A tournament consists of a finite set of players equipped with a beating relation describing pairwise comparisons between each pair of players. Determining a ranking of the players in a tournament has applications in voting, where players represent alternatives and x beats y if a majority of voters prefer x over y, paired comparisons analysis, where players represent products and the beating relation expresses the preferences of a consumer, search engines, sports and other domains.

Bipartite tournaments consist of two disjoint sets of players A and B such that comparisons only take place between players from opposite sets. We consider ranking methods which produce two rankings for each tournament – one for each side of the bipartition. Such tournaments model situations in which two different kinds of entity compete indirectly via matches against entities of the opposite kind. An example is education, where A represents students, B exam questions, and student a “beats” question b by answering it correctly. The ranking of students then reflects their proficiency, and the ranking of questions reflects their diﬀiculty. This may be particularly useful in the context of automated grading of crowdsourced questions provided by students themselves, which may vary in their diﬀiculty.

This project will explore the concept of bipartite tournaments in the field of education. It aims to shed light on how bipartite ranking can be used to measure student proficiency and question difficulty in an educational context, particularly focusing on automated grading of crowdsourced questions provided by students.