|Abstract:||Error-driven ranking algorithms (EDRAs) perform a sequence of slight re-rankings of the constraint set triggered by mistakes on the incoming stream of data. In general, the sequence of rankings entertained by the algorithm, and in particular the final ranking entertained at convergence, depend not only on the grammar the algorithm is trained on, but also on the specific way data are sampled from that grammar and fed to the algorithm. The robust analysis of EDRAs pinpoints at properties of the predicted sequence of rankings that are robust, namely only depend on the target grammar, not on the way the data are sampled from it. Tesar and Smolensky (1998) develop a tool for the robust analysis of EDRAs that perform constraint demotion only, that is reviewed in detail. The paper then develops a new tool for the robust analysis of EDRAs that perform both constraint demotion and promotion. The latter tool is applied to the robust analysis of the EDRA model of the child early acquisition of phonotactics, through a detailed discussion of restrictiveness on three case studies from Prince and Tesar (2004), that crucially require EDRAs that perform both demotion and promotion.