Willravel

Bias is simply being prone to a particular perspective or ideology. It something we all have, but the less we have of it, the more objective we can be. It interferes with the ability to be impartial and objective. In order to overcome personal bias, we (humans) have developed various verifiable methodologies to determine objective facts about the world.
I don't the the life insurance example fits well, but for the sake of argument I'll use it. Assuming you've been tested using various verifiable methods, methods that have been demonstrated to provide a certain reliability, that there is an outcome based on these methods, it is logical to trust these methods taking into account their reliability of success. If a certain test has an 87% likelihood of being correct, you can trust that outcome 87%. If it has a 99.9999% likelihood of being correct, you can trust that outcome 99.9999%. Should something happen that is unlikely, it would automatically be a part of whatever percent is incorrect, something you can take into account as an unlikely but possible outcome. If your life insurance says you're about 96% likely to live to be 83 and likely won't have a heart attack, and you have a heart attack, your insurance isn't wrong, you're simply in that 4%. Still, if the methodology that determined that 96% likelihood was based in sound methodology, nothing outside of that methodology or to disprove that methodology has occurred. It's all a simple matter of likelihood.

If, in your hypothetical situation, we were presented with the exact same figures of likelihood and one of us chose to agree with them and one did not, it's likely a bias came into play. Here's where it gets funny: it's entirely possible that the person with the bias could end up making the right decision ultimate, but he will have made that correct decision accidentally, which means it was the wrong decision. It was a gamble where the bias was put up against verifiable methodology, and in such a gamble the smart money is on the latter.

Let's say that you were to wager me that you could toss a coin and get heads 5 times in a row. If you win, you get $100. If I win, I get $10. Simple math tells me that the odds of 5 consecutive head tosses are one in 32, which means the odds are strongly in my favor. I will make the bet, even knowing that there's a chance I lose I will lose much more than I stand to gain simply because the odds favor my outcome more than yours even to the point of superseding the factor of 10 difference between risk/reward. There may be some outside factor I cannot perceive, but based on all the information I have, I'm making the prudent and logically defensible choice.
I'm the one using deductive reasoning. If there is little verifiable evidence that Saddam is a threat, how can I conclude that the risk is higher than the absolute risk of losing soldiers if we go to war? That's simple enough. As soon as objective methodology is adopted by one side and not the other, the side with it gains a logical upper hand. Ruling by rough approximation and bias cannot be as reliable as verifiable methodology.

I'll put it in different terms. One man says the earth is 4.7 billion years old. Another man says the earth is 6,015 years old. The first person is using verifiable geological and physical methodology to determine the age of the earth, the second person is using the biased source of the Bible. As science isn't a democracy, there aren't two votes to be counted, there are two theories to be tested. Both are processed using the verifiable methodology of the scientific method, and the crucible burns away the fallacy of the young earth so that only the truth remains.