Travail de recherche/Working paper
| Résumé : | This paper proves two results about why investors rely on the crowd instead of their own judgment, and one result about how those two reasons combine. The first, an ambiguity driven conformity theorem, shows that during a crisis a fully rational investor, facing no resource constraint at all, optimally shifts weight toward the public market consensus. The reason is that the reliability of the investor’s own valuation model has become genuinely uncertain, not that checking things has become harder. The second, an anchored complacency theorem, shows that a narrow price cap can rationally reduce an investor’s own incentive to verify information, because the visible range of price movements serves as an anchor for how much is believed to be at stake. A cap narrow enough to look calm on the surface produces a sharp threshold below which no verification is worth the trouble, and this threshold result is then shown to hold under general convex, diminishing-returns cost assumptions, not only the closed-form example used to state it. A compounding corollary shows these two mechanisms, together with a third, already well understood channel tied to bounded attention, do not substitute for one another but add up, most severely when a crisis and a narrow cap occur together. These three results are the paper’s contribution and are presented in full in the main text, as a purely theoretical argument: no data is used or required anywhere in this paper. Two short supporting results, standard consensus mathematics showing how individual conformity aggregates across a population and an entropy-based measure of borrowed versus earned conviction, are proved in full in an appendix, independently of any unpublished source, so that a reader can consult them without taking anything on faith. |
