2020/03/17 by Aronov, Boris, de Berg, Mark, Gudmundsson, Joachim +1
#Computational Geometry (cs.CG) #F.2.2 #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2003.07513
Let V be a set of n points in ℝd, called voters. A point p∈ ℝd is a plurality point for V when the following holds: for every q∈ℝd the number of voters closer to p than to q is at least the number of voters closer to q than to p. Thus, in a vote where each v∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal p will not lose against any alternative proposal q. For most voter sets a plurality point does not exist. We therefore introduce the concept of β-plurality points, which are defined similarly to regular plurality points except that the distance of each voter to p (but not to q) is scaled by a factor β, for some constant 0