Majority voting in Ensembles

Question

Majority voting considers the summation of log(error rate/ 1-error rate), where error rate = (misclassification/ total hit). Now what happens when a rule is hundred percent accurate i.e. it doesn't misclassify a single instance from the training data? In such a situation, error rate equals to 0 and the metric cannot be calculated.

Answer 1

If error rate=0, then error rate/(1-error rate)=0. While $\log 0$ is not defined, $\lim_{x\searrow 0}\log x =-\infty$, and you can take $-\infty$ as the answer.
If the error rate=1, then because of $\lim_{x\nearrow 1} \frac{x}{1-x}=+\infty$, one would take $\lim_{x\nearrow 1} \log\frac{x}{1-x}=\lim_{x\nearrow +\infty}\log x=+\infty$ as the value of the metric.