You have 4 people, 3 liberals and 1 conservative, graduating from high school at 18, 75% are liberal. When they are in their late 30s, one of the liberals dies, so 66% are liberals. Then at age 50 another liberal dies, so the group is 50% liberal. One year after retirement (65) the last liberal dies and now the entire cohort is conservative. Without looking at the size of the population, one would think that the group of 4 slowly became more conservative over time.

Death, not persuasion, causes the political leaning of the population to shift as they get older. It is the very concerns of those that are liberal which also lead to their earlier deaths. If you are less likely to die from something that can be fixed with politics, you are more likely to be conservative and not want to rock the boat.