A general model of fluency effects in judgment and decision making

Processing or cognitive fluency is the experienced ease of ongoing mental processes. This experience infl uences a wide range of judgments and decisions. We present a general model for these fluency effects. Based on Brunswik’s lens-model, we conceptualize fluency as a meta-cognitive cue. For the cue to impact judgments, we propose three process steps: people must experience fluency; the experience must be attributed to a judgment-relevant source; and it must be interpreted within the judgment context. This interpretation is either based on available theories about the experience’s meaning or on the learned validity of the cue in the given context. With these steps the model explains most fl uency effects and allows for new and testable predictions

On Gaps Between Primitive Roots in the Hamming Metric

We consider a modification of the classical number theoretic question about the gaps between consecutive primitive roots modulo a prime $p$, which by the well-known result of Burgess are known to be at most $p^{1/4+o(1)}$. Here we measure the distance in the Hamming metric and show that if $p$ is a sufficiently large $r$-bit prime, then for any integer $n \in [1,p]$ one can obtain a primitive root modulo $p$ by changing at most $0.11002786...r$ binary digits of $n$. This is stronger than what can be deduced from the Burgess result. Experimentally, the number of necessary bit changes is very small. We also show that each Hilbert cube contained in the complement of the primitive roots modulo $p$ has dimension at most $O(p^{1/5+\epsilon})$, improving on previous results of this kind.Comment: 16 pages; to appear in Q.J. Mat