Understanding citizens' values in participatory systems is crucial for citizen-centric policy-making. We envision a hybrid participatory system where participants make choices and provide motivations for those choices, and AI agents estimate their value preferences by interacting with them. We focus on situations where a conflict is detected between participants' choices and motivations, and propose methods for estimating value preferences while addressing detected inconsistencies by interacting with the participants. We operationalize the philosophical stance that "valuing is deliberatively consequential." That is, if a participant's choice is based on a deliberation of value preferences, the value preferences can be observed in the motivation the participant provides for the choice. Thus, we propose and compare value estimation methods that prioritize the values estimated from motivations over the values estimated from choices alone. Then, we introduce a disambiguation strategy that addresses the detected inconsistencies between choices and motivations by directly interacting with the participants. We evaluate the proposed methods on a dataset of a large-scale survey on energy transition. The results show that explicitly addressing inconsistencies between choices and motivations improves the estimation of an individual's value preferences. The disambiguation strategy does not show substantial improvements when compared to similar baselines--however, we discuss how the novelty of the approach can open new research avenues and propose improvements to address the current limitations.