Voting procedures are  typically motivated by social choice desiderata or criteria of performance. These are, however, largely omitted in the design and evaluation of voting rules in practice. We present some important voting paradoxes and theoretical results stating incompatibilities between various choice desiderata. We also discuss possible reasons for omitting these results in institution design. While most rule innovations are based on other than social choice results, one proposed relatively recently takes its cues from the theory. We briefly evaluate the proposed voting procedure and stress the importance of a comprehensive comparative analysis of several voting rules and criteria of performance in the rule selection process.