Twitter: @pakremp

The probability that an individual voter would end up determining the outcome of the election is extremely low. But it varies dramatically across states. We use the posterior distribution of the state-by-state vote intentions forecast on election day to replicate the calculation detailed in Gelman, Silver and Edlin’s (2012) Economic Inquiry article, “What is the probability that your vote will make a difference?”.

The R code is available here.

The intuition behind this calculation is simple: your vote can decide the outcome of the election if and only if two conditions are met:

How These Probabilities Were Calculated

To calculate this probabilities, we simply apply Bayes’s rule:

\[\begin{aligned} \textrm{Pr(your vote is decisive)} & = \textrm{Pr(your state's EV are critical} \cap \textrm{your state is tied)} \\ & = \textrm{Pr(your state's EV are critical)} \times \textrm{Pr(your state is tied | your state is critical)} \end{aligned} \]

The following graph shows the conditional probability \(\textrm{Pr(your state is tied | your state's EV are critical)}\) on the logarithmic x-axis, and the probability \(\textrm{Pr(your state's EV are critical)}\) on the logarithmic y-axis.