This article deals with circumstances leading to the dismissal of a soccer coach. The article is based on results from the Premier League in England over 12 consecutive years. In this paper, we converted the scores of matches (win, draw, and loss) into an index based upon how results were perceived by club owners-those empowered with the decision as to whether or not to fire the coach. The index is based on the difference between the actual and expected results reflected by betting odds. We conclude that to ensure job preservation, the manager does not have to succeed-he just must not fail.
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Our paper provides a justification for the proportional representative (PR) election system for politically diversified societies. We employ the Shapley value concept to measure the political power of parties in a parliament. We prove that for the PR system if parties' size add up to 1 and is uniformly distributed, the expected ratio of a party size to its political power converges to 1, and the variance decreases to 0 as the number of parties increases. The rate of convergence is high. An empirical evidence from the Netherlands elections supports our result. Using the Shapley-Owen index we obtain similar result (this time numerically only) for a voting model that takes into account ideological differences between parties and voters.
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