Everything Has A Limit

I see from a BBC article today that there has been a "dramatic" fall in the prescription of antibiotics by general practitioners (GPs). I make it about 8%, which I guess could be described as "dramatic". One can only be certain when one knows the circumstances of each doctor's decision.
However, it did get me wondering.

As the article states: 

"The government has offered a financial incentive to get GPs to cut down on their prescribing.
Clinical commissioning groups (CCGs) get a Quality Premium payment if family doctors hit the target.Reducing unnecessary prescribing saves the NHS money in drug costs.
The figures show GPs have overshot the targets."

Now, it seems plain to me that doctors would not, if functioning as proper doctors, prescribe antibiotics if they knew that they would do no good (let's ignore the placebo potential here).
But if there is a 50:50 chance that the antibiotics will do some good, I presume that a doctor would feel obliged by a duty of care to prescribe the antibiotics. So, where, roughly, do we have to get to in the probability arena for the doctor to decline to prescribe antibiotics -- to put the general good above the individual good?

And this is the paradox. Theoretically (I would have thought) the doctor always has to put the individual good first, but clearly in practice this is not the case.
The Department of Health's Standing Medical Advisory Committee rather ducked the issue in the early 2000s, recommending that doctors not prescribe antibiotics over the phone, for sore throats ("most" of which were viral) and for "simple" colds and 'flu (nearly all of which were viral). Effectively they were saying "don't prescribe antibiotics as a first resort".

The Nursing Times observed in January 2004 that

 "There will always be a dilemma for prescribers in deciding whether promoting the interests of individual patients outweighs the legitimate public health concerns regarding resistance. "

but failed to address how the dilemma could be resolved.

Ars Technica in December 2015 seemed to me to completely miss what the dilemma was. It wrote

"Yet doctors face a daily dilemma: to be good doctors, they must only prescribe antibiotics when the drugs are needed. But to make patients think they’re good doctors, they must hand out antibiotics freely—at least according to a new nationwide healthcare survey in England."

I don't think that this is the dilemma at all.
Geoffrey Scott May, in "Handbook Essentials Antibiotics", addresses the paradox (p2) when he writes.

"Rarely, an experienced doctor will withhold antibiotics because he thinks a patient has a virus infection, but the patient later dies from meningitis. This is an unanswerable paradox."

The paradox is only unanswerable because organizations such as the SMAC refuse to assign numbers to the problem. Because of this their advice has to be vague. But it's interesting that financial incentives are having an effect.

That leads me to think that there is a possible way to defeat the "overshoot" in NHS budgets (they will ALWAYS overshoot, because individual departments will always ensure that they spend 100% of their budget as a minimum, to avoid certain cuts the following year. Meanwhile, some departments will be unable to keep to 100% of their budget -- thus leading to an overall overshoot).

Put simply, offer either individuals or groups a personal financial incentive to come in 10% under budget. For year one it could be 50% of the undershoot, with a promise that they overall budget for that department will not be reduced by more than 10% of the undershoot.