20th century: Gustaf Eneström and Edvard Phragmén.

While Phragmén is known for his iterative minimax method, the combined Eneström-Phragmén approach offers a unique twist. Instead of focusing solely on minimizing the maximum disadvantage, it begins with a pre-defined quota – the number of votes needed to secure a seat. This foundation in approval voting aims to improve representation, and proportional outcomes in parliamentary elections.

How Does the Eneström-Phragmén Method Work?

Diverse voters casting ballots with multiple checkmarks, symbolizing the power of approval voting.

The Eneström-Phragmén procedure is an iterative method designed to distribute a set number of seats among candidates based on approval voting. Here's a breakdown:

At each step, a seat is allocated to the candidate with the highest number of approval votes from eligible voters.

Voters express approval for multiple candidates, not just one.
A quota is pre-determined, representing the number of votes needed to win a seat.
The method proceeds iteratively, allocating seats one at a time.
After each seat allocation, the value of votes used is adjusted based on a pre-defined quota.

This process continues until all seats are filled, and this adjustment of vote value ensures a proportional outcome reflecting voter preferences across the board. The properties of this method can be summarized as follows:

Is Approval Voting the Answer?

The Eneström-Phragmén method provides a compelling alternative to traditional 'first past the post' systems, offering a pathway towards more proportional and representative election outcomes. While challenges and variations exist, the core principle of empowering voters to express approval for multiple candidates holds the potential to revitalize democratic processes and foster greater political engagement.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

Everything You Need To Know

What is approval voting, and how does it differ from 'first past the post' systems?

Approval voting allows voters to express support for multiple candidates, unlike the 'first past the post' system where voters choose only one candidate. This difference is crucial because it reduces strategic voting, where individuals feel pressured to vote for the 'lesser evil.' Approval voting, particularly when implemented with methods like those of Eneström and Phragmén, aims for more proportional representation, ensuring that elected officials reflect a broader range of voter preferences and potentially curbing political polarization.

Who were Gustaf Eneström and Edvard Phragmén, and what role did they play in the development of approval voting methods?

Gustaf Eneström and Edvard Phragmén were Swedish mathematicians who pioneered methods for approval voting. Eneström-Phragmén's approach is a unique iterative method that allocates seats based on the number of approval votes a candidate receives, using a pre-defined quota to determine how many votes are needed to win a seat. Their work laid the groundwork for more proportional and representative election outcomes compared to traditional systems.

How does the Eneström-Phragmén method work to allocate seats in parliamentary elections?

The Eneström-Phragmén method is an iterative process. Initially, voters express approval for multiple candidates. A quota, representing the votes needed for a seat, is pre-defined. The method then allocates seats one at a time to the candidate with the most approval votes. After each allocation, the value of the votes used is adjusted based on the quota. This continues until all seats are filled, ensuring a proportional outcome.

What are the potential benefits of using approval voting with the Eneström-Phragmén method in elections?

The Eneström-Phragmén method offers several potential benefits. It can lead to more proportional and representative election outcomes by allowing voters to support multiple candidates. This can decrease strategic voting and voter apathy. The method aims to ensure that elected officials better reflect the diverse preferences of the electorate. This approach may also mitigate political polarization by encouraging broader support and representation.

Why is the traditional 'first past the post' system often criticized, and how does approval voting address these criticisms?

'First past the post' systems are often criticized for leading to skewed representation, where the elected officials don't accurately reflect the diverse preferences of the electorate. This system frequently encourages strategic voting. Approval voting, particularly when using methods like those developed by Eneström and Phragmén, addresses these issues by enabling voters to support multiple candidates. This fosters a more proportional representation, reduces the need for strategic voting, and potentially increases voter engagement and satisfaction with election outcomes.