Then there is the ‘Dual Level Voting’name

That wikipedia enty has led me to, 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.