In present-day society, government public service outsourcing has become an irreversible trend due to the gradually increasing public pursuit of service quality and efficiency. To better meet the needs of the public and effectively improve the quality of service, it has been a crucial issue for government departments to choose the most desirable one from a series of public service outsourcers (PSOs) with distinct characteristics. In this paper, to deal with such decision problems, we propose the improved elimination and choice translating reality (ELECTRE) II method with unknown weight information under the double hierarchy hesitant fuzzy linguistic (DHHFL) environment to accurately and effectively select the best PSO. Firstly, aiming at the shortcomings of the original comparison method for double hierarchy hesitant fuzzy linguistic elements (DHHFLEs), we define the hesitant deviation degree (HDD) for DHHFLEs and, based on this, further propose a new comparison method for comparing DHHFLEs more reasonably. Secondly, inspired by the classical power average (PA) operator proposed by Yager, a new method is introduced to determine the weights of experts with respect to each attribute, based on the support degree between attributes. Afterwards, an improved ELECTRE II method is proposed to address the problem of PSO selection. A numerical case about e-government outsourcer selection is given to demonstrate the enforceability of the method. Finally, comparisons between previous methods and our method are carried out to illustrate the effectiveness and strengths of the proposed method.Sustainability 2020, 12, 2315 2 of 34 harmonious relationships among the government, the PSOs, and the public through the intermediary of the supplier. That is, by outsourcing public services to the service suppliers, the government can enhance both the economic effectiveness and the public satisfaction in line with the service target.Driven by friendly policies, public service outsourcing has been rapidly promoted, and has gradually expanded from basic service areas, such as public infrastructure and solid waste management [9], to high-level public service areas, such as online IT service [10], energy supply [11], medical care [12], and social security [13]. As outsourced contractors, private organizations have the obligation to produce high-quality and efficient public services. The internal management level, scale, experience, and service capability of the contractor can directly determine the quality of public services, select the most efficient contractors, and standardize the contractors. When purchasing services and selecting the most appropriate service providers, the key to guaranteeing the quality of public services is to screen and inspect the service capabilities of contractors.Regarding different service outsourcing providers as alternatives and their performances as criteria, respectively, the public service outsourcer (PSO) selection issue can then be identified as a typical multi-criteria decision-making (MCDM) problem [14]...