# Assessing which variable is more predictive in a logit model

I am trying to estimate the impact on a politician's re-election of bills dealing with immigration. Suppose that the number of bills on immigration represents a high share of total bills and the two counts are correlated (correlation is around 0.7). If I run a logit model like this

$$Reelection = \beta_{1} immigration$$

$$\beta_{1}$$ is significant. If I run a model including both the counts (immigration and total)

$$Reelection = \beta_{1} immigration + \beta_{2} total$$

$$\beta_{1}$$ becomes insignificant and $$\beta_{2}$$ is significant. Is this evidence that the effect is driven by the total number of bills rather than immigration bills?