Approval Ballot Triangles and Strict-Sense Ballots
Andrew Beveridge, Ian Calaway

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.
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Taxonomy
TopicsGame Theory and Voting Systems · Internet Traffic Analysis and Secure E-voting · Cryptography and Data Security
