Conversational digital assistants (CDAs), driven by artificial intelligence, are emerging innovative technologies to assist customers with online shopping. Despite the benefits of CDAs, customers resist their use for online shopping. Hence, studying what factors motivate consumers to adopt OSAs is necessary. The study first identifies twelve CDA acceptance factors through a literature review and expert opinion. It then uses a unique grey-DEMATEL method to evaluate the cause-and-effect relationships among the factors. The grey-DEMATEL approach effectively analyzes causal interactions among elements, overcoming the bias of imprecise human judgments in real life. The authors find that the critical cause factors that affect other factors of CDAs’ adoption are anxiety, trust, social presence, enjoyment, and humanness. Managers and policymakers can use the study’s findings to drive CDAs’ acceptance. The study uniquely identifies the critical success factors for CDAs’ acceptance for online shopping and analyzes their causal relations in a grey environment.