MSI Weekly Bulletin - Week starting Monday 26 June, 2006

How should one analyse court rulings to extract key voting patterns? In 2003 an analysis by Sirovich of the Second Rehnquist U.S. Supreme Court was published in the prestigious Proceedings of the U.S.A. National Academy of Sciences and received a lot of attention in the American media. In this presentation Sirovich\\\\\\\'s results will be reviewed and it will be shown how to get an even clearer picture of the voting pattern. Other approaches that have been attempted also will be described

A $[3,K,2]_4$ code is a set of $K$ 3-tuples (codewords) using 4 symbols, of which any pair of codewords differ in at least 2 places. The problem of finding the largest ball of radius 1 around a $[3,K,2]_4$ code is considered. A graph can be associated with the code, with each vertex representing a codeword. If two codewords have the same symbol in the $i^{th}$ coordinate then the vertices representing them are joined by an edge of colour $i$. Various properties of the graph are investigated to determine the size of the ball around the code.