  We report a comprehensive investigation of the average and local structure of
La$_{5.4}$WO$_{12-\delta}$, which has excellent mixed proton, electron and
oxide ion conduction suitable for device applications. Synchrotron X-ray and
neutron powder diffraction show that a cubic fluorite supercell describes the
average structure, with highly disordered lanthanum and oxide positions. On
average the tungsten sites are six-fold coordinated, and we detect a trace
(4.4(2) %) of anti-site disorder. In addition to sharp Bragg reflections,
strong diffuse neutron scattering is observed, which hints at short-range
order. We consider plausible local configurations, and show that the defect
chemistry implies a simple 'chemical exchange' interaction that favours ordered
WO6 octahedra. Our local model is confirmed by synchrotron x-ray pair
distribution function analysis and EXAFS experiments performed at the La K and
W L3-edges. We show that ordered domains of around ca. 3.5 nm are found,
implying that mixed conduction in La$_{5.4}$WO$_{12-\delta}$? is associated
with a defective glassy-like anion sublattice. The origins of this ground state
are proposed to lie in the non-bipartite nature of the fcc lattice and the
pairwise interactions which link the orientation of neighbouring octahedral WO6
sites. This 'function through frustration' could provide a means of designing
new mixed conductors.
