These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics students.
 
 

When an election is nigh, as it happens to be the case now, one sees electoral pendulums of the type shown here, in the newspapers informing us that if one of the parties, say Labor were to increase their vote by x% say, they would capture y number of seats, and thus form the Government. The relation between the x% and the y number of seats is the obvious one as indicated by the swing of the pendulum. The prediction rarely comes true. A more scientifically based relation between the number of seats won and the two-party preferred vote is as follows: The proportion of seats won by the victorious party varies as the cube of the proportion of the votes cast for the party over the country as a whole. This is the law of Cubic Proportions, and in the first part of the talk we examine why the law applies. In the second part of the talk, we consider the decision making process involved when a group of people such as an electorate, a jury, or a university department votes. We show why a minority of resolute participants more or less determine the outcome of a proposition they are voting on. This is the square-root law of the resolute minority.

Convenor: Matthew Ovens