Imagine a ballot (or something) that had the pre-printed names on them something like those paper "call me for xyz" things you see on bulletin boards everywhere (or well you used to)?
Basically the names would be on pieces of paper (maybe with a QR code?) about the size of what you get in a fortune cookie, that can be tore off the "ballot" and dropped in a box for later counting. With a QR code (or something similar), the counting could even be done with a machine.
Such a paper ballot could arguably have many names attached (here in the US we have so many positions and votes to cast on so many things it's mind boggling, especially during certain election times). I'm not sure if or how well it would work, but I think it might be doable - at least enough to attempt.
Compare https://upload.wikimedia.org/wikipedia/commons/d/dc/France_%... with http://etc.usf.edu/clippix/pix/2012-presidential-election-ba...
You only need a pen/pencil if you want to change the parties default ranking of their candidates (e.g. who in the party you want to see as prime minister) or you want to vote for a minor party which doesn't have ballots (write-in votes)
[I'm not endorsing the Swedish system just explaining how it works]
Also in local elections we can write in other people and give people on the ballot an "extra" vote for which we use a pen (but this is voluntary and I assume most don't bother).
I think in the USA there tends to be several issues on the ballots however, so I guess it's not very practical in that case. It probably makes the counting harder however.