Comparisons: Summary (Single-Winner) 1

Contrasting properties and features of ranked ballot CHPV in relation to other single-winner voting systems that are highlighted in the preceding sections of this chapter are summarised below:

CHPV versus Plurality [First-Past-The-Post (FPTP)]

• FPTP satisfies the majority criterion while CHPV does not.
• In FPTP, a candidate may however win with considerably less than one half of the vote.
• Both FPTP and CHPV satisfy the two-thirds majority criterion.
• In CHPV, a candidate may however win with considerably less than two thirds of the vote.
• FPTP focuses on first preferences only and hence favours polarized candidates over consensus ones.
• CHPV focuses on the array of high-ranking preferences and may favour either a consensus candidate with a sufficiently high-rank preference or a polarized one with a sufficiently high level of support.
• By only allowing one preference to be expressed, FPTP encourages tactical voting to avoid 'wasted' votes.
• As all preferences count towards a tally and by allowing a preference for each candidate to be expressed, CHPV discourages tactical voting.
• As predicting outcomes using CHPV compared to FPTP is much riskier, tactical voting is more difficult and much less likely to occur.
• Vote splitting is more likely to affect the result of a FPTP election than a CHPV one.
• In simultaneous single-winner FPTP elections, parties with geographically concentrated support will prosper over those with similar levels of support but more evenly distributed.
• This may result in one party having more seats but less votes than another party.
• It may also result in one party having a majority of seats on a relatively small minority share of the vote.
• FPTP constituency boundaries can be manipulated (gerrymandered) to skew election outcomes in favour of a given party.
• In FPTP elections with numerous candidates, the number of 'wasted' votes may typically outnumber the number of those not wasted.
• Consequently, parties focus only on 'swing' voters in 'marginal' FPTP constituencies and largely ignore all the other voters.
• This breeds voter alienation and poor turnouts by the electorate in FPTP elections.
• In terms of the collective candidate rankings, FPTP is equivalent to GV with a common ratio of zero (r = 0) while CHPV is GV with r = 1/2. [Hence, see CHPV versus GV(r) for further comparisons.]

CHPV versus the Borda Count

• The Borda Count employs a linear progression of points with a common difference of one point.
• In contrast, CHPV employs a geometric progression of weightings with a common ratio of one half.
• The Borda Count does not satisfy the majority or the two-thirds majority criteria.
• Indeed, the candidate with the fewest first preferences may win.
• Further, a candidate with a large majority of first preferences may be beaten by a candidate with a second preference from every voter.
• The Borda Count focuses on the average preference for a candidate and hence favours consensus over polarized ones.
• CHPV focuses on the array of high-ranking preferences and may favour either a consensus candidate with a sufficiently high-rank preference or a polarized one with a sufficiently high level of support.
• For the Borda Count, the average rank position of the preferences for a candidate also determines the collective rank position of the candidate in the election.
• The Borda Count does not suffer from vote splitting.
• Unlike CHPV, the Borda Count is highly and inherently vulnerable to teaming.
• In terms of the collective candidate rankings, the Borda Count is equivalent to GV where the common ratio approaches one (r → 1) while CHPV is GV with r = 1/2. [Hence, see CHPV versus GV(r) for further comparisons.]

CHPV versus GV(r)

• As the common ratio varies from r = 0 (≡ FPTP) through r = 1/2 (CHPV) to r → 1 (≡ Borda Count), GV is able to represent a wide range of positional voting systems.
• For three candidates, this range forms a circular arc when plotted from the top-preference apex to the centre of a three-preference triangular map.
• Any three-candidate positional voting system between plurality and the Borda Count is equivalent to a GV(r) vector with a common ratio r = (w₂-w₃)/(w₁-w₂).
• The effect of exchanging adjacent preferences in a three-candidate GV contest can be visualised by plotting irregular hexagons on a triangular map.
• On a three-candidate map, the average preference shares per voter can be plotted for each candidate and is fixed for any given GV election irrespective of the value of r.
• Parallel iso-tally (common tally value) grid lines can be superimposed onto such maps where the common gradient of the lines reflects the value of r.
• As r increases from 0 (≡ FPTP) towards 1 (≡ Borda Count), the gradient of the grid lines also increases.
• By varying the gradient of the parallel grid lines, it is easy to visually observe how the choice of the common ratio (r) affects the outcome of any three-candidate positional voting election.

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