Designing algorithm to split chores, create harmony in the home

Ayumi Igarashi, an associate professor at the Graduate School of Information Science and Technology, studies mathematical models and algorithms for the fair allocation of resources. The research, called the theory of fair division, mathematically defines the notion of fairness and analyzes methods of allocation. In 2021, Igarashi was selected as one of MIT Technology Review’s Innovators Under 35 Japan, an annual list recognizing outstanding individuals younger than 35 in various fields, from different regions around the world. In the following year, together with nonprofit organization Code for Japan, she developed a web application called Kajibuntan (meaning “division of household chores” in Japanese), which visualizes inequalities in sharing housework between partners and proposes “envy-free” alternatives based on the theory of fair division.

From taking out the garbage and cleaning to cooking and doing the laundry, sharing household chores with a partner can often lead to frustration. How can domestic duties be split fairly in a way that both parties can be satisfied with by not causing envy? To solve this problem, Igarashi developed a mathematical model that allocates housework based on each person’s strengths and preferences. And she created an app for “promoting harmony in the home” through the fair division of household chores.

The way to use it is simple. Users first select chores that need to be shared from a list shown on the screen, then input detailed information for each chore, such as how many times a week they do the work, how long it takes to finish, and indicate how they feel about each task by clicking the “like,” “neutral” or “dislike” icon. The app then calculates the current burden each person feels and suggests a more ideal division, displayed as pie charts. What Igarashi aimed to achieve with the app was “envy-free” division — a notion central to the concept of fairness in the theory of fair division.

“What counts as fair depends on each person’s perspective,” Igarashi said. “Envy-free division means, under each individual’s own evaluation, they feel they’ve received the best possible share.”

Igarashi also hoped to use the app as a tool for reaching out and introducing her research to a wider audience, including those without any expert knowledge. “I want many people to use the app casually, just like playing a game. I also hope that it will lead couples to have a conversation about the way they go about sharing housework,” she said.

The web app had roughly 13,000 unique visitors a month after it was covered by public broadcaster NHK.

Indivisible items, such as office labor or housework, are considered as something that cannot be split in a perfectly fair and efficient way. “But we have yet to answer the question of whether we can divide indivisible items while maintaining a reasonable level of fairness and efficiency. I want to find a solution to that,” she said.

Mathematical models to realize “fairness”

Mathematics had always been Igarashi’s favorite subject, ever since childhood. “Math has clear answers. It was fun, like solving a puzzle,” she said. While growing up, she dreamed of becoming a researcher, like her mother. After graduating from high school, Igarashi enrolled in the University of Tsukuba’s College of Policy and Planning Sciences, with the hope of studying math and applying it to benefit society. At university, Igarashi studied optimization problems and game theory, and in her master’s studies, focused on the fair allocation of profit and cost.

Igarashi began researching the theory of fair division when she was a doctoral student in the Department of Computer Science at the University of Oxford in the U.K. It was a research presentation on fair division at a workshop in Budapest, Hungary, that piqued her interest. There, she joined a fair-share scheduling project and was drawn to the mathematical “elegance” underpinning the theory.

After receiving her Ph.D., Igarashi has continued her research on the theory of fair division, exploring the notion of fairness and algorithm design. Among the areas she decided to investigate was household chores.

“How can we accurately calculate a fair distribution of domestic chores when the burden felt by each person varies? This is a mathematically challenging problem,” she said. “It would be extremely difficult to find the best way to split, for example, 100 tasks fairly by going through every possible combination, which would be around 2 raised to the power of 100 (a number greater than 1 followed by 30 zeros). Instead, I’ve been focusing on designing efficient algorithms that would arrive at an optimal allocation.”

The household-chore app was Igarashi’s first crack at applied research. According to a survey conducted with some 120 app users, the developers received positive feedback from around 60% of them. On the other hand, some users found the input process too complicated or the chore categorization too detailed. Taking these opinions into account, she is planning to update the app to make it more user-friendly.

“The user feedback made me realize aspects I hadn’t noticed before. And that helped me to understand the kind of theoretical model I need to develop,” she said. “I want to create a cycle where user feedback is used for advancing theoretical research, and insights gained from such research lead to real-world applications.”

Voting systems that give minorities a voice

One of the research topics Igarashi is currently working on is participatory budgeting. Initially adopted by Brazilian municipal governments in the 1980s, the initiative allows citizens to propose and vote on how a portion of a local government’s budget should be allocated. Today, the scheme is used in more than 3,000 cities in the world, including New York, Boston and Paris. In Japan, Mie Prefecture and the town of Ami in Ibaraki Prefecture have used the system in the past. It has recently been drawing attention as a hot research topic, and Igarashi is hoping to contribute to it.

Her focus is voting systems for participatory budgeting. For example, if a system is designed to adopt a project based simply on the highest number of votes, only the majority’s opinion is reflected, while that of the minority gets completely ignored. Igarashi hopes to design a more balanced system that incorporates and represents the voices of all citizens fairly.

Looking ahead, Igarashi said she wants to engage in both theoretical and applied research, while contributing to socially significant decision-making.

“If I were to focus solely on theoretical research, I may have a long list of research papers I could boast about 30 years from now,” she said. “But even if such a result could be regarded as ‘beautiful’ mathematically, I feel I’ll lack having a sense of fulfillment, gained from having achieved something concrete. That’s why I also want to engage in applied research and be able to say one day that my work has made an impact on society, however small it may be.”