chalkdust we can also make statements about all possible elections run under a voting system, such as “the alternative vote is clone-proof”. Many diﬀerent voting systems are in use around the world, and it is a mathematical certainty that every electoral system lacks some desirable characteristics, so when discussing which system is the “best” it can only ever be a debate about which criteria people think are most important, and that may depend heavily on the context of the election.
Alexander Bolton is a PhD student at Imperial College London, applying Bayesian change point models to detect regimes in multivariate stochastic processes.
References and further reading Arrow KJ (1950). A diﬀiculty in the concept of social welfare. Journal of Political Economy 58 (4) 328–346. Johnson PE (2005). Voting Systems. hp://pj.freefaculty.org/Ukraine/PJ3_VotingSystemsEssay.pdf May KO (1952). A set of independent necessary and suﬀicient conditions for simple majority decision. Econometrica 20, 680–684. Woodall DR (1994). Properties of preferential election rules. Voting maers 3, 8–15.
My favourite shape
We can start with just a point which, believe it or not, is already a simplex. Then if we introduce a second point, we can connect the two to get a new shape called a 1-simplex (or a line to you and me). Next, if we take a third point, and connect it to our two other points, we have the 2-simplex, otherwise known as a triangle. But if we then connect our three points in the triangle to yet another new point, we get a three-dimensional shape: the tetrahedron (or the 3-simplex).
What’s more, there is yet another member of the family: a four-dimensional shape. This shape is called the 4-simplex, and it has five vertices. The 4-simplex is useful in population biology because if you have, for example, five diﬀerent species, you can represent the fractions of each population by ploing a point in the 4-simplex. If that’s not enough for you, you can make a five-dimensional, six-dimensional or even an n-dimensional simplex! chalkdustmagazine.com