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

Until recently, multiple synthetic data sets were always released to analysts, to allow valid inferences to be obtained. However, under certain conditions - including when saturated count models are used to synthesize categorical data - single imputation ($m=1$) is sufficient. Nevertheless, increasing $m$ causes utility to improve, but at the expense of higher risk, an example of the risk-utility trade-off. The question, therefore, is: which value of $m$ is optimal with respect to the risk-utility trade-off? Moreover, the paper considers two ways of analysing categorical data sets: as they have a contingency table representation, multiple categorical data sets can be averaged before being analysed, as opposed to the usual way of averaging post-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 multiple categorical synthetic data sets. Finally, the synthesis methods are demonstrated empirically.