Standard of proof in common law: Mathematical explication and probative value of statistical data

Abstract

As a result of recent amendments to the procedural legislation of Ukraine, one may observe a tendency in judicial practice to differentiate the standards of proof depending on the type of litigation. Thus, in commercial litigation the so-called standard of “probability of evidence” applies, while in criminal proceedings – “beyond a reasonable doubt” standard applies. The purpose of this study was to find the rational justification for the differentiation of the standards of proof applied in civil (commercial) and criminal cases and to explain how the same fact is considered proven for the purposes of civil lawsuit and not proven for the purposes of criminal charge. The study is based on the methodology of Bayesian decision theory. The paper demonstrated how the principles of Bayesian decision theory can be applied to judicial fact-finding. According to Bayesian theory, the standard of proof applied depends on the ratio of the false positive error disutility to false negative error disutility. Since both types of error have the same disutility in a civil litigation, the threshold value of conviction is 50+ percent. In a criminal case, on the other hand, the disutility of false positive error considerably exceeds the disutility of the false negative one, and therefore the threshold value of conviction shall be much higher, amounting to 90 percent. Bayesian decision theory is premised on probabilistic assessments. And since the concept of probability has many meanings, the results of the application of Bayesian theory to judicial fact-finding can be interpreted in a variety of ways. When dealing with statistical evidence, it is crucial to distinguish between subjective and objective probability. Statistics indicate objective probability, while the standard of proof refers to subjective probability. Yet, in some cases, especially when statistical data is the only available evidence, the subjective probability may be roughly equivalent to the objective probability. In such cases, statistics cannot be ignored

Development of Advanced Methodology of Experimental Research on Oscillation Processes Intensity for Machine-Tractor Units

“…The obtained digital signals from the accelerometer sensors of the tablet computer (see Figure2) were imported into the Mathcad software environment to determine their statistical characteristics(Zhiltsov, 2015;Borysova, 2021;Mazhayskiy et al, 2021;Hassan et al, 2022;Khadim et al, 2023).a) b) Fig. 2 -Accelerometer Meter software environment interface based on Android a) the measuring system as part of the PC; b) measurement of vertical acceleration (marked Z).…”