Possible sources of legitimation for Authorities between trust and distrust

Trust appears to be one of the structural conditions for Authority in general, but politics, institutions and public bodies seem to suffer today, all over the world, from a serious crisis (and lack) of trust.
In response to this crisis, a growing need of certifications, authorizations and other attestations which can assure their objects’ reliability can be observed in every sector, strengthening the role of independent and responsible Authorities which can release such decisions and measures.
The “trust issue”, however, though changing its features, still remains: the problem therefore becomes to find a strong source of legitimation for the work, powers and acts of those Authorities, and in practice for themselves as main actors on the public stage, in an ongoing discussion between the political, technical, competence-founded or consensus-based nature of their accountability.