[specialist]

FWIW, I now advocate Approval Voting because a) superior election integrity prospects and b) nearly ideal fairness.

Score Voting and Instant Runoff Voting are a bit more fair than Approval Voting, but much more difficult to implement, execute, audit, describe / educate, etc.

[dragonwriter]

Approval voting and score voting are problematic for reasons standard analyses overlook; there's no obvious mapping from actual preferences to ballot markings. Ranked preference ballots don't have this problem (well, unforced ranking that allows ties doesn't, forced rankings do, but to the degree that approval and score voting do.)

Both scores and approvals are ambiguous in meaning and different people with the exact same preferences would map ballot papers differently. (In situations other than standard public elections, this may not be the case: approval is great for voting on group activities where either “approve” is a binding commitment to participate if the choice is chosen, or “disapprove” is a binding opt-out if the option is chosen.)

[specialist]

I supported instant runoff voting until I figured out that it's difficult to explain, implement, audit. Pretty much all the reasons election administrators dislike it.

Approval Voting seems like the best compromise between fairness and simplicity (to better ensure election integrity).

[rojoca]

Proportional voting is the only way to eliminate gerrymandering. Approval voting is great but single winner elections are always going to have gerrymandering issues.

[specialist]

See other comment. TL;DR: Approval Voting for executive races, eg mayor, governor.