  Given a sequence of independent random vectors taking values in ${\mathbb
R}^d$ and having common continuous distribution function $F$, say that the
$n^{\rm \scriptsize th}$ observation sets a (Pareto) record if it is not
dominated (in every coordinate) by any preceding observation. Let $p_n(F)
\equiv p_{n, d}(F)$ denote the probability that the $n^{\rm \scriptsize th}$
observation sets a record. There are many interesting questions to address
concerning $p_n$ and multivariate records more generally, but this short paper
focuses on how $p_n$ varies with $F$, particularly if, under $F$, the
coordinates exhibit negative dependence or positive dependence (rather than
independence, a more-studied case). We introduce new notions of negative and
positive dependence ideally suited for such a study, called negative
record-setting probability dependence (NRPD) and positive record-setting
probability dependence (PRPD), relate these notions to existing notions of
dependence, and for fixed $d \geq 2$ and $n \geq 1$ prove that the image of the
mapping $p_n$ on the domain of NRPD (respectively, PRPD) distributions is
$[p^*_n, 1]$ (resp., $[n^{-1}, p^*_n]$), where $p^*_n$ is the record-setting
probability for any continuous $F$ governing independent coordinates.
