The book "How Democracies Die" by Steven Levitsky outlines how party gatekeepers play a crucial role in democratic processes and can significantly influence election outcomes. The author argues that these gatekeepers failed at critical points during the electoral process, specifically at the invisible primary stage, during the actual primaries, and in the time leading up to the general election. These failures can undermine the integrity and fairness of the democratic process, impacting the selection of viable candidates and ultimately the election results.