
When you acquire a belief, you have two initial choices. Either you keep it to yourself or you tell others. If you keep it to yourself, your belief will not affect anyone. If you tell others, your belief may influence them and give them the same choices.

The effect that your belief has on you and others is important to consider. It may be good or bad for you and it may affect only you or others as well.
D1 => 0
D2 => (E1 or E2 or E3 or E4)
Giving in descending order of probability:
E3 > E1 > E4 > E2
The probability that you will decide D1 or D2 depends on the effect of the belief. E3 has the highest probability because the avoidance of suffering is universally prioritized above the accrual of happiness and this applies even more when groups of people are involved. E1 comes next because the belief benefits a group of people as well as yourself and this makes it important to share. E4 follows because it is bad, and E2 is last because the accrual of personal happiness is the least necessary effect to share and may receive poor reception.
These are generalizations and there are plenty of exceptions. You could break this down further using degrees or levels of good and bad effects and by basing probability on them. It would make a difference, but it gets complicated and gets away from the point I want to make.
What is my point? I want to show that, generally speaking, when we acquire a belief that benefits or harms ourselves as well as others, we are very likely to tell others about it. It would be irrational under most circumstances to keep it to ourselves.
Why should you care? I also want to show that it is only natural for people to share their most important beliefs. Many people carry around beliefs that they think are important and keep them to themselves.
Think about religious beliefs. Most religious beliefs fall within E1 and E3, so it is only natural that people who have them should want to share them. Yet, you often find theists and atheists saying that they prefer to keep their respective religious beliefs to themselves.
Why do they say this? The most common reason I have found is that they do not want to force their beliefs on others. This is usually justified with different reasons. Theists argue that people must acquire the "right" belief on their own. Atheists argue that theists should be left alone as long as they do not harm anyone.
These are poor justifications, for, to repeat, it is irrational that people should choose not to share their most important beliefs. There are good and bad consequences for everyone who believes what theists and atheists believe, so sharing should be implicit. When Jesus said in Mark 16:15, "Go ye into all the world, and preach the gospel to every creature," he was speaking common sense.
If you carry around an important belief, I encourage you to share it. Let others know and listen to their responses. If you cannot share your most important beliefs, then how do you know that you actually believe them? Maybe you are agnostic.
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