# How should one treat probability in taking a decision?

Suppose, I have a machine that accurately gives me the probability of any event occuring.

It's obvious what to do when

1. The probabilities are 0.5 and 0.5 (Do nothing)
2. The probabilities are 0 and 1 (Remain an atheist)
3. The probabilities are 1 and 0 (Become a Muslim)

However, consider a more nuanced scenario. Say I obtained from that machine that the probability of Islam being true is 50.1%, and that the probability of Islam being false is 49.9%. What would you do in this situation? Would you become a Muslim or stay an atheist/agnostic?

Edit:

Some commenters have raised a very good point. Only taking actions based on probability is not prudent. You have to weigh the consequences too. "If there's a 40% chance of rain, it's still reasonable to take an umbrella, unless carrying the umbrella is an excessive burden." So, it seems like I am just heading towards a traditional Pascal's wager :-)

• If there were truly a 50% chance that Islam is true, then you should become a Muslim, because of Pascal's wager. Even a 10% chance would warrant conversion, unless some other religion had an even higher chance. Rational atheism depends on the chance being very low, certainly <1%, which is usually justified by the excess complexity of supposed deities (in comparison to the formally much simpler laws of physics) interpreted through a Bayesian version of Occam's razor. Also, a sociological understanding of how religions form and evolve. Commented May 18, 2023 at 17:29
• You also need a machine that accurately gives you payoffs of proposed decisions in each case, and their utilities. Then you calculate the expected utilities and choose the decision with the highest one. If only life worked like math... What we learned from Pascal's wager is that one should leave probability and payoffs out of religious decisions altogether. Commented May 18, 2023 at 18:33
• @Conifold Calculating utilities is one way to take a decision based on probabilities, but not the only one. Commented May 18, 2023 at 18:49
• The chance of what? The chance that another "probability" question gets asked tomorrow? Commented May 18, 2023 at 19:42
• If there's a 40% chance of rain, it's still reasonable to take an umbrella, unless carrying the umbrella is an excessive burden. Commented May 19, 2023 at 15:08

I object to the grounds of your question. It is impossible to calculate a probability for the truth of a religion. Even if you could allocate a probability, a probability alone is no basis for decision making. You need to take into account all of the applicable pros and cons associated with the choices you are presented with, weighing them against each other in terms of their importance to you and their likelihood.

I would first argue that there is no such thing, and that if a machine is trying to spit out a "true" probability of Islam being true, it would simply be wrong if it displayed 50.1, since the real answer should either be 0 or 1. Islam is or isn’t true. There's no in between.

Any “probability” of it being true or false is just a human guess that maps into getting into the thorny issue of when it’s considered justified or unjustified to believe in a statement like “Islam is true”.

There is no such thing as a “true” or “objective” probability, especially when it comes to existential matters such as the Islamic god existing.

• "if a machine is trying to spit out a true probability of Islam being true, it would simply be wrong if it displayed 50.1 since the real answer should either be 0 or 1. Islam is or isn’t true. There’s no in between." I agree that there is no in-between between Islam being true and Islam being false. However, I never made the claim that there is something in-between Islam being false and Islam being true. I only stated that the probability of Islam being true/false is such and such. Commented May 18, 2023 at 16:16
• @tryingtobeastoic Islam is a complicated theoretical system, and parts of it are true and parts of it are not, so the notion that it's all or nothing is black and white thinking. The principle of bivalence doesn't always apply when making claims.
– J D
Commented May 18, 2023 at 16:19
• @JD I am having trouble understanding how parts of Islam can be true and other parts false. Could you please give an example to elucidate the matter? Commented May 18, 2023 at 16:31
• @tryingtobeastoic Islam is correct in that Muhammad is a great prophet. Many people follow his prophecies. The religion he led in founding conquered great swaths of North Africa, the Middle East, and parts of Europe. Arabic has become a lingua franca in many of those countries united by a common language and belief system. Islam recognizes Abraham and Jesus of Nazareth as fellow prophets, which is also true. Islam preaches tolerance, and tolerance is good for peace. These are all practically speaking truths. But, there are no supernatural gods. So, it gets that wrong.
– J D
Commented May 18, 2023 at 16:41
• @JD We are arguing semantics here. When I say that Islam is false, I don't (for the sake of argument) deny that the truths you mentioned are false. I only mean that there is no Allah. In other words, I mean that the disputed aspects (i.e. Allah being the one and only God, Muhammad being the messenger of Allah etc.) of Islam are false. Commented May 18, 2023 at 16:52

It depends on subjective criteria. For example, you may decide that a difference of 0.2% is not significant to you, and conclude "do nothing". Or you might use a Pascal wager type argument. Or you can look at the utilities of each choice in some other way. The probability values alone are not enough to decide, you need to supply some decision function that will probably include some amount of subjectivity.

• 0.2 [Pa, Kg, L, ...] Is a circle. Commented May 21, 2023 at 3:12

Say I obtained from that machine that the probability of Islam being true is 50.1%, and that the probability of Islam being false is 49.9%.

I would say that the machine has determined that, with all the available information, there is a 50-50 chance of Islam being true.

My first question is; What information was used by the machine to arrive at these probabilities? I want to determine for myself whether the methodology and use is appropriate.

If no flaw can be found, then this leaves you with two choices:

1. Find a fair coin, flip it, and make your choice or a random number generator that spits out numbers from 1 to 1000. Any number 499 or less and the choice is Islam is false. Otherwise, Islam is true.

2. Read the Koran, the Bible, and all other religions and make a choice.

The coin flip is MUCH easier.

Edit for umbrella and 40% chance of rain.

1. Get a random number generator that randomly spits out integers from 1 to 10.

2. Any number of 4 or less: Carry the umbrella. Otherwise go umbrella free.

The other choice is to use the probability information as basis for further analysis: A forty percent chance of rain may lead to checking current weather satellite information to determine whether this general probability for rain applies to my specific region.

Decisions based solely on probability are a last resort to be used when there is no ability to get further information necessary to give the decision more certainty.

A common method to deal with rain probabilities is to buy an inexpensive 6 pack of collapsible umbrellas and keep one in each vehicle, one at work, etc. That way there is no math involved in keeping dry.

• Arigato for the clarification! Non cigito you're wrong about how we could be wrong. Commented May 21, 2023 at 3:10

Decision Analysis

Decision Analysis is a formal method for assigning probabilities to outcomes in the context of making decisions. Another search term would be decision-making with probabilities.

The idea is to compute the expected value or expected payoff for each course of action then take the decision based on the prospect of gain or loss. Then the expected values are mapped to a decision tree. I cannot find a good reference via simple keyword search.