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Until recently, multiple synthetic data sets were always released toanalysts, to allow valid inferences to be obtained. However, under certainconditions - including when saturated count models are used to synthesizecategorical data - single imputation ($m=1$) is sufficient. Nevertheless,increasing $m$ causes utility to improve, but at the expense of higher risk, anexample of the risk-utility trade-off. The question, therefore, is: which valueof $m$ is optimal with respect to the risk-utility trade-off? Moreover, thepaper considers two ways of analysing categorical data sets: as they have acontingency table representation, multiple categorical data sets can beaveraged before being analysed, as opposed to the usual way of averagingpost-analysis. This paper also introduces a pair of metrics, $\tau_3(k,d)$ and$\tau_4(k,d)$, that are suited for assessing disclosure risk in multiplecategorical synthetic data sets. Finally, the synthesis methods aredemonstrated empirically.

On integrating the number of synthetic data sets $m$ into the 'a priori' synthesis approach