SEARCH WITHIN CONTENT
Citation Information : Statistics in Transition New Series. Volume 19, Issue 2, Pages 351-357, DOI: https://doi.org/10.21307/stattrans-2018-020
License : (CC BY-NC-ND 4.0)
Published Online: 29-July-2018
This is a simple but provocative note. Consider an election with two candidates and suppose that candidate A was the leader until counting n votes. How to use this information in predicting the final results of the election? According to the common belief the final number of votes for the leader should be a strictly increasing function of n. Assuming the votes are counted in random order we derive the Maximum Likelihood predictor of the final number of votes for the future winner and loser based on the first leadership time. It appears that this time has little effect on the predicting.
AZZALINI, A., (1996). Statistical Inference based on the Likelihood, Chapman & Hall, London, UK.
BRÉMAUD, P., (1994). An Introduction to Probabilistic Modelling, 2nd ed., Springer- Verlag, New York.
FELLER, W., (1968). An Introduction to Probability Theory and its Applications, Vol. 1, 3rd ed., Wiley, New York.
GOULDEN, I. P., SERRANO, L. G., (2003). Maintaining the spirit of the reflection principle when the boundary has arbitrary integer slope, J. Comb. Theory Ser. A, 104, pp. 317–326,
LENGYEL, T., (2011). Direct consequences of the basic Ballot Theorem, Statist. Probab. Lett., 81, pp. 1476–1481.
RENAULT, M., (2007). Four proofs of the Ballot Theorem, Math. Mag., 80, pp. 345–352.
SCHERVISH, M. J., (1995). Theory of Statistics, Springer-Verlag, New York.
STĘPNIAK, C., (2015). On distribution of leadership time in counting votes and predicting winners, Statist. Probab. Lett., 106, pp. 109–112.
TAKACS, L., (1997). On the ballot theorem, In: Advances in Combinatorial Methods and Applications to Probability and Statistics, Birkhauser, pp. 97–114.