  Magnetism of the spin-$\frac12$ $\alpha$-KVOPO$_4$ is studied by
thermodynamic measurements, $^{31}$P nuclear magnetic resonance (NMR), neutron
diffraction, and density-functional band-structure calculations. Ferromagnetic
Curie-Weiss temperature of $\theta_{\rm CW}\simeq 15.9$ K and the saturation
field of $\mu_0H_s\simeq 11.3$ T suggest the predominant ferromagnetic coupling
augmented by a weaker antiferromagnetic exchange that leads to a short-range
order below 5 K and the long-range antiferromagnetic order below $T_{\rm
N}\simeq 2.7$ K in zero field. Magnetic structure with the propagation vector
$\mathbf k=(0,\frac12,0)$ and the ordered magnetic moment of 0.58 $\mu_B$ at
1.5 K exposes a non-trivial spin lattice where strong ferromagnetic dimers are
coupled antiferromagnetically. The reduction in the ordered magnetic moment
with respect to the classical value (1 $\mu_{\rm B}$) indicates sizable quantum
fluctuations in this setting, despite the predominance of ferromagnetic
exchange. We interpret this tendency toward ferromagnetism as arising from the
effective orbital order in the folded chains of the VO$_6$ octahedra.
