Considering that converting linear ordinal ranking (LOR) information into interval utility values can not only improve the computability of LOR information but also explore the degree of preference for different alternatives for decision-makers hidden behind LOR information, this paper proposes a conversion-based LOR aggregation method to aggregate LOR information under risk. Given that the behaviours of decision-makers are influenced by risk, this paper adopts prospect theory to depict the decision-makers' behaviours under risk in the conversion-based aggregation process. To achieve this, the information energy for LOR is constructed firstly, and its features are analysed, which makes a basis for the conversion process. After that, the details about how to integrate the prospect theory with variable reference points into the conversion-based aggregation framework are presented. Finally, an example (exploring the financial product preferences of a group of respondents) evidences the practicality of the proposed method. Further, some analyses and discussions are conducted to verify the rationality and stability of the method.