Writing and assessing arguments are important skills and there is evidence that using rubrics to assess the arguments of others can help students write better arguments. Thus, this study investigated whether students were able to write better arguments after using rubrics to assess the written arguments by peers. Students in 4 secondary 4 classes at a publicly funded Hong Kong high school used an online assessment system to assess the arguments of peers for one year. Students first used a rubric to assess arguments along four dimensions: claims, evidence, reasoning, and application of knowledge. Then they compared their assessments with assessments by their teachers using the same rubrics. Data included student-teacher agreements on rubric dimensions, students' evaluation comments, and their perceptions of the assessment activity. Results indicated that the quality of students' written arguments could be predicted based on the number of student-teacher agreements on the rubrics dimension of evidence and on the number of students comments identifying problems and reflecting on assessment. This study shows that providing students with rubrics for assessing the written arguments of peers can lead them to write better arguments.