Hesitant Pythagorean fuzzy sets have remarkable theoretical and practical features, which derive from their role as a generalization of Pythagorean fuzzy sets that embeds the benefits of hesitation. Their advantages motivate us to extend existing decision-making methods to the case where data and information are in the form of several values. We propose an ELimination and Choice Translating REality-II (ELECTRE-II) technique under hesitant Pythagorean fuzzy (HPF) information to handle diverse opinions of decision experts. The main contribution of this work is the formulation of the basic structure of an HPF ELECTRE-II method, including three kinds of outranking sets (concordance, indifferent, and discordance), two types of outranking matrices (concordance and discordance), two kinds of outranking relations (weak and strong), and two types of outranking graphs (strong and weak graphs). Further, we discuss some quantitative applications to guarantee the applicability and flexibility of the presented framework. To endorse the advantages and accuracy of HPF ELECTRE-II technique, we provide a comprehensive comparative analysis with existing techniques, such as ELECTRE-II approach under hesitant fuzzy data, ELECTRE group decision-making method under fuzzy knowledge, PF ELECTRE-1, and HPF ELECTRE-II methods. Moreover, we state some important insights and discuss the limitations of the model here proposed. (C) 2021 Elsevier B.V. All rights reserved.