Experiment 1: No key signature
1A: Always use the simplest possible accidental (the choice between Ab and G# will depend on whether the neighbouring notes are flats or sharps).
No remembering of accidentals during the bars. Note: with this system, Eb and C# will often be juxtaposed (Bb – G# will be always Bb – Ab, and Ab – F# will be always G# – F#). Conclusion: not a good system. Too much mixing of sharps and flats.
1B: Always sharps going up, flats going down. Conclusion: not good. Too rigid. C-D-Eb = B#-D-D#
1C: Decide according to context
Experiment 2: With key signature
Sharp key signature – always use sharps but never any double-sharps.
Flat key signature: always use flats but never any double-flats.