Because of the negative term, we cannot simply sample events following such frequencies. However, if we suddenly become unable to differentiate between events b and c, this would result on our funny coin turning into a standard fair coin. Similarly, if we stop differentiating events a and b, then the funny coin would turn into an unfair coin. Because of this, one can think of quasi-probabilities as unobservable ‘sources’ that can give rise to multiple somehow interrelated probabilistic scenarios —
If the coin were (0.5, 0.4, 0.1) wouldn’t it still be true that, by not differentiating b and c you get a fair coin, and not differentiating a and b would give you an unfair coin
The point is that a coarse-graining can turn a quasi-probability into a probability. This is significant because quasi-probabilities are limited in that they cannot be sampled etc.
If the coin were (0.5, 0.4, 0.1) wouldn’t it still be true that, by not differentiating b and c you get a fair coin, and not differentiating a and b would give you an unfair coin
what’s the point of that bit
The point is that a coarse-graining can turn a quasi-probability into a probability. This is significant because quasi-probabilities are limited in that they cannot be sampled etc.
Does that make sense?
yes