Hidden Object-Ranking Problems (HORPs) are object-ranking problems stated as classification or instance-ranking problems. There exists so far no dedicated algorithm for solving them properly and HORPs are usually solved as if they were classification (multi-class or ordinal) or instance-ranking problems. In the former case, item-related ordinal information is negated and only class-related information is retained; in the latter case, item-related ordinal information is considered, but in a way that emphasizes class-related information, so that the items are not only sorted but also clustered. We propose a kernel machine that allows retaining itemrelated ordinal information while avoiding emphasizing class-related information. We show how this kernel machine can be implemented with standard optimization libraries provided slight modifications on the original kernel. The proposed approach is tested on Tahitian pearls quality assessment and compared with four other classical methods. It yields better results (93.6% ± 3.9% of correct predictions without feature selection, 94.3% ± 3.4% with feature selection) than the best of the other tested methods (91.3%±3.4% and 92.6%±4.3% without and with feature selection for the instance-ranking approach), this improvement being significant (p-value < 0.05). Moreover, this method exhibits no significant difference in the results with and without feature selection (p-value = 0.33), which may be a hint that its learning bias fits the problem well and can thus alleviate the data preprocessing workload.