The Patient's Dilemma.

The patients’ choice for opting Doctor A and hypothetical increase in Doctor B’s next patient survival has been shown by the orange curve, while the patients’ choice for choosing Doctor B for treatment is shown by the blue curve. The green line shows people choice for either of the doctors in a relaxed state.

The 50% theory leading to The Patient Dilemma.

If doctors A and B treat equal number of patients and both have a cure rate of 50%. Given that the last patient of doctor B died while doctor A survived. It is seen that most patients chose to get treated by doctor A.

It is a Universal fact, that doctor A next case has a probability of survival of 50%, and doctor B next case also has a survival probability of 50%. But as the last case of doctor A has got cured, so there is a slight probability that the next case will survive is 50^- % (50 – 0⁺)%, while doctor B has a probability that the next case will survive as 50⁺% (50 + 0⁺)%.

But then patients won’t choose doctor B for treatment, but rather opt doctor A for treatment, and therefore increase their risk of dying by a hypothetical probability of 0⁺%. This is somewhat of a paradox in the presumed decision making, and so termed as The Patients’ Paradox.

Similarly, if the number of last cases of doctor B dying increases, there will be a hypothetical increase in the probability of the next case getting cured. But then there will be a sharp exponential drop in number of patients willing to opt doctor B. And with increase in doctor A’s last cases having survived, the hypothetical probability of doctor A’s next case surviving will be drastically reduced. But then more patients will flock to doctor A based on current reference point. The overall curve comes out to be like a parabola (shown in the Fig.).

However, when people are in a completely relaxed state (like on Facebook), the choice tends to fall in a straight line as marked by the green line. People can opt either doctors when emotions are ruled out or only logic and reason stays.

In real life, the stress is higher. The emotional aspect playing with life will be more. So people will tend to choose Doctor A, based on reference point. However doing this experiment practically on live patients and real Doctors will be highly unethical.