Geometric Voting and Consecutively Halved Positional Voting - Comparisons: Summary (Single-Winner) 3

Comparisons: Summary (Single-Winner) 3

Unlike CHPV, Condorcet methods by definition satisfy the Condorcet Winner criterion.
Unlike CHPV, Condorcet methods do not satisfy the consistency and participation criteria.
The counting process is significantly longer for Condorcet methods than for CHPV.
Pairwise comparisons used by Condorcet methods only focus on the signs of the differences in support for candidates and ignores their magnitudes.
Therefore, intransitive preference cycles and paradoxical results are commonplace.
The differential weighting (w_x - w_y) for any two CHPV weightings is unique.
Intransitive candidate rankings do not occur when using CHPV.
Unlike CHPV, some Condorcet methods satisfy the Independence of Clones criterion.
Like the Borda Count, Condorcet methods favour consensus candidates over polarized ones.

The AV algorithm is based on the transfer of votes following the elimination of a candidate.
AV satisfies the majority criterion while CHPV does not.
CHPV satisfies the summability, consistency, participation and monotonicity criteria while AV does not.
Unlike CHPV, the AV algorithm is not deterministic as (non-repeatable) random selection may be required prior to the final round.
The winner may hence vary in a rerun despite the election profile being unaltered.
The counting process is considerably longer for AV than for CHPV.
Unlike CHPV, AV satisfies the Independence of Clones criterion so it does not suffer from vote splitting or teaming.
Like FPTP, AV focuses on the top-ranked preferences only (after each elimination) and hence favours polarized over consensus candidates.
In AV, many if not most of the preferences expressed by voters (the lower ones) are never used while in CHPV every preference counts.

During each vote-processing round, a PR method establishes a tally for each option, ranks the options according to those tallies and selects a subset of options with the highest tallies.
A single-round or direct PR method only requires a winner to have a plurality and not a majority of the tallies.
A multiple-round or iterative PR method requires a winner to have both a majority and a plurality by the final round.
CHPV yields a definitive result after a single round of counting in comparison with iterative PR methods such as exhaustive plurality, two-round plurality, the supplementary vote, Coombs method and Bucklin voting and it is often easier to understand and easier to use.
Unlike CHPV, some other direct PR methods such as approval voting and range voting are neither preferential nor positional voting systems.
In contrast to CHPV and especially to FPTP, approval and range voting are more likely to select a 'consensus' candidate over a 'polarized' one.
Tactical voting is much less likely to occur in CHPV than in either approval or range voting.
Using Instant Run-off CHPV instead of random selection to resolve critical CHPV ties is not recommended.