Davidson refereed four matches over his World Cup career; two games in 1962, and a single game in each of the other competitions. In the 1962 tournament in Chile, he took charge of the Group B match between Italy and West Germany on 31 May 1962, plus West Germany against Chile on 6 June 1962, in the same group. He was also one of the linesmen during the Final between Brazil and Czechoslovakia on 17 June 1962 at the Estadio Nacional, Santiago under referee Nikolay Latyshev.