Balance of probability illustrated

Introduction

In former articles and more particularly the articles on disciplinary charge formulation, constructive dismissal and the article titled: Common Sense and Fair Play, I made mention (in passing) of the onus of proof, namely a balance of probability, which applies in civil law cases and by implication, in internal disciplinary cases, CCMA arbitrations and in labour court proceedings. This is as opposed to the onus of proof which applies in criminal cases, such as theft, fraud and murder namely, beyond all reasonable doubt.

By implication, when discharging the onus of a balance of probability, the conclusion reached could, theoretically, still be open to some doubt, but faced with two opposing versions of the truth, the decision maker, applying his/her mind properly to the tested evidence put before him/her, will, in his/her decision, veer towards the more probable version of the truth.

This poses the question: How does one go about establishing a balance of probability and is it also possible to establish an indisputable fact on a balance of probability?

The reasoning which underpins the application of the onus of a balance of probability is best illustrated by the following conundrum. Admittedly, this conundrum is not related to an employee relations situation, but since the basic tenets of decision making are universal in its application, this conundrum will still ably illustrate the application of a balance of probability as onus of proof:

Scenario sketch

The Execution

Three missionaries from a prominent church organisation are caught and arrested while busy with missionary work in a war-torn hostile country. They are charged with espionage and infiltration, are brought before a court, are convicted and sentenced to death.

For purposes of this exercise, the three gentlemen are referred to as Mr A, Mr B and Mr C. All of them are highly intelligent, responsible and they know each other extremely well.

On the day of the execution, they are brought to an arena, where make-shift gallows were erected, equipped with three hanging ropes (nooses) and collapsible individual platforms, each such structure situated two metres apart. Each of the condemned is made to take position at a hanging rope, in such a way that Mr C faced the back of Mr B and Mr B faced the back of Mr A. A distance of 2 meters separated Mr C from Mr B and Mr B from Mr A. The hanging ropes were affixed to their necks and they were prohibited from communicating to each other and were kept under constant observation.

As it is customary at executions in this country, a priest visits the condemned just prior to the execution. The head of state was also present at this public execution. He called the priest and announced that he will pardon the three gentlemen, but only if they are able to provide the correct solution to the following riddle:

“The Riddle”

The head of state gave the priest an opaque bag containing 5 wooden crosses. The measurements of these crosses were 15cm vertically and 10cm horizontally. Attached to each cross was a white rope, long enough to hang the cross with it around a person's neck. The crosses were painted and three of the crosses were painted red and two black.

The priest is ordered to retrieve crosses from the bag at random and to hang a cross around the neck of each of the condemned, but in such a way that the cross is displayed on the person's back and not his chest. The priest would then approach the condemned missionaries from the rear, take a cross at random from the bag and hang it in the prescribed manner around their necks, starting with Mr C, then Mr B and finally Mr A.

Only the priest will know what colour cross is displayed on each of the three gentlemen’s backs. He is, however, prohibited from communicating, in any way, with the condemned while hanging the crosses and until the time period designated for solving the riddle has lapsed. No one could see which two crosses remained in the bag. Before the crosses were hung, all spectators were ordered to clear an area comprising 30 metres around the gallows and not to communicate in any way with the three gentlemen.

The priest did as he was ordered and was accompanied by a government guard who would see to it that the priest followed orders, while he was also prohibited from communicating to the condemned. After the crosses were hung, first Mr A, then Mr B and then Mr C were blindfolded and a government official explained the riddle, which they had to solve, to the condemned.

They were told that there were only five crosses in the bag, three of which were red crosses and two were black crosses and that they were granted, jointly, 10 minutes to determine what the colour of the cross is displayed on their backs. Each one had to endeavour to determine the colour of the cross on his own back. Before the countdown began, the condemned were given the opportunity to examine the contents of the bag.

As soon as anyone of them is of the opinion that he knows the colour of the cross on his own back, he must, immediately, put up his hand and declare the colour of his cross aloud. In the event of the first one making such declaration being correct, all three will be pardoned. If, however, he is wrong, all three will, immediately be hanged in public, as would also be the case if none of them responded within the designated ten minutes.

They were also told that a gong, which will be sounded on the expiry of each of the 10 minutes, would announce the elapse of time. (Remember, they were not allowed to communicate with each other in whatever way or to declare the colour of the cross on the back of another condemned).

The countdown began, and a deadly silence prevailed while the three condemned frantically endeavoured to solve the riddle. The silence was only broken by nine consecutive gong sounds, exactly one minute apart. Then, approximately 5 seconds before the final gong sounded, Mr A broke the silence and declared that he had a red cross on his back. He was correct and all three were pardoned.

Application of the mind

Mr A was the person, who could visually observe the least – basically nothing that could assist in solving the conundrum. In fact, he could see none of the three crosses that were hung - not his own and most certainly not any of his co-condemned, yet he solved the riddle. He did not guess, but he was convinced in his own mind when he declared that he had a red cross on his back. He applied the balance of probabilities as a method in order to produce the answer.

How did he argue according to the balance of probabilities?

Firstly, he departed from certain realistic assumptions, based on probabilities and improbabilities which could reasonably be derived from the situation, such as:

·        The three gentlemen were all intelligent, responsible, alert and observant.

·        The three gentlemen knew each other well and probably trusted each other.

·        The three gentlemen were probably of good character with high moral values and would therefore not act compulsively, thereby potentially endangering the lives of their co-condemned or their own.

·        It was improbable that there was room for any cheating or assistance from elsewhere to solve the riddle.

·        During the brief period before the three gentlemen were blindfolded, it was evident that Mr C could see the colour of the cross which was hung around Mr B’s neck, as displayed on the latter’s back, as well as the colour of the cross hung around Mr A’s neck, as displayed on the latter’s back.

·        Mr A could not see the colour of any of the crosses hung around the necks of Mr C and Mr B, displayed on their backs, as he stood at the front, looking straight ahead.

Secondly, he started his reasoning based on the probabilities he identified, as one gong sound followed the other, him gradually becoming convinced that it was seemingly upon him to derive some conclusion regarding the persistent silence from his co-condemned Messieurs C and B, in order not to be hanged by default along with his two co-condemned.

Mr C was arguably in the very best position to determine the colour of the cross on his (Mr C’s) back, since he could see the colour of the cross on the back of Mr B and that on his own back (that of Mr A).

Why then Mr C’s silence? Most probably, he did not see anything, before being blindfolded, which could enable him to work out the colour of the cross on his back. Then Mr A shifted his reasoning to the “what if”-scenario, asking himself the question: What should Mr C have seen on the back of Mr B and his own back (that of Mr A) to be able to determine the colour of the cross on his back (that of Mr C)?

Knowing that there were only two black crosses and three red crosses, it stands to reason that if Mr C saw two black crosses in front of him on the back of Mr B and on his own back (that of Mr A), he would have known that he could only have a red cross on his back and would have spoken out. He however kept silent.

Then Mr A transferred his reasoning to Mr B, who also remained silent. Mr A argued in his mind that Mr B also knew that should Mr C have seen black crosses on his (Mr B’s) back and on his own back (that of Mr A), Mr C would have spoken out. Mr B, hypothetically having seen a black cross on his back (that of Mr A), knowing that Mr C did not see two black crosses in front of him, Mr B would have realised that he had to have a red cross on his (Mr B’s) back, yet he remained silent.

Mr A then came to the conclusion that Mr B could, on a balance of probability, only have seen a red cross on his (Mr A’s) back, hence he (Mr A) spoke out declaring that he had a red cross on his back and so he saved the lives of his co-condemned, as well as his own. In the circumstances, it was totally out of character for Mr A to guess or to speculate on the basis of considering “the odds” favouring a red cross, as the red crosses were in the majority. He was in pursuit of reasonable certainty and in achieving that, he resorted to arguing on the basis of a balance of probability.

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Conclusion

An open mind, being unbiased and possessing a good sense of judgement, are essential ingredients for any person tasked with presiding in a case, adjudicating between two opposing positions taken.

These essential ingredients apply equally in both civil law cases and criminal law cases, but its practical application, when reaching a considered conclusion, differs, as indicated above. Obviously, decision makers should always endeavour to position their findings as close as possible to the truth, but realising that not all decision makers are legally trained individuals, the lesser onus of proof applicable in, for instance, internal disciplinary cases, makes it less onerous for such decision makers to fulfil their adjudicative obligation. As the illustrative riddle above pointed out, it is even possible to establish an indisputable fact through the application of the onus of a balance of probabilities.

In the final analysis, basing a conclusion on a balance of probabilities is by no means a guessing game , but requires careful observation of the material elements of the case at hand, followed by weighing up the probabilities and then choose the version placed before you which is, all things considered, the more probable version of the truth.

Assistance in this regard is available by simply contacting the JJK ER/IR Consultancy at [email protected].

Author: J J (Koos) van der Merwe – Chartered HR Professional, registered with the SABPP

08 June 2020