Comparisons: Geometric Voting 11
CHPV versus other GV Variants
Although GV with a common ratio of zero is equivalent to plurality, it is plurality that would be used in any practical election as only first preferences have any value. Similarly, although useful for analysis, GV with a common ratio approaching one is impractical for an actual election. Here, the conventional Borda Count method would be retained instead. The middle value between these two extremes is numerically one half but this does not necessarily mean that GV with r = 1/2 is the best alternative to these two polar opposites. So why is CHPV the optimum variant of GV and worthy of use in real elections?
Firstly, when expressed using integers, its common ratio is simply 2:1. For a practical system, these two minimal integers make it very easy for electoral staff to allocate preference weightings and to calculate candidate tallies. As demonstrated in the earlier Description: Counting section, no rounding is either required or permitted in CHPV so ensuring perfect accuracy for any election outcome. While tactical voting potentially affects all GV variants, in terms of fairness however, it is the type of support needed by a candidate to win and its ability to combat party manipulation of outcomes where CHPV demonstrates its superiority.
CHPV: Strategy for Winning
Clearly, every candidate should try to maximise the rank of every preference awarded by a voter. Unlike GV with r = 0 (or plurality), CHPV promotes a healthy democracy where no voter should be ignored and all should be canvassed. With CHPV, a polarized candidate needs a two-thirds majority of first preferences for victory to be guaranteed; see the Evaluations: Majority Criteria 3 page. However, unlike GV with 1/2 < r < 1 (or the Borda Count), a consensus candidate with no first preferences cannot win in an election where only three candidates stand; see the Evaluations: Majority Criteria 2 page. Even with any number of candidates, a consensus candidate with a unanimous nth preference from every voter cannot win where this preference is lower in rank than the mean-weighted one; see page 5 of this section. For CHPV, this rank (n) is approximately equal to the binary logarithm of the number of candidates (log2N).
For low values of r, a candidate could win with a plurality - but very low minority - of the first preferences. For high values of r, a candidate with a majority of first preferences could easily lose to one gaining a larger number of somewhat lower preferences. With CHPV, a candidate needs to accumulate high proportions of the high (above-mean-weighted) preferences to win. Unlike GV with r = 0, every preference from every voter counts in CHPV. GV with r → 1 is equivalent to electing the candidate with the highest average rank position; which could be almost as low as the middle rank.
In contrast, CHPV is not biased in favour of either polarized or consensus candidates. It evenly balances the need to seek increases in the rank of the high preferences against the need to increase their proportion too. With CHPV, a promotion of one place in rank for a preference is worth the same as receiving one additional preference of the original rank instead. With ranked ballot CHPV, polarized candidates with a narrow electoral base and consensus ones with weak support will fail to win. Candidates must therefore attempt to broaden their appeal as much as to strengthen it.
CHPV: Minimising Manipulation
As described earlier, strategic nominations are where clone candidates are insincerely added (or deleted) by parties purely to effect a more preferred outcome with the same voter input. Adding clones in a GV with low r (or plurality) election will split the vote for that party. Any resultant change in outcome will be detrimental to that party. It is clearly not in the interests of a party to nominate identical clones for fear of self-harm. Therefore, avoidance of vote splitting is the responsibility of the candidates and parties and not of the voting system itself.
However, the reverse is true for teaming. As fraternal cloning is designed to gain victory through cheating, then ideally the voting system should prevent this unfair outcome. The major handicap of a GV with high r (or Borda Count) election is that it is highly vulnerable to teaming and is wide open to abuse. GV variants with common ratios above one half are still inherently vulnerable to teaming; albeit less so with decreasing r; see the Evaluations: Teaming Thresholds 5 page. These same GV variants also fail the mono-raise-random and mono-sub-top monotonicity criteria unlike CHPV and the GV (r < 1/2) variants; see the Evaluations: General Criteria 3 page.
CHPV is therefore the GV variant with the highest common ratio that always retains the capacity for teaming to be thwarted. Although the system itself cannot prevent it, the voters opposing the clone candidates can always successfully combat teaming using the standard slate-reversal retaliation strategy; see the Evaluations: Teaming Thresholds 4 page. With CHPV, there is never any incentive to clone or to retaliate by cloning provided this strategy is enacted where necessary; see the Evaluations: Clones & Teaming 7 page.
Also, as highlighted on page 6 of this section, CHPV evenly balances both the chances and consequences of vote splitting and of teaming when attempting to get supporters to adhere to a party slate. The teaming index that indicates the potential scope for successful teaming is 1/2 for CHPV; see the Evaluations: Teaming Thresholds 5 page. This too represents the condition for equilibrium between the GV extremes of r = 0 (or plurality) and r → 1 (or the Borda Count).
CHPV: Summary
A common ratio of one half is therefore not an arbitrary value but one with several advantages and many threshold properties. In comparison with other GV variants, CHPV is the most practical electoral method. It is also the best voting system in terms of simultaneously requiring a winning candidate to have broad as well as strong support while still retaining the capacity for voters to thwart attempts at cheating.
Proceed to next section > Comparisons: Positional Voting
Return to previous page > Comparisons: Geometric Voting 10