Chapter Overviews

Description

This introductory-level chapter describes and explains Geometric Voting (GV) and Consecutively Halved Positional Voting (CHPV). The Introduction section outlines the concept and nature of GV and CHPV while the Analogy one illustrates examples of how they work. The following formal Weightings section - that may be skipped - defines the value of all ranked preferences in any election. Next, the Voting, Counting and Outcomes sections describe how ranked-ballot CHPV/GV works in practice for single-winner elections. For multiple-winner contests, the Party-List section explains how this proportional version of CHPV/GV works when voting for parties. The Summary lists the significant properties and features identified in this chapter.

Evaluations (Ranked Ballot)

This intermediate-level chapter assesses the properties of CHPV/GV in relation to numerous voting system criteria and their vulnerability to manipulation. The Introduction section previews the evaluations performed in this chapter. The General Criteria section assesses whether CHPV/GV satisfies or fails the summability, consistency, participation, Pareto, resolvability, reversal symmetry, monotonicity and Condorcet criteria. The separate Majority Criteria one explores the various issues that arise from the majority criterion. Arrow's Impossibility Theorem and the independence of irrelevant alternatives and of clones is addressed in the Clones & Teaming section. It also deals with tied preferences, vote-splitting, teaming, identical and fraternal clones as well as forward and reverse slates. The Teaming Thresholds section evaluates the conditions for teaming to be successful within a variety of scenarios. The Summary lists the significant properties and features identified in this chapter.

Evaluations (Party List)

The party-list version of CHPV/GV is explored in this intermediate-level chapter. The Introduction section previews this version and the need for optimal proportionality. It also introduces two analytical tools; namely stick diagrams and multi-party maps. These two tools are developed in the following Diagrams & Maps section. The CHPV Maps one displays examples of two-party and three-party multiple-winner maps. The proportion of optimal outcomes in multiple-party multiple-winner elections is studied in the Optimality of CHPV section. The Party Cloning one compares the susceptibility of CHPV to party cloning with that of an optimally proportional system. The Proportionality of CHPV section investigates how this parameter varies with the number of winners required and of parties standing. The Summary lists the significant properties and features identified in this chapter.

Comparisons (Ranked Ballot)

This chapter compares the ranked ballot version of CHPV against many of its numerous single-winner rivals; at an intermediate level. The Introduction section previews these rivals and many of the aspects for comparison. The Plurality [≡ GV(r=0)] and the Borda Count [≡ GV(r→1)] sections briefly describe these systems and their properties as a prelude to the Geometric Voting section that covers GV(0≤r<1) and equivalent positional voting systems. This GV section also covers preference exchanges, three-candidate elections and maps, preference weightings and rankings for consensus, balancing polarization and consensus, balancing vote-splitting and teaming as well as tactical voting. In the Positional Voting section polarization and consensus indices for vectors are developed to establish a basis for comparing system biases. The effects of truncation on these indices are also investigated. Condorcet Methods and the Alternative Vote are briefly described and compared to CHPV in these sections. The Plurality Rule Methods one defines this rule, lists further single-winner methods, compares them against CHPV and considers instant run-off CHPV. The Summary lists the significant properties and features identified in this chapter.

Comparisons (Party List)

This intermediate-level chapter compares party-list CHPV with some of its alternative multiple-winner methods where the Introduction section previews these competing party-proportional voting systems. The Single Transferable Vote one describes this method, its various quotas and also its properties against CHPV. An analysis of the Largest Remainder versus the Highest Averages versions of proportional representation systems is found in the Party-List section. The Party-List ~ Hare Quota, the Party-List ~ Droop Quota, the Party-List ~ D'Hondt and the Party-List ~ Sainte-Laguë sections cover these four rival methods. Each one provides a brief description, some example maps and an analysis of their optimality, party cloning susceptibilities and proportionality against CHPV; see Maps, Opt, PC and Pro links opposite. In the Mixed Member Systems one these types are briefly described and compared with CHPV. The Summary lists the significant properties and features identified in this chapter.

Conclusions

The Ranked Ballot CHPV section concludes that it is a simple, transparent, efficient, reliable and balanced voting system for use in single-winner elections where there is no bias in favour of polarized or consensus candidates and where the capacity for voters to thwart teaming is retained while the effects of vote splitting are minimised.

The Party-List CHPV section concludes that it is a simple yet reliable, practical and party-proportional voting system for use in multiple-winner elections partitioned into concurrent closed-list contests across numerous local few-winner (W ≤ 6) constituencies where invulnerability to cloning by parties with minority support is required. Additionally, supporters of a party may be permitted a free party-list in the form of a CHPV ranked ballot of their party candidates in order to select the winners of the seats won by their party.

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