In 1971, Parkinson was nominated as a candidate for the position of Rector of the University of Dundee. In one of the closest-ever contests for that position, he was very narrowly defeated by incumbent Peter Ustinov after two recounts. The result was controversial, as it was alleged earlier results indicated Parkinson had won, and a further recount should have taken place to confirm the result. As a result, pressure grew for the poll to be rerun. While the University decreed that the original result was to stand, a new poll was organised by the Students' Association, which also featured the candidature of a goat. However, this time Ustinov won a decisive victory over Parkinson, the goat, and Paul Foot.