In this paper, we study how a combination of random ballot ordering and concurrent elections can increase invalid votes in the context of South Korea. In South Korea, elections for the nonpartisan superintendent of education are held concurrently with other partisan races. Whereas the ballot order for candidates in the nonpartisan superintendent of education elections is randomized and rotated, this order for other partisan races is determined according to the number of seats each party has in the national legislature. In this study, we found that a match between candidates’ partisan preferences and their ballot positions decreases invalid votes. Our findings suggest that combining two different ballot-order schemes for concurrently held elections can confuse voters and increase invalid votes.