I'm trying to understand a scenario in which it would make any sense to have a single candidate appear more than once on the ballot for a single office. The primary effect would seem to be to confuse voters.

Let's say you're nominated by the Democratic Party and the Green Party. The dual nomination says something about who you are and what you believe in. Or, let's say you are nominated by the Republican Party and the Libertarian Party. Again, it says something about who you are as a candidate. If a candidate is nominated by by more than one party, absent a mechanism to list all the nominating parties with a single candidate entry, why should only the Democratic or Republican Party get billing? Further, by allowing someone to vote for the Green candidate or the Libertarian candidate, you also allow a third party to show strength (even if the nominee from that party is also the mainstream party candidate).

But why "absent a mechanism to list all the nominating parties with a single candidate entry"? It seems to make more sense to just do that and get this right.

If I walked into the booth and found the same name listed twice, under two different parties, I'd be left wondering which is the John Smith that I'd walked in intending to vote for. Even if I figured out it was the same guy, then I'd worry that the two might be tallied separately, and worry that if I vote for the wrong (minority) one, my guy could lose.

I expect that most people would share my confusion, or something like it. The spirit of this is just fine, it's the mechanism that's lousy.

If you list the candidate with all of their party nominations under one line you still lose the ability for a non-mainstream party to show it has strength. Again, I may want to show that I support the Green Party or Right To Life Party but also don't want to "throw away" my vote on a non-viable candidate. If the Green Party candidate is also the Democratic candidate, I can vote for him/her as the Green candidate to show my support for the Green Party and still have my vote count towards the total for the candidate as an individual. If the candidate is listed just once as both the Green and Democratic Party candidate, then you have no way of knowing that I am really a Green Party supporter, and not a Democrat. This distinction is important because public funding formulas, party access to the ballot, etc., are often linked to performance of party candidates in the last election cycle (i.e., a demonstration of the party's viability).