  The Greenberger-Horne-Zeilinger (GHZ) puzzle has been used to study quantum
nonlocality and provide an all-or-nothing, no-go theorem for local
hidden-variable models. Recent experiments using coincident-detected entangled
photons prepared in a three-particle GHZ state have been used to test quantum
nonlocality, but fail to rule out local realism due to a reliance on the
fair-sampling hypothesis and insufficient detection efficiency. This paper
describes a physically motivated local hidden-variable model based on
amplitude-threshold detection that is capable of producing similar results.
Detection efficiencies for the model are within the bounds permitted for local
realism and, interestingly, exhibit statistical correlations between detectors,
even when the detection events are spacelike separated. Increasing the
detection threshold improves agreement with the ideal quantum predictions at
the cost of decreased detection efficiency. A curious emergent feature of the
model is that detection efficiencies may depend upon which observables are
chosen for measurement.
