Idiots trade in certainties. Wise men in probabilities.
Imagine a hedge fund manager walks down to his risk department, and asks for their assessment of a certain share. Their assessment is that it will certainly loose all it's value.The manager is surprised they are so certain, but takes them at their word and goes back upstairs.
A few days pass, and again the manager takes the lift to the risk department. He asks for an assessment of another share. The response is that the share will certainly increases in value substantially. Elated, he goes back upstairs and that night, over dinner with his boss, he talks about what a great deal he found. The grizzled CEO feels a tad uneasy. After all, he's never heard of the number cruncher in risk being absolutely certain of anything, let alone two things in succession. He tells his younger colleague to hold off on the purchase for a while while he sniffs around.
The next morning, the CEO goes down to risk. He presents them with the same share, and gets the same response. He asks the risk team how they can be certain that the share will rise. Their answer is simple. They performed their usual analysis, and determined with 90% certainty that the share will rise. Hence, their assessment is that there is 100% certainty of a growth in price. The manager is furious. These idiots cost him millions. Expected payoff = predicted_payoff*risk. Setting risk to 1 throws away valuable data and wastes millions in doing so. He fires the risk team, shuts the business down and moves to California where he uses his wealth to buy a surf shop which will work in for the next twenty or so years. A year in, he meets his future wife. Three years and his first child. He's not as rich as he could have been, but he is happier. Yet, his happiness comes at a cost. The company he led was very good. It would not have survived otherwise. It did excellent research, allocated funding efficiently and made a profit by doing so. It's purpose was to generate wealth, but its function was to manage the flow of money through society, to direct resources to where they could be used best. Now the company gone, those which step into it;s place are a bit worse at the allocation, the use of resources a bit less optimal, and the quality of life for the millions and billions of people in the interconnected global economy, that tiny bit harder, shorter and poorer than they could have been.
It's hard to know what the right thing to do is, especially when it comes to balancing your desires against the good you can do by forgoing them.
It's also usually dumb to ignore reality because simplicity is easier. The courts do this when the split people into Guilty or Innocent. Maybe a better system would be one where a probability of guilt is assigned and punishment = assigned_punishment*probability_guilt. We could still keep a baseline level of guilt necessary in order to prevent abuses of power. i.e: reasonable_doubt = 95% and no punishment below that threshold. If the edge case is troubling for our intuitions, we can smooth it out by gradually increasing the punishment from nothing at 95% to 0.96*sentence at 96%,
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