Conclusions: Ranked Ballot CHPV 1

No single electoral method is suited to every election scenario. And every voting system has its weaknesses as well as its strengths. So, to which applications is ranked ballot CHPV best suited? Also, why is it a better solution than any alternative method? This concluding section aims to assemble the answers to such questions and hence to promote ranked ballot CHPV as a viable, effective and balanced voting system for certain specified electoral scenarios.

A Practical Voting System

Consecutively Halved Positional Voting (CHPV) is a form of preferential voting, positional voting and geometric voting. As a preferential system, voters express their relative preferences for candidates via a ranked ballot. As it is a variant of geometric voting, the absolute value of any CHPV preference is irrelevant. Starting with any conveniently weighted first preference, each subsequent preference is then worth half of the preceding one. However, having this common ratio of 2:1 for adjacent weightings is crucial for the outcome candidate rankings. It is a key property of CHPV that each preference is worth the same as the sum to infinity of all the lower preferences.

CHPV is classified as a direct plurality rule method. The tally for each candidate is the sum of the products of the number of preferences at each rank position and its positional weighting. So the individual voter rankings of the candidates are readily converted in one round into a collective and decisive ranking of them. The candidate with the highest tally wins a single-winner election. If more than one winner is needed, then the top-ranked candidates fill the requisite vacancies.

Ranked ballot CHPV is the most practical variant of geometric voting. With a common ratio of 2:1, the various weightings are numerically easy to handle and, most importantly, no rounding is ever required or permitted. Therefore, full accuracy is maintained throughout and false rankings are never produced. As well as manual counting, CHPV is equally suitable for electronic voting given that its weightings are also those of the binary number system.

Every CHPV preference expressed by a voter counts and it may therefore affect the election outcome. In contrast, first-past-the-post (FPTP) only allows first preferences to be cast and with the alternative vote (AV) many if not most preferences are never utilized in determining the winner. In CHPV, unlike FPTP and the Borda Count, its differential weightings are unique. By only generating transitive rankings, ranked ballot CHPV avoids the intransitive ranking cycles and resultant paradoxes that plague Condorcet methods.

As a positional voting system, CHPV passes the summability, consistency, participation, resolvability and Pareto criteria. Unlike the Borda Count, CHPV satisfies the mono-raise-random and mono-sub-top monotonicity criteria. Condorcet methods and AV fail the consistency and participation criteria. Additionally, AV fails the summability criterion and is not monotonic. Unlike AV, CHPV employs a straightforward and deterministic counting algorithm. Ranked ballot CHPV is a simple, transparent, efficient and reliable voting system for use in single-winner elections.

Preventing Election Outcome Manipulation

Any fair voting system treats all voters as equal participants and likewise all candidates. The Gibbard – Satterthwaite theorem concludes that all such preferential systems are vulnerable to tactical voting. This occurs when a voter has an incentive to vote insincerely in order to effect a more preferred outcome. Some degree of manipulation may be inevitable but some systems offer more incentives than others. For example, FPTP does not even allow voters to express their preferences. Voters are frequently faced with either 'wasting' their vote on their most preferred but probably losing candidate or voting for their more preferred of two lower-ranked but potentially winning candidates.

Unlike FPTP, CHPV does not encourage or force some voters to vote tactically but enables them all to express their full set of sincere preferences. Tactical voting requires voters to predict in advance which candidates are potential or likely winners. As this is much more difficult in CHPV elections compared to FPTP ones, tactical voting is a risky option here and hence much less likely to occur. Unlike the Borda Count, CHPV is less susceptible to the tactical option of burying candidates.

The manipulation of election outcomes by candidates or parties is however of more concern. The strategic nomination of clone candidates is designed to affect the collective candidate rankings. AV is not vulnerable to cloning so, unlike positional systems, it does not experience the effects of teaming or vote splitting. FPTP suffers from vote splitting but not teaming. At the other vector extreme, the Borda Count does not experience vote splitting but it is inherently vulnerable to teaming. The same is true for all geometric voting anti-vectors. While vote splitting is self-harming, teaming attempts to gain an unfair advantage over others. Hence, systems ranging from the Borda Count to Anti-Plurality are intractably wide open to cheating.

Ranked ballot CHPV elections may experience either vote splitting or teaming depending upon how voters actually cast their preferences. As a voting system, CHPV does not prevent teaming but it does retain the capacity for those voters opposed to cloning to thwart any such teaming attempt. When a clone set attempts teaming by issuing a slate, supporters of other candidates only need to reverse the slate and vote accordingly. This tit-for-tat retaliation strategy is always successful in combating teaming and, indeed, it often inflicts harm on the offending clone set. In CHPV elections, there is simply no incentive to clone or to retaliate by cloning when this defensive strategy is ready to be deployed.

CHPV is the central GV variant that evenly balances the magnitude and scope of vote splitting against the magnitude and scope of teaming. A lower common ratio increases the effect of vote splitting on an election outcome. A higher common ratio increases the effect of teaming and here the slate-reversal strategy is no longer guaranteed to be successful. Ranked ballot CHPV is therefore the positional voting system with the optimum trade-off in the conflict between vote splitting and teaming.

Proceed to next page > Conclusions: Ranked Ballot CHPV 2

Return to previous page > Comparisons: Summary (Multiple-Winner) 2