Proportionality Notion

Proportionality, in the context of resource allocation and decision-making, aims to ensure fair representation of diverse preferences or groups. Current research focuses on developing and analyzing algorithms and mechanisms, such as variations of the Method of Equal Shares and Phragmén's rule, that achieve proportionality while addressing computational complexity and strategic manipulation in various settings, including participatory budgeting, committee elections, and facility location. These efforts aim to improve fairness and efficiency in diverse applications, ranging from public resource allocation to algorithmic fairness in machine learning, by providing mathematically rigorous frameworks for achieving proportional outcomes. The impact spans both theoretical advancements in social choice theory and practical improvements in the design of fair and efficient systems.