Do Percentages Matter in a One-Time Decision?

I write a lot about decision-making. It’s clearly something that interests me. As a result, I often find myself thinking about how to make better decisions or how to help people make better decisions. That’s why I’m already up to Part 10 of that series on decision-making (and I’ve got at least 4 more to go). I’m not including today’s post as part of that series, but it serves as an interesting addendum. Meaning, it should at least give you something to think about. So, here we go!

As I said, I often find myself thinking about how to optimize decisions. Often times, when people are trying to make a decision about something in the future, there may be percentages attached to the success of a decision. For example, if you’re the elected leader of a country, you might have to decide about a mission to go in and rescue citizens that are being held hostage. When you’re speaking with your military and security advisors, they may tell you the likelihood of success of the different options you have on the table.

I was going to end the example there and move into my idea, but I think it might make it easier to understand, if I really go into detail on the example.

So, you’re the President of the United States and you’ve got citizens who are being held hostage in Mexico (but not by the government of Mexico). The Chief of the Joint Chiefs of Staff presents a plan of action for rescuing the citizens. After hearing about the chance of success of this plan, you ask the Chief what the chance of success is and he tells you 60%. The other option you have is to continue to pursue a diplomatic solution in tandem with the Mexican government. As the President, what do you do?

So, my wondering is whether that 60% number really matters that much. In fact, I would argue that the only “numbers” that would be useful in this situation are 100%, 0%, or whether the number is greater than 50 or less than 50 (to make sure that this is still three numbers, we could call this last number ‘x’). This sounds silly, right? A mission that has a 80% chance of success would make you more inclined to choose that mission, right? The problem is that 20% of the time, that mission is still going to fail. And my point is that since this is a one-time decision (meaning, it’s astronomically unlikely that the identical situation would occur again), there won’t be iterations such that 80% of the time, the decision to carry out that mission will be successful.

I suppose the argument against this idea is that in a mission that has only a 51% chance of success, there’s a 49% chance of failure and one would presume that there are more factors that might lead to failure with these percentages (or at least a higher chance of these failures coming to fruition).

I realize that this idea is off-the-wall, but I’d be interested to read an article in a math journal that explains why this is wrong (using reasoning beyond what I’ve explained here) or… why it’s right!

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