@Jack-Waugh, Thanks for working through all these examples. I, too, had some questions about the GF vote, or the more general instructions regarding always voting for every alternative subjectively preferred over the focus. For a GF vote to be instrumental in impeding termination, the G vote total would have to be at least a strict majority (that is: F > half, because equal to half is not sufficient), and the F vote total would have to be the maximum vote count and exactly equal to the G vote total. Thus it is possible for a GF vote to hinder termination. However, in addition to G blocking termination, G is preferred by the voter over F, so G blocking theloop termination with F as the final winner is also indicating the possibility for G to be a later focus and possibly a better final outcome.
For testing purposes I wrote voter-agent code for voting to stop the loop. This strictly speaking is not part of SAVE, but it does indicate what I think voters might do. Each voter-agent has a property called indifference, which is a fraction between 0.0 and 1.0. At 0.0 the slightest difference matters, while at 1.0 the voter is totally indifferent to the alternatives. All voters start at 0.0 and increment their indifference value (1) every time the focus is a Condorcet winner (because if we cannot improve upon a Condorcet winner we will eventually accept it), and (2) whenever the focus subjectively improves after having first moved away (when the focus move away, such as when in a majority cycle, we also want to be more accepting, but only as we're coming back). These are the five basic reasons for an agent to vote for the focus:
Ideal - the focus is close to the voter's subjective ideal alternative.
Cluster - the best and the worst of the most recent focus alternatives are really close together.
Top-half - the spread between the best and the worst is moderately close (3x indifference) and the focus is in the top half of that spread.
Limited-gain - the focus is close to the upper limit to any potential future gains.
Peak - the focus is as good or better than a focus that was followed by a movement away from the agent's idea.
All of these conditions except Peak use the indifference value. The conditions are ordered from most difficult to satisfy to the easiest to satisfy.
The reason I bring this up is because I think voters might well vote for loop termination on the off-chance they can get a better result more quickly. Which implies a vote to terminate usually does not mean "I really want to terminate now" but instead is the kinder and gentler "it is okay to terminate now". Under those circumstances, the GF vote is perfectly reasonable, and supports the possibility of termination without foregoing the chance to influence the next focus choice.