This article compares one-dimensional and multi-dimensional dialogue act tagsets used for automatic labeling of utterances. The influence of tagset dimensionality on tagging accuracy is first discussed theoretically, then based on empirical data from human and automatic annotations of large scale resources, using four existing tagsets: damsl, swbd-damsl, icsi-mrda and maltus. The Dominant Function Approximation proposes that automatic dialogue act taggers could focus initially on finding the main dialogue function of each utterance, which is empirically acceptable and has significant practical relevance.