Post by Jameson Quinn
I just published "Reweighted" methods are second rate
This is of course my own personal opinion only, but I'd welcome comments
either here or on Medium.
To be a bit nitpicky, I don't think it's true that good proportional
methods ignore considerable amounts of the ballot data. Consider Schulze
One could argue that every subset contest (e.g. ABCD vs ABCE) only takes
some of the ballot information into account, but the same is true of
single-winner Schulze (the A vs B contest only considers how many voters
preferred A to B), and I would say Schulze uses the full information
available to it.
My strategy-hardened variant of BTV
also considers more than just a fixed quota of the ballots each time a
candidate is to be elected; and it does so for the purpose of reducing
free riding. When it considers whether A should be elected, it maximizes
the number of voters who can be counted towards A subject to that every
candidate already elected has the support of more than a Droop quota.
I think the reason that RRV doesn't work is because RV itself doesn't
obey Majority. This lets information from the downweighted ballots bleed
through to the no-longer-downweighted ballots in a way that makes free
riding particularly easy. The reweighted party list methods that use
only Plurality ballots (e.g. Sainte-Laguë, D'Hondt) don't have that
problem because there's no possibility of such a bleedthrough, and
Plurality passes the Majority criterion.
Does PAV pass Droop proportionality according to the submitted ballots?
Approval passes Majority according to the submitted ballots (i.e. not
necessarily the preferences leading to the ballots, but the yes-or-no
preferences expressed on them).
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