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A race to Number 10
J.M.
22/07/2019
On the 24th of May 2019 Theresa May, at the time the Prime Minster of the United Kingdom, announced her resignation. This triggered a Conservative party leadership election, in which the Conservative party membership ( 0.28% of the UK population ) vote by postal ballot on one of two candidates. These two candidates were chosen by Conservative MPs to Boris Johnson and Jeremy Hunt.
We wish to anticipate the outcome of this race, so first we consider what we already think the outcome will be. For the proportion of votes for Johnson We take a beta distribution with our prior mean as approximately 0.72 and our prior variance is about 0.03. This distribution is graphed below and corresponds to a 0.88 probability of Johnson winning.
We then look at the most recent polling data (from YouGov, Opinium and ComRes respectively) to see what we can learn.
Johnson Hunt YouGov 710 247 Opinium 605 331 ComRes 312 198
Using this data we get the following posterior distribution.
Then our new probability of Johnson winning is approximately 1, with a posterior mean of 0.68 and posterior variance 9.110^{-5}.
Feel free to change the prior distribution below to see how it affects the results.
Prior Mean 0.010.99000.720.010.110.210.310.410.510.610.710.810.910.99
Prior Variance 0.0010.1000.030.0010.0110.0210.0310.0410.0510.0610.0710.0810.0910.1
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An Euler characteristic two, one dimensional, aperiodic projection tiling.
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A (uniform) random tiling of the plane.
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