# Improbability Principle and the Seanad election

## Given enough opportunities, something extraordinary is bound to occur

The frequency for all the possible values follows a bell-shaped curve centred on the mean value.

A byelection for the Seanad Éireann Dublin University constituency, arising from the election of Ivana Bacik to Dáil Éireann, is in progress. There are 17 candidates, eight men and nine women. Examining the ballot paper, I immediately noticed an imbalance: the top three candidates, and seven of the top 10, are men. The last six candidates listed are all women. Is there a conspiracy, or could such a lopsided distribution be a matter of pure chance?

To avoid bias, the names on the ballot paper are always listed in alphabetical order. We may assume that the name of a randomly chosen candidate is equally likely to appear at any of the positions on the list; with 17 candidates, there is about a 6 per cent chance for each of the 17 positions; the distribution for a single candidate is uniform. However, when several candidates are grouped, the distribution is more complicated.