Diverse voters casting ballots into a radiant ballot box.

Voting Made Easy: How the Minimax Method Can Simplify Your Choices

Nico Varela in Politics & Policy August 2025 • 4 min read.

"Tired of complex elections? Discover how the Minimax voting method, enhanced with key axioms, offers a straightforward path to fair decisions."

Voting is a cornerstone of democracy, but let's face it: deciding among multiple options can be a headache. We've all been there – staring at a ballot with too many names or proposals, wondering if our choice will even matter. The good news is, researchers are constantly working to improve voting methods, making them fairer and easier to understand.

One voting method that's gaining attention is the Minimax method. It's designed to make the best possible decision by minimizing the potential for a bad outcome. Think of it as a way to avoid the worst-case scenario, ensuring that the winning option is the least objectionable to the most voters.

New research has refined the Minimax method by adding a set of straightforward rules, or axioms, that clarify how to vote when there are three or more choices. By focusing on simplicity and fairness, this updated approach promises to make elections more transparent and trustworthy.

What is the Minimax Voting Method and Why Does It Matter?

Diverse voters casting ballots into a radiant ballot box.

The Minimax method is a voting system designed to choose the alternative that minimizes the maximum "loss" in head-to-head comparisons. Imagine each candidate or option being pitted against every other option. The Minimax winner is the one whose worst performance against any other option is the least bad.

Why is this important? Traditional voting methods can sometimes lead to unexpected or unfair results. For example, a candidate with broad but shallow support might lose to a candidate with intense but narrow support. The Minimax method aims to balance these competing interests, selecting the option that is generally acceptable to the majority of voters. Several sophisticated Condorcet-consistent voting methods coincide with or refine Minimax in three-alternative elections: Kemeny (1959), Ranked Pairs (Tideman 1987), Beat Path (Schulze 2011), Split Cycle (Holliday and Pacuit 2023a).

Fairness: Aims to reduce the impact of "spoiler" candidates and ensure that the winning option has broad support.
Simplicity: Easier to understand and implement than some other complex voting methods.
Transparency: The decision-making process is clear and straightforward, building trust in the outcome.

In essence, the Minimax method offers a way to cut through the noise and make the best possible decision, even when faced with a multitude of choices. When applied to more than three alternatives, our axioms also distinguish Minimax from other known voting methods that coincide with or refine Minimax for three alternatives.

The Future of Voting: Simple Steps Towards Fairer Elections

The research highlights that by incorporating desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives (setting aside tiebreaking). Ultimately all of the Condorcet methods listed above should be axiomatically characterized with no restriction on the number of alternatives, as has been recently done for Split Cycle (Ding et al. Forthcoming). Minimax has the potential to transform how we make collective decisions. By embracing its principles, we can move towards a future where elections are fairer, more transparent, and truly reflect the will of the people.

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.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2312.14256,

Title: An Extension Of May'S Theorem To Three Alternatives: Axiomatizing Minimax Voting

Subject: econ.th cs.gt cs.ma

Authors: Wesley H. Holliday, Eric Pacuit

Published: 21-12-2023

Everything You Need To Know

What is the core principle behind the Minimax voting method, and how does it aim to improve election outcomes?

The Minimax voting method operates on the principle of minimizing the maximum potential "loss" in head-to-head comparisons between candidates. It seeks to select the candidate whose worst performance against any other candidate is the least bad. This approach aims to improve election outcomes by balancing competing interests and selecting the option that is generally acceptable to the majority of voters, potentially mitigating the impact of "spoiler" candidates and ensuring broad support for the winning option. It is important to note that Minimax focuses on the least objectionable choice rather than the most preferred, a key distinction from methods prioritizing first-choice votes.

In what ways does the Minimax method enhance fairness, simplicity, and transparency in the voting process?

The Minimax method enhances fairness by reducing the impact of "spoiler" candidates and ensuring that the winning option has broad support. Its simplicity lies in being easier to understand and implement compared to some other complex voting methods. It promotes transparency through its clear and straightforward decision-making process, which builds trust in the outcome. It is important to understand that the addition of axioms further refines the decision making process making it more fair and transparent.

How does the Minimax method differ from traditional voting systems in addressing the potential for unfair or unexpected results?

Traditional voting methods can sometimes lead to unexpected or unfair results, such as a candidate with broad but shallow support losing to a candidate with intense but narrow support. The Minimax method aims to balance these competing interests by selecting the option that is generally acceptable to the majority of voters. This approach contrasts with methods that might prioritize the number of first-place votes without considering the overall acceptability of the candidate. The minimax method is better positioned to handle these edge cases.

Beyond the basic concept, what are some specific Condorcet-consistent voting methods that align with or refine the Minimax approach, especially in elections with three alternatives?

Several sophisticated Condorcet-consistent voting methods coincide with or refine Minimax in three-alternative elections. These include Kemeny (1959), Ranked Pairs (Tideman 1987), Beat Path (Schulze 2011), Split Cycle (Holliday and Pacuit 2023a). Each of these methods shares the goal of identifying the Condorcet winner (if one exists) and often involves pairwise comparisons of candidates to determine the overall preference order. These methods offer different refinements and variations on the Minimax principle, providing a range of options for implementing fair and transparent voting systems, and each have their own advantages and disadvantages.

What implications does the research on incorporating axioms into May's axioms have for the future of voting, and how does it relate to the broader goal of achieving fairer elections?

The research demonstrates that incorporating desirable axioms to May's axioms uniquely determines how to vote on three alternatives. This finding has significant implications for the future of voting because it provides a more rigorous and well-defined framework for designing voting systems. The ultimate goal is to axiomatically characterize all Condorcet methods, including Minimax, without any restriction on the number of alternatives, as has been recently done for Split Cycle. By embracing these principles, we can move towards a future where elections are fairer, more transparent, and truly reflect the will of the people. A full axiomatic characterization gives the method even more mathematical weight.