On Tuesday 10 November 2020, the first online NETWORKS Seminar Talk is organized. This is the first in a new series of monthly Seminar Talks organized by Jop Briët, Stella Kapodistria and Martín Zubeldía and it is an online event for all members and affiliated members. Mark de Berg (TU/e) will be the speaker on the first Seminar Talk with a talk entitled "Spatial Voting Games".
Voting theory is concerned with mechanisms to combine preferences of individual voters into a collective decision. A desirable property of such a collective decision is that it is stable, in the sense that no alternative is preferred by more voters.
In spatial voting games this is formalized as follows. The space of all possible decisions is modeled as Rdand every voter is represented by a point in Rd representing the ideal decision for that voter. A voter v∈Rd now prefers a proposed decision in p∈Rdover some alternative decision q∈Rd when v is closer to p than to q. Thus p represents a stable decision for a given set Vof voters if, for any alternative q, the number of voters who prefer p is at least the number of voters who prefer q. Such a stable decision is also called a plurality point. The concept of plurality point leads to various interesting combinatorial and algorithmic questions: Under which conditions does a plurality point exist? Can we efficiently find a plurality point, if it exists? If a plurality point does not exist, can we compute the “most stable” decision? In this talk I will discuss some recent work in this direction.