[EM] Arrow's theorem and cardinal voting systems

[Kristofer Munsterhjelm]

On 15/01/2020 21.57, Forest Simmons wrote:
> Just a couple of additional thoughts:
> 
> Besides Arrow and Gibbard-Sattherwaite we have lots of criterion
> incompatibility results from Woodall, and defensive strategy criteria
> from Mike Ossipoff, Steve Eppley, et. al..  In particular we never
> worried about Later No Help and later No Harm until Woodall came along.
> Venzke and Benham picked up the torch and brought Woodall into the EM
> Listserv discussion.
> 
> Many EM contributors have clarified which combinations of various
> criteria of more practical than academic stripe are compatible or not:
> Participation, FBC, Precinct Summability, Chicken, etc. 
> 
> In particular, we now know through the work of Ossipoff, Venzke, Benham,
> and others that the Chicken Defense and Burial Defense (against CW
> burial) are incompatible in the presence of Plurality and the the FBC,
> unless we allow an explicit approval cutoff or some other strategic
> switch on the ballots.  Standard ordinal ballots are not adequate for
> this even when truncation and equal rankings (including equal top) are
> allowed.   A non-standard ballot that allows us to get compatibility to
> all of these except the CC is MDDA(sc) which is Majority Defeat
> Disqualification Approval with symmetric completion below the approval
> cutoff.  This method also satisfies other basic criteria such as
> Participation, Clone Independence, Mono-Raise, Mono-Add, and IDPA, for
> example.
> 
> In the context of the current discussion, the approval cutoff or some
> equivalent strategic switch is essential for the compatibility of
> chicken resistance and burial resistance..  No strategy, no
> compatibility. So basically there is no decent method that is resistant
> to both Burial of the CW and Chicken offensives.  (IRV is chicken
> resistant and has a form of burial resistance, but routinely buries the
> CW unless voters strategically betray their favorite to save the CW.
> Furthermore, it fails mono-raise.)

The various Condorcet-IRV hybrids do help there, e.g. Benham passes
DMTBR. But I see what you mean :-)

> Before collaborative efforts of EM List members there was no known clone
> independent, monotonic method for electing from the uncovered set.  The
> closest thing was Copeland, which is clone dependent.
> 
> Again the main point is that Arrow, and Gibbard-Satterthwaite are not
> the "end of history" for election methods, just like the collapse of the
> USSR was not the end of history as Fukuyama once proclaimed or
> Thatcher's famous TINA "there is no alternative" (to capitalism).  Arrow
> and G-S give very valuable insights and help us avoid cul-de-sacs, but
> they are not the last word in election methods progress.  The "end of
> history" and TINA slogans are an excuse for giving up prematurely for
> lack of imagination.

If anything, it's the other way around. If there were a perfect method,
there would be no need for imagination: just find out what that perfect
method is and settle on it, done. That there is no perfect method is
what gives room for imagination.