The advantage to toss a coin is that a decision made by chance is usually perceived as acceptable to all parties involved. The wisdom of Greek philosophers also trusted in decisions by chance. In decision-making it is good scientific practice to mention error margins, a bit like in weather forecasts. In case error margins are very high it, therefore, can make sense to leave the ultimate decision to a toss of a coin as this might be just as valuable as making one or the other choice with high uncertainty. Of course we feel uneasy about such a procedure as we tend to be convinced that we have sufficient information to make a better decision than just a shortcut by chance decision. Hence, there may be many more cases than we would like to admit to which can be left to a by chance decision.
