#30in30 – Two Bags of Marbles

You are presented two bags. One contains 700 red chips and 300 blue chips, while the other one is opposite with 700 blue chips and 300 red ones. You are given the choice between the bags. Take one and begin to sample with replacement. In twelve samples, you get 8 reds and 4 blues. What is the probability that this is the bag that contains more red chips?

If you answered like most persons who participated in a study by the American psychologist Ward Edwards, you likely guessed a probability of about 70 percent. According to statistical mathematics, the right answer is about 97 percent. It appears that humans react slowly to new information (like the samples). This reluctance to integrate new information in our decision-making is called Conservatism Bias. Newer studies on cognitive biases assume that the issue derives from mixing up the essential memories. The newer memories of a stated high likelihoods are mixed with the older memories with content of a lower likelihood. The result is a lower likelihood as the average of all memories of the information we retrieved.

In the legal profession, one can encounter Conservatism Bias either as a member of a jury or even as a lawyer. Often it occurs if there are several pieces of information presented that ambiguously hint to one’s culpability or one’s innocence. The Bias obfuscates the process of evaluating the importance of new information in comparison to the old information. Thus, it is harder to convince people from the opposite if they initially believed the opposing position.

How to overcome this bias? As usual, it is hard to avoid cognitive biases unless you are a completely rational machine. Since the issue is due to misprocessed information it might help to objectively analyze given information and bring it (if necessary) on paper in a timely order to prevent white noise in the connection between (objective) input and (subjective) judgement.