On Random Walks, Projecting Election Results and Statistical Physics
Keywords:Random Walk, Density of States, Statistical Physics, Elections, Forecasting
Several important statistical tools and concepts are covered in upper division undergraduate Statistical Physics courses, including those of random walks and the central limit theorem. However, some of their broad applicability tends to be missed by students as well as the connection between these and other physical concepts. In this work, we apply a 1D random walk to study the evolution of the probability that a candidate will win an election given she holds some lead over her opponent, and connect the result found to the concept of density of states and occupation probabilities. This paper is intended to serve as a guide to the Statistical Physics instructor who wishes to motivate students beyond the boundaries of the official syllabus.
D.S. Lemons & P. Langevin, An introduction to stochastic processes in physics (JHU Press, USA, 2002), Chapter 5.
Actually, the normalization condition is not perfectly met because of the approximations made to arrive at Eq. 13. However, for n = 1000, the sum over all discrete values of P (Eq. 13) yields 0.999, and the sum gets closer to 1 as n increases. Thus, we can assume that, for practical purposes, Π1 is normalized for n > 1000.
D.V. Schroeder, An introduction to thermal physics, (Addison Wesley Longman, USA, 2000), Chapter 7.
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