A single-issue spatial election is a voter preference profile derived from an arrangement of candidates and voters on a line, with each voter preferring the nearer of each pair of candidates. We provide a polynomial-time algorithm that determines whether a given preference profile is a single-issue spatial election and, if so, constructs such an election. This result also has preference representation and mechanism design applications.
Knoblauch, Vicki, "Recognizing a Single-Issue Spatial Election" (2008). Economics Working Papers. Paper 200826.