Evaluations: Summary (Ranked Ballot) 1

Ranked Ballot GV and CHPV Elections

Properties and features of GV/CHPV that are highlighted in the preceding sections of this chapter are summarised below:

• Both GV and CHPV satisfy the summability criterion; with a first order function of N.
• The GV/CHPV count process is therefore completed in a quick time.
• Both GV and CHPV satisfy the consistency, participation and resolvability criteria.
• Both GV and CHPV satisfy the pareto condition for a fair voting system.
• Neither GV nor CHPV satisfies the reversal symmetry criterion.
• Both GV and CHPV satisfy the mono-raise, mono-raise-delete, mono-append, mono-remove-bottom, mon-sub-plump, mono-add-plump and the mono-add-top monotonicity criteria.
• The mono-raise-random and the mono-sub-top monotonicity criteria are satisfied by CHPV and GV (r < 1/2) but not by GV (r > 1/2).
• Both GV and CHPV satisfy the later-no-help criterion but only GV (r = 0) satisfies the later-no-harm criterion.
• Neither GV nor CHPV is a pairwise or Condorcet electoral method.
• Neither GV nor CHPV satisfies the Condorcet winner criterion or the Condorcet loser criterion.
• Neither GV nor CHPV satisfies the majority criterion; except for GV (r = 0).
• CHPV satisfies the two-thirds majority criterion irrespective of the number of candidates.
• With few candidates competing in a CHPV election, a lower majority threshold (m) in the range 1/2 ≤ m < 2/3 applies.
• With GV, a consensus candidate with second preferences from every voter cannot win against two polarized ones who share all the first preferences between them provided r < 1/2.
• With GV, a consensus candidate with second preferences from every voter may win against two polarized ones who share all the first preferences between them provided r > 1/2; this possibility increasing linearly as r rises.
• CHPV (GV with r = 1/2) is hence the threshold for such a consensus candidate being able to overtake two more popular but polarized candidates; at best only a three-way tie being possible here.
• With strong support (high proportion of first preferences), a polarized candidate is more likely to win a GV election when the common ratio is low or zero.
• With broad support (preferences with a high mean rank position), a consensus candidate is more likely to win a GV election when the common ratio is high or approaches one.
• Another candidate may simultaneously beat a polarized candidate and a consensus one when the common ratio is intermediate; such as with CHPV.
• Neither GV nor CHPV satisfies the Independence of Irrelevant Alternatives (IIA) criterion.
• This failure to satisfy IIA is the sole reason that both GV and CHPV conform to Arrow's Impossibility Theorem.
• Teaming and vote splitting can be successful in affecting CHPV election outcomes.
• Tied voter preferences are prohibited to restrict opportunities for successful teaming.
• The strategic nomination of identical clones promotes vote splitting in GV and CHPV elections.
• The strategic nomination of fraternal clones promotes teaming in GV and CHPV elections.
• Fraternal clones are created when a party instructs its supporters to adhere to a (forward) rank-ordered slate of its own multiple candidates when voting in a single-winner election.
• Identical clones are created by default when no such slate is issued.
• Where a party nominates identical clones (no slate), self-harm may occur due to vote splitting.
• Where a party nominates fraternal clones (slate issued), unfair advantage may be gained through teaming.
• By reversing the forward slate, supporters of an opposition party may thwart such attempts at teaming.
• Where there are several opposition parties, the cloning party may even suffer self-harm through teaming attempts.
• Using truncation to avoid expressing any preference for clone candidates is an even more effective method of punishing the cloning party.
• As a voting system, CHPV does not satisfy the Independence of Clones criterion.
• However, with CHPV, voters are always capable of successfully thwarting teaming attempts.
• Using CHPV, there is never any incentive to clone as cloning is either unsuccessful or self-harming; provided slate-reversal retaliation is enacted where necessary.
• For GV, the analysis of various cloning scenarios employs a square cloning map.
• Teaming thresholds represent the boundaries between attempts at strategic nominations being successful (teaming) or counterproductive (vote splitting).
• Teaming thresholds are functions of the common ratio (r) and the number of competing non-clone candidates (M).
• Teaming thresholds appear as a pair of straight parallel lines on a cloning map for a given r and M.
• Vote splitting results for scenarios located between these two lines.
• Teaming occurs for scenarios located elsewhere on the map.
• For GV with r = 0, only vote splitting results (as the teaming thresholds are co-incident with the two sides of the cloning map).
• For GV with 0 < r < 1/2, the anti-teaming strategy of slate reversal is always successful in punishing any attempt to gain advantage through cloning.
• For GV with r = 1/2 (CHPV), the anti-teaming strategy of slate reversal is always successful in at least thwarting if not actually punishing any attempt to gain advantage through cloning.
• For GV with 1/2 < r < 1, the anti-teaming strategy fails to guarantee success and indeed becomes increasingly counterproductive as r and M rise.
• For GV with r → 1, only teaming results (as the two teaming thresholds are co-incident with each other).
• To ensure that teaming can always be thwarted, GV with r ≤ 1/2 must be employed.
• CHPV is therefore the upper threshold GV variant that allows voters to successfully combat teaming.

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