Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable in lack of hints indicating otherwise; yet, a recent line of research spun from the idea of deriving this information from the revision process itself. In particular, the history of previous revisions and previous merging examples provide information for performing subsequent mergings.
Yet, no examples or previous revisions may be available. In spite of the apparent lack of information, something can still be inferred by a try-and-check approach: a relative reliability ordering is assumed, the merging process is performed based on it, and the result is compared with the original information. The outcome of this check may be incoherent with the initial assumption, like when a completely reliable source is rejected some of the information it provided. In such cases, the reliability ordering assumed in the first place can be excluded from consideration. The first theorem of this article proves that such a scenario is indeed possible. Other results are obtained under various definition of reliability and merging.
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