I came across something interesting today. When the House of Commons has a tie vote, the Speaker breaks the tie. (In the British Parliament, the Speaker is a non-partisan parliamentarian rather than a party leader.) In doing so, the Speaker follows a convention to always vote against (1) motions that would curtail debate; (2) amendments to a bill; and (3) final passage of a bill. The theory behind this is that only a majority should be able to do any of these things, and a tie means there is no majority.
Contrast this with the practice in the United States Senate. The Vice-President just votes as he thinks best (though, in practical terms, he takes the position of the President). John Adams established this precedent in casting the first vote to break a tie. I wonder to what extent Adams thought about this.