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Analysing Guarantees in Australian Senate Outcomes

Michelle Blom

Abstract

Single Transferable Vote (STV) is used to elect candidates to the 76 seat Australian Senate across six states and two territories. These eight STV contests are counted using a combination of ballot scanners, manual data entry and tabulation software. On election night, some properties of the set of cast ballots are determined by hand. This includes the first preference tallies of each party. This technical report considers whether there are some properties, such as individual candidates' first preference tallies, that, if assumed to be accurate, imply a portion of the election outcome. The paper also presents an interesting example showing that the rules of STV tabulation used for the Australian Senate can allow bizarre behaviour, such as votes increasing in value over time.

Analysing Guarantees in Australian Senate Outcomes

Abstract

Single Transferable Vote (STV) is used to elect candidates to the 76 seat Australian Senate across six states and two territories. These eight STV contests are counted using a combination of ballot scanners, manual data entry and tabulation software. On election night, some properties of the set of cast ballots are determined by hand. This includes the first preference tallies of each party. This technical report considers whether there are some properties, such as individual candidates' first preference tallies, that, if assumed to be accurate, imply a portion of the election outcome. The paper also presents an interesting example showing that the rules of STV tabulation used for the Australian Senate can allow bizarre behaviour, such as votes increasing in value over time.
Paper Structure (4 sections, 3 equations, 1 figure, 1 table)

This paper contains 4 sections, 3 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Preliminaries
  4. Establishing Tally Bounds and Guaranteed Seatings

Figures (1)

  • Figure 1: Segment of a ballot paper for the 2016 Australian Senate Election for the State of Victoria. The full ballot paper contained 40 groups (columns) and 116 candidates. Source: Wikimedia Commons.

Theorems & Definitions (3)

  • definition thmcounterdefinition: STV Election
  • definition thmcounterdefinition: Tally $t_i(c)$
  • definition thmcounterdefinition: Transfer value $\tau_i$