Richard Posner is known as one of America's greatest legal theorists, and is probably the leading supporter of a legal philosophy called pragmatism. Posner disagrees with the standard refrain that legal theory is governed by rules and that judges just apply the rules without any discretion. His theory requires judges to use their discretion to resolve difficult legal questions, because the rules do not always lead to a clear answer.
Sometimes we will have two rules that conflict and the judge will be required to make a discretionary decision. Or sometimes there will be no rule. For example, let's say someone argues that the 13th Amendment (banning slavery and involuntary servitude) bars government regulation of abortion because it forces women to carry a child to term, and that is a form of involuntary servitude. How is a judge supposed to decide this question?
No rule really exists to help us decide if the Amendment should apply to abortion. So the judge can look to see if the argument is plausible. But that's just a form of using discretion.
Judicial ideologies, such as originalism, were designed to deal with the discretion question. The judge will look to see if the original understanding of the Amendment included abortion. If it does, then he will strike down all abortion laws that conflict. If it doesn't, then he will allow them to stand.
Of course judicial ideologies create problems of their own and also, despite arguments to the contrary, leave much to the judges' discretion.
What exactly is discretion? Discretion is the judge's "common sense." Common sense is something that is dictated by experience, which is why Posner suggests that courts be diverse, to take into account society's different perceptions. But common sense is also something that stems from a result-oriented look at the law. If a judge feels that abortion is murder, he is more likely to believe, when no legal rules guide his decision, that a reasonable interpretation of the law would ban abortion.
How does any of the above apply to Halacha? Well the same problems that confront judges bother poskim (legal decisors). What is a posek (legal decisor) to do when faced with a question that has two equally plausible answers? If the posek uses his discretion, is he not supplying his own personal beliefs to answer the question?
Asked another way, how does Hashkafa (religious outlook) influence Halacha? Is it a mere coincidence that Rav Herschel Schacter, who is Modern Orthodox, supports Slifkin while Rav Elyashiv believes, at the very least, that his views should not be read? Or that in Mea Shaarim, a very gender segregated society, women shave their heads because of strict interpretation of Jewish law? Or that in places like Lakewood, where Torah learning is considered paramount, Halacha is interpreted to require men to study Torah rather than learn a livelihood?
I don't believe that Poskim interpret the law according to their own personal whims. I'm sure they try to see what's reasonable under the circumstances. But someone needs to do a study to determine whether Hashkafa does influence Halacha, to see whether people with stricter Hashkafas decide Halacha strictly.