That wikipedia enty has led me to Dualvoting.com, a site mainly in German but with the mainpage translated to English.
This site suggests the second choice of party vote. I suggests that the second choice might be dealt with by allowing voter to but an ‘x’ against their preferred party, and a ‘2’ against their second choice. Just a question of ballot design.
This site also points out that two choice voting is a form of two-round voting. It has the advantage over two rounds on different days that people cannot change their mind between two rounds.
People are I think well used to the idea of second choices in many areas of life. They make it wasy to give everyone a choice and be sure that everyone will get something.
This idea of a second choice is also used for electing individuals, in a system called supplementary vote.