Focusing efficiently on potential weaknesses in the validity argument of writing assessments--such as writing subjectivity, content coverage, criteria vagueness, and raters' incompetence--has been shown to positively enhance teachers' overall writing assessment competence (AC). In this study, we propose a computational bootstrapping model of validity argument in L2 writing assessment and compare it to argument-based models such as Practical Reasoning (PR), Assessment Use Argument (AUA), and Rubric Use Argument (RUA). Specifically, this computational model gradually improves the validity argument by addressing subtle deficiencies in previous assessment competence and constructing a bootstrapping process for the validity argument. We collected data from the Chinese English Teachers' Writing Assessment Competence Corpus (CETWACC), which includes texts from a total of Chinese L2 teachers in higher education. The corpus comprises six levels and 60 items detailing how these teachers perform in: (i) construction, (ii) reflection, (iii) externalization, (iv) internalization, (v) enhancement, and (vi) reconstruction. The findings suggest that the Cognitive Bootstrapping Model (CBM) significantly enhances teachers' assessment competence through reasoned arguments and more scientific measures of validity arguments using computational algorithms. Overall, this study emphasizes the computational evidence of validity arguments and explores the subtle process of micro-changes in L2 writing assessment, transitioning from argument-based approaches to algorithmic methods. The results have implications for discussions on the role of validity argument bootstrapping in current writing assessments, offering a universally applicable and operationally feasible model for validating writing assessments.