  Recent experiments on the conductance of thin, narrow superconducting strips
have found periodic fluctuations, as a function of the perpendicular magnetic
field, with a period corresponding to approximately two flux quanta per strip
area [A. Johansson et al., Phys. Rev. Lett. {\bf 95}, 116805 (2005)]. We argue
that the low-energy degrees of freedom responsible for dissipation correspond
to vortex motion. Using vortex/charge duality, we show that the superconducting
strip behaves as the dual of a quantum dot, with the vortices, magnetic field,
and bias current respectively playing the roles of the electrons, gate voltage
and source-drain voltage. In the bias-current vs. magnetic-field plane, the
strip conductance displays what we term `Weber blockade' diamonds, with vortex
conductance maxima (i.e., electrical resistance maxima) that, at small
bias-currents, correspond to the fields at which strip states of $N$ and $N+1$
vortices have equal energy.
