Results from social choice theory are increasingly used to argue about collective decision making in computational multiagent systems. A large part of the social choice literature studies voting paradoxes in which seemingly mild properties are violated by common voting rules. In this paper, we investigate the likelihood of the Condorcet Loser Paradox (CLP) and the Agenda Contraction Paradox (ACP) using Ehrhart theory, computer simulations, and empirical data. We present the first analytical results for the CLP on four alternatives and show that our experimental results, which go well beyond four alternatives, are in almost perfect congruence with the analytical results. It turns out that the CLP---which is often cited as a major flaw of some Condorcet extensions such as Dodgson's rule, Young's rule, and MaxiMin---is of no practical relevance. The ACP, on the other hand, frequently occurs under various distributional assumptions about the voters' preferences. The extent to which it is real threat, however, strongly depends on the voting rule, the underlying distribution of preferences, and, somewhat surprisingly, the parity of the number of voters.