SummaryThe Australian Senate is elected using a form of proportional representation in each of the six States and two Territories. Those candidates who receive more than a “quota” of votes are elected. In those cases where not enough candidates receive a quota of votes, the surplus votes of each elected candidate (that is, votes over and above the quota) are transferred to the remaining candidates, according to preferences expressed by the voters. These surplus votes are chosen at random and although constraints are placed in order to reduce the sampling error, there is nevertheless a small error introduced in most elections due to sampling. ‐The method of calculating this error has several unusual features and is therefore given in detail for one case, that of the 1974 Senate election for Victoria. Results are tabulated for all States for the elections of 1970, 1974 and 1975. An estimate of how often the wrong candidate will be elected by chance is given. Finally, a simple method for avoiding the sampling problem is sugg