Auditors’ Evaluations of Uncertain Audit Evidence: Belief Functions versus Probabilities

Abstract

Recently, Shafer and Srivastava [1], Srivastava and Shafer [2], Srivastava [3]–[4], and Van den Acker [5] have identified appealing features of belief function evidential networks. These networks can express the support that audit evidence provides for assertions, accounts and financial statements. These networks can also aggregate many pieces of evidence into an overall level of support for a particular assertion, account or an entire set of financial statements. There is little empirical evidence about the ability of practicing auditors to express their evaluations of the strength of audit evidence in terms of belief functions. Many traditional models assume the use of probabilities. These might be called the traditional type of subjective probabilities. They are additive by definition, i.e. P (a) + P (~a) = 1. Throughout the remainder of this paper they will simply be referred to as probabilities. This study examines the question of expressing the support provided by audit evidence empirically. Auditors are asked to express the level of support that evidence provides for or against an assertion or account and the ignorance that remains about the assertion or account after considering the evidence. Many auditors who use probabilities to measure risk express ignorance by giving equal weight to support for and support against the objective. Belief functions express ignorance by allocating mass to all elements of the frame (all possible outcomes), an alternative that is distinct from assigning equal mass to each element of the frame. Thus, belief functions show ignorance as an amount separate from the amounts of support for and against the objective. Forty-nine experienced auditors were asked to estimate the strength of the evidence provided in twenty-eight different audit situations. These auditors were given the opportunity to model their estimates of support and ignorance in ways that were consistent either with belief functions or with Probabilities. In this study, a statistically significant percentage of the auditors represented their estimates in ways that were consistent with belief functions and were inconsistent with probabilities. This suggests that future practitioner decision aids may include belief functions as a way of naturally expressing the ignorance and risk that persist in many audit engagements. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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