If X received $56\%$ of the votes, Y must have received $44\%$. The difference between their votes is $12\%$.

This $12\%$ difference corresponds to $1440$ votes. Therefore, the total number of votes cast is: Total votes cast = $1440/0.12 = 12000$

Since $80\%$ of the total voters cast their votes, the total number of voters is: Total voters = $12000/0.80 = 15000$

Hence, the total number of voters in the list is $15000$.