Other ballots ... Borda systems.

Borda gives every voter one or two votes to lose with.

An example: Limited to 2 picks

4 votes for "A > B" (this majority helps itself lose)
3 votes for "B > C".

Here's a case where four people vote for "A" but will settle for "B", and three other people vote for "B" with a side order of "C". If it's 3 points for first and 1 point for second, Borda elects "B". The winner can be almost predetermined because someone, currently in power, will decide how many picks each voter must choose (maybe 3) and how much each pick is worth (say 5 - 3 - 1). Not choosing seconds and thirds is the perfect strategy in any point system, therefore Borda usually forces a voter to pick the limit. In this example, "B" will make sure that his supporters have a safe place to put every other pick (that's his own poorly funded, doesn't have a chance "C"). Educated voters will turn Borda into FPTP. They really don't have a choice.

Fair Vote (USA) has it right when they suggest that "Later no harm" is an important part of judging a fair voting system. No one should be allowed to make themselves lose so easily. It's not that hard to protect a voter's stated preference, try IRV+/-.