Knowing how small violation individuals would accept against stochastic dominancerules is a prerequisite for applying almost stochastic dominance criteria. Different fromprevious results obtained by experiments, this paper estimates acceptable violation againststochastic dominance rules with 940,904 observations of real data on a deductible choiceof automobile theft insurance. We find that for all policyholders in the sample who chose a low deductible, the upper bound estimate of acceptable violation ratio is 8.198−08 which is close to zero. On the other hand, considering most decision makers, such as 99% (95%) of the policyholders in the sample, who chose the low deductible, the upper bound estimate of the acceptable violation ratio is 0.0399 (0.0727). Our results provide reference values of the acceptable violation ratio and justification for applying almost stochastic dominance rules.