An algorithm returns an EJR+ committee in the ARRV spatial model using O(d log d k) Planar queries per voter in expectation, independent of candidate count, for any distribution over rectangular preferences when the electorate is large enough.
Proof.Fix a levelℓ∈[k], callc∈Ctinyifp c,ℓ ≤ℓ/(k+ 1)andlargeifp c,ℓ ≥ℓ/k−δ 1, and write g :=ℓ/(2k(k+ 1))−δ 1/2for the gap separatingq ∗ from each of these two bounds
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Multiwinner Voting with Spatial Preferences under Incomplete Information
An algorithm returns an EJR+ committee in the ARRV spatial model using O(d log d k) Planar queries per voter in expectation, independent of candidate count, for any distribution over rectangular preferences when the electorate is large enough.