Approval Ballot Triangles and Strict-Sense Ballots

TL;DR

This paper introduces approval ballot triangles (ABTs), a combinatorial structure linked to symmetric plane partitions, and shows how strict-sense ballots can be decomposed into sequences of ABTs, connecting voting processes with advanced combinatorics.

Contribution

It establishes a bijection between ABTs and TSSCPPs and demonstrates how strict-sense ballots can be represented as sequences of compatible ABTs, bridging voting theory and combinatorics.

Findings

ABTs are in bijection with TSSCPPs

Strict-sense ballots can be decomposed into ABTs

Connects voting processes with combinatorial structures

Abstract

We consider a family of binary triangular arrays, called approval ballot triangles (ABTs), that are in bijection with totally symmetric self-complementary plane partitions (TSSCPPs). These triangles correspond to a ballot process in which voters select their collection of approved candidates rather than voting for a single person. We situate ABTs within the ballot problem literature and then show that a strict-sense ballot can be decomposed into a list of sequentially compatible ABTs.