**Disclaimer: I am not affiliated with any candidates.**

*TL;DR, Jokowi will win with approximately 59% votes.*

Today, I stumbled upon a news that Litbang Kompas just released their election survey.

Survey | JM (Jokowi-Ma’ruf) | PS (Prabowo-Sandi) | Undecided |
---|---|---|---|

Litbang Kompas (Feb-Mar) | 894 | 748 | 268 |

SMRC (Jan) | 890 | 520 | 210 |

Konsep Indonesia (Feb) | 658 | 409 | 133 |

The result above is quite clear and seems like Jokowi-Ma’ruf is going to win the election. If we drop the undecided voters and sum up all three surveys, we know that Jokowi-Ma’ruf (JM) has ~59% of votes and Prabowo-Sandiaga has ~41%. But, I am curious what’s the probability of JM winning the election given this survey data. Hence, what we have is the likelihood function `f(data|K)`

and what we want to find is `f(K>0.5|data)`

. Let’s assume there will be no major vote shift from both supporters and undecided voters.

To answer the question, we have to obtain posterior distribution for K to evaluate `p(K>0.5)`

. In Bayes’ theorem, posterior distribution is proportional to the product of the likelihood and prior distribution.

First, we use the survey from all three sources to form the likelihood function.

Then, since we don’t have prior information, we’ll use non-informative beta prior (because the likelihood is binomial) where `a = 1`

and `b = 1`

.

Therefore, the posterior becomes

The posterior in the plot below suggests that the election will be almost certainly won (`f(data|K) = 1`

or 100% win) by Jokowi-Ma’ruf with votes about 59%. If we look at the survey individually, Litbang Kompas puts Jokowi on 100% win with about 54% votes while SMRC puts Jokowi on 100% win with 63% votes.

*Posterior distribution with data from three surveys, estimating Jokowi’s number of votes*

Congrats, Pak Jokowi-Ma’ruf!