All relevant contigencies have been investigated in order to establish the frequency with which a Condorcet winner is elected under the plurality and approval procedures when voters are assumed to act sophisticatedly, and given that: (1) there are three candidates of whom one must be elected; (2) voters have complete information regarding all other voters (strict) preference orderings; (3) the electorate consists, alternatively, of three, four, or five blocks of voters; 4) all contingencies are considered equally likely. The main results are: (i) the approval procedure is significantly more Condorcetefficient than the plurality procedure; (ii) when a Condorcet winner exists, a non-Condorcet winner is elected very rarely under both voting procedures; (iii) voting under the approval procedure results more often in a determinate winner when a Condorcet winner exists, whereas voting under the plurality procedure results more often in a determinate outcome when there are cyclical majorities; (iv) sophisticated voting under the approval procedure seems to be more Condorcet-efficient than the sincere version of this procedure, whereas the Condorcet-efficiencies of sincere and sophisticated voting under the plurality procedure are not significant different.