Violations of betweenness or random errors

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Stochastic models for binary discrete choice under risk: a critical primer and econometric comparison (2008, background): “Blavatskyy (2007) has offered an interesting heteroscedastic model based on the notion that subjects will trim or truncate ‘‘illogical’’ errors.”
Stochastic Utility Theorem (2008, background): “0 < x , ( ) 2 1 = Ψ x if 0 = x and ( ) p x − = Ψ 1 if 0 > x , where 0 > p is constant, stochastic utility representation becomes a tremble model of Harless and Camerer (1994). Axiomatization of stochastic utility allows characterizing the above mentioned models in terms of the properties of individu”