Tim Hull wrote:
Regarding IRV, I do know it isn't ideal. In fact, if someone can show
me it's necessarily worse than plurality, I'd just stick
with plurality in single-winner and use STV in multi-winner.
Plurality's only advantages over IRV are just a lot of monotonicty and
mathematical elegance properties.
IRV's advantages over Plurality:
meets Majority for Solid Coalitions, Dominant Mutual Third, Condorcet
Loser, Clone-Winner.
The incentive for the voter to use the Compromise strategy is much much
weaker than in Plurality.
On this topic, does anyone know of a modified,
kind-of-Condorcet-but-not-quite method which preserves later-no-harm?
A method that would well handle all the 3-candidate examples you (Tim)
and Juho have been trading is one where the voters
can give an approval cutoff in their rankings. Rankings below the
'approval' cutoff cannot harm candidates ranked above it.
1. Voters rank candidates, truncation allowed but otherwise
equal-preferences not, and voters give an 'approval' cutoff.
Default placement is just above strict bottom or truncated candidates.
2. If one (remaining) candidate X is top-ranked (among remaining
candidates) on more than half the (unexhausted) ballots,
then elect X.
3. If not eliminate and drop from the ballots the least approved
candidate. Then ignore ballots that make no preference distinction
among remaining candidates (as 'exhausted') in resetting the majority
threshold. Ballots that no longer make any explicit approval
distinction among remaining candidates are now given the "default
placement" as if though the eliminated candidate/s had never
existed.
4. Repeat until there is winning X..
To answer your question more specifically, you might find CDTT methods
interesting.
http://nodesiege.tripod.com/elections/#methcdtt
The CDTT is a set of candidates defined by Woodall to include every
candidate A such that, for any other candidate B, if B has a
majority-strength beatpath to A, then A also has a majority-strength
beatpath back to B. (See Schulze <#methsch> for a definition of a
beatpath.) Another definition (actually, the one Woodall chooses to
use) of the CDTT is that it is the union of all minimal sets such that
no candidate in each set has a majority-strength loss to any candidate
outside this set. (Candidate A has a "majority-strength loss" to
candidate B if v[b,a] is greater than 50% of the number of cast votes.)
Markus Schulze proposed this set earlier, in 1997. His wording was to
take the /Schwartz/ set resulting from replacing with pairwise ties,
all pairwise wins with under a majority of the votes on the winning side.
http://wiki.electorama.com/wiki/CDTT
Limiting an election method's selection to the CDTT members can permit
it to satisfy the Minimal Defense criterion
</wiki/Minimal_Defense_criterion> (and thus the Strong Defensive
Strategy criterion </wiki/Strong_Defensive_Strategy_criterion>) and
the Majority criterion for solid coalitions
</wiki/Mutual_majority_criterion>, while coming close to satisfying
the Later-no-harm criterion </wiki/Later-no-harm_criterion>.
Specifically, the CDTT completely satisfies Later-no-harm
</wiki/Later-no-harm_criterion> in the three-candidate case, and
failures can only occur in the general case when there are
majority-strength cycles.
Chris Benham
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