  While dry mergers can produce considerable scatter in the (black hole mass,
$M_{\rm bh}$)-(spheroid stellar mass, $M_{\rm *,sph}$) and $M_{\rm
bh}$-(spheroid half-light radius, $R_{\rm e,sph}$) diagrams, the virial theorem
is used here to explain why the scatter about the $M_{\rm bh}$-(velocity
dispersion, $\sigma$) relation remains low in the face of such mergers. Its
small scatter has been claimed as evidence of feedback from active galactic
nuclei (AGNs). However, it is shown that galaxy mergers also play a significant
role. The major merger of two S0 galaxies with $M_{\rm *,sph}\sim10^{11}$
M$_\odot$ advances a system along a slope of $\sim$5 in the $M_{\rm
bh}$-$\sigma$ diagram. However, a major E$+$E galaxy merger moves a system
(slightly) along a trajectory with a slope of $\sim$9, while mergers of
lower-mass S0 galaxies with $M_{\rm *,sph}\sim10^{10}$ M$_\odot$ move
(slightly) along a trajectory with a slope of $\sim$3. This produces a steeper
distribution for the E (and Es,e) galaxies in the $M_{\rm bh}$-$\sigma$
diagram, reported here to have a slope of 7.27$\pm$0.91, compared to the S0
galaxies which have a slope of 5.68$\pm$0.60. This result forms an important
complement to the AGN feedback models like that from Silk and Rees, providing a
more complete picture of galaxy/(black hole) coevolution. It also has important
implications for nanohertz gravitational wave research. Abridged.

Astrophysics of Galaxies