Improbability Principle

Don't forget the Monty Hall problem. I still talk to people who don't get it.

~~ Paul

Think of all the professionals who got the Monty Hall problem wrong.

Great minds think alike.

Don't forget the Monty Hall problem. I still talk to people who don't get it.

~~ Paul

Well, I notice lots of people, proponent and non-proponent alike, who don't get it.

Do you think this misunderstanding contributes to whether or not someone is a proponent?

Linda

There aren’t many large scale psi-experiments that have a control measure (other than chance expectation) that I know of.

One was described in a book called The Challenge of Chance: Experiments and Speculations by Hardy, Harvie and Koestler. It described an experiment in which twenty people in cubicles in the small hall would try to recreate or describe the image being viewed by someone who was also in the hall.

The control version of the experiment simply compared the responses to the targets for a different day. When these were judged, they found 89 direct hits out of 1,800, or about 1 in 20 (a better hit rate than the actual experiment). A “direct hit” was defined as “drawings or written descriptions made by the ‘percipient’ which we both judged to bear a close relation to the target drawing or slide being shown in the particular experiment concerned.” 

The idea that two random images or descriptions should be strikingly similar with odds of only 1 in 20 seems too frequent. After all, there are thousands of potential images and thousands of potential responses. Can it really be that commonplace?

There was another experiment with a control method that can be compared to this one and it is taken from the paper Remarkable Correspondences Between Ganzfeld Mentation and Target Content: Psi Or A Cognitive Illusion? by Westerlund, Parker, Dalkvist and Goulding (Proceedings of the PA Convention 2004). This was a ganzfeld experiment with the usual 1 in 4 base chance of a direct hit. But I’m more interested in the “remarkable correspondences” aspect of the paper. Since the overall results were at chance I’m taking the assumption that, for this experiment, psi was not active.

An external judge bookmarked those parts of the trial where he felt the mentation from the receiver matched the video clip in real time. They found 18 “hits” out of 128* which is a surprisingly high 1 in 6, although you have to bear in mind that the mentation was fourteen minutes long, so had plenty of opportunities to sync up to the repeated video clip. Certainly more than a single image has to match another single image.

There must be other psi experiments which did something similar, but I don’t know what they are. Apart from Moreman’s attempt to replicate the Cross Correspondences with random texts[1], but he didn’t give a numerical value for expected results by chance. 


[1] Moreman, C.M, A Re-Examination of the Possibility of Chance Coincidence as an Alternative Explanation for Mediumistic Communication in the Cross-Correspondences, JSPR Vol 67.4, No. 873, pp 224-242

* The paper lists twenty "remarkable hits", but says that two of these came from a subject who was not included in the 128-trial experiment (becuase the subject was not a novice). If we include those two, then we cannot say for sure how many trials were used since the paper doesn’t specify how many other excluded trials were judged for remarkable correspondences. If we remove those two, however, we can be sure of the figures.

Thank you for the Moreman reference.

Another study which looked at remarkable correspondences in a qualitative way in a control group was Kelly's An Investigation of Mediums Who Claim to Give Information About Deceased Persons. Out of 40 subject, she describes 5 subjects finding remarkable correspondences in the correct readings and "a few" subjects finding remarkable correspondences among the incorrect readings. 14 subjects in each group (correct and incorrect readings) also made more general comments about accuracy like "I knew this was the correct reading, it sounded just like my mom/daughter/husband". Note, in this case, there was a 1 in 4 base chance of choosing the correct reading, however the mediums weren't fully blind as to the subject of their reading.

Linda

Fascinating, never heard of it before.

Acting intuitively, I also fell straight into into the trap and gave the last two doors 50:50.

But, found it much more difficult to fall into the trap when there were more doors, and didn't fall into the trap at all when it was presented as the pea under one of three cups.

Despite spending an hour reading about it, returning back to the initial problem again, I could still feel I was intuitively attracted to giving the last two doors 50:50.

When I teach the Monty Hall problem I always add doors until it becomes more obvious...if there were 1,000,000,000,000 doors to begin with, we can feel very secure that we did not choose the car initially, so it feels less tempting to just assign a 50% probability to that door at the end, particularly when revealing that all of the other doors (except one) are car-less says absolutely nothing about whether or not my door has the car (since those doors could be revealed in that way regardless of whether or not I've selected the door with the car).

When I teach the Monty Hall problem I always add doors until it becomes more obvious...if there were 1,000,000,000,000 doors to begin with, we can feel very secure that we did not choose the car initially, so it feels less tempting to just assign a 50% probability to that door at the end, particularly when revealing that all of the other doors (except one) are car-less says absolutely nothing about whether or not my door has the car (since those doors could be revealed in that way regardless of whether or not I've selected the door with the car).

I too had never heard of this. Nor am I known for my mathematical or statistical acumen but a couple of minutes reading the Wiki page on the problem clarified it immediately. To be more specific, the little diagram showing the one-third and two-thirds relationship before and after the opening of the third door made it obvious. 

Now, perhaps someone could explain to me the gambler's fallacy and whether there is a relationship to this Monty Hall problem? As a naive young man, I visited a casino and figured that if I waited for the roulette wheel to deliver three blacks in a row then I had a much better chance of winning on red. Not only that but if I didn't win on that bet, I would double the stake on the next spin. And so on. As it happened, I won a fair amount so, believing that I had stumbled upon a foolproof system, I went back the next night and lost all of my winnings (and more). The great lesson for me was to stay away from gambling. I only discovered later that this was a well known fallacy.