I'm working on an NPC for Pathfinder who runs a cult based on Cosmic Balance. Basically, they believe that every action as an exact opposite action, i.e. anytime you do something good, something bad happens somewhere else in the world. So he believes by doing obviously evil things, like sacrificing captives to his pet Shadow, he his causing the amount of good in the world to increase. So he legitimately believes he is doing good, so what should be alignment be? Doing evil for the sake of evil is usually NE, but he is doing evil for the sake of good so I'm not really sure where to put him? Any thoughts?

I could see him anywhere between true neutral and lawful evil, depending on how he applies the philosophy. It is really hard to say, though. I really like the concept. It's like a complete twist on karma.

I'd peg him as lawful evil. Just because he believes what evil he is doing ambiguously creates good elsewhere, that still doesn't make him a good person as he is just using arbitrary rules of good ends to justify his evil means. In the cosmic sense, he's a psychopath.

Is he using his philosophy of balance to justify the evil things he wanted to do, or is he doing evil things because of his philosophy? And how does he think his acts result in a net good? Does he inflict evil on evil people so good will happen to statistically random people?

He is doing evil things because he honestly believes that the universe will act on its own to add good to balance out the evil that he does. He's is totally crazy of course, but he is a true believer. I would say he probably does a mix of evil both evil and good people, like taking in condemned prisoners as a front to placate the authorities and keep attention of the crazyer aspects of his cult, but probably kidnaps good people in secret to do terrible things to them, because the more evil he does, the more "good" the universe will do to make up for it. He probably views it as a holy burden that he as been righteously given by the universe, so he at least claims to not take any pleasure in doing evil things to people.

Sounds lawful good to me then. He's doing his best to fulfill the duty he believes is set out for him, in pursuit of the greater good.

I am still not sure why he thinks he's increasing Good by committing Evil. Unless he doesn't think Good and Evil cancel out and great Good in the world is positive even if there is equal amount of great Evil.

He's Good if there is a metaphysical Good out there that his actions are actually contributing to. But otherwise, simply because he thinks he's pursuing the greater good, it does not make him Good. Such a definition would render the whole idea of alignment meaningless. Good in D&D and Pathfinder include respect for life and concern for the dignity of other beings. Someone who kills people who are not active threats to increase some arbitrary, vague Good somewhere else is not Good.

Why is pinning down the character's alignment necessary?

I would guess that he's trying to act as a filter of sorts. By filling his own sphere of influence with as much evil as possible, he decreases evil in the rest of the world.

For the purpose of Detect Alignment things. He acts nice most of the time, but If the paladin uses detect evil, I need to figure out what he senses.

I would say he senses an evil psychopath. The character you are describing sounds like a crazy person (which you admit to) who knowingly does evil acts for an assumed good that he believes happens, but never actually sees the fruits of. The thing about games that use alignment rules is that good and evil sort of stop being philosophical concepts and become measurable quantities. If you knowing do evil, you are evil.

Your NPC may be misguided in his evil ways, or maybe he's not wrong for doing evil for whatever reason he does it, but he's doing evil on the side of Evil and expecting the manifestations of Good to sort of pick up the slack (without much proof that it even can beyond his own belief). And he's not indiscriminately being evil either, he's got rules, structure, codes of conduct in his evil to maximize the output of imagined good elsewhere. He's rather lawful in that respect.

Anyway, long story short, your dude is Lawful Evil.

Those pesky Detect Alignments. If you are concerned the paladin will out your villain before you want them to, maybe finagle like a magic item of cosmic balance that makes people appear Neutral that the villain wears, not to hide that he's Evil but because he sees himself as a cosmic balancer. Or throw off Detect Evil by making mundane evil folk appear more often. Like the mildly Evil tax collector who is sadistic but not actually committing crimes or hurting people outside of his duties or the mildly Evil milkmaid who would be willing to kill someone if it came up but it just never did.

Conversely, just have them meet up with your NPC in a town that happens to be run by a Lawful Evil government structure, like a military governorship dedicated to some LE War God (Bane?). There should be enough residual evil there to mask your NPC for a while.

The town doesn't have to be a roiling den of villainy or anything, just "Yeah, I guess Banites are technically on the "evil" side of the Good/Evil divide, but their overly cruel punishments tend to keep the criminal lowlifes in check, the streets are always clean (the punishment for littering is....harsh), everything around here runs like clockwork (because inefficiency isn't tolerated), and families are relatively safer here than out in the wilds." Is the government evil? Sure. Is that a problem? Not enough of one to fight over.

Just get rid of the alignment system altogether. It gets weird when you dig into it, not because it is hard to picture a world where good and evil, but because the whole idea is logically incoherent.
Is it the killing that's evil? Then wouldn't most PCs be evil be merit of having killed (a lot)? If it\s intent that matters, then I'd say MR.PSycho is in the clear. If it's just the outcome, then anytime your PCs inadvertently caused damage to somebody down the line they were being evil.

I'm not super concerned whether or not my Paladin does sense him, just whether or not he should sense him, and I was curious about where a character like this would fall on the track. But now I can see him as being in the lawful evil camp.

I don't understand this character. If he believes every action has a counteraction of opposite morality, then he wouldn't carry out evil actions in the belief that they result in good, he would believe that the outcome of every action is neutral. In his eyes, everything has an equally good and evil outcome, even if they can be relatively less or more equally good and evil.

I understand where he's trying to go with the idea.

Reminds me of anti-heroes in a sense. In another sense it reminds me of the paladin protagonist from the second D&D movie. To me, it's like you want that character to do bad in the name of good. Like the undercover cop. When in Rome as the saying goes.

If you stick to the cult belief you described, what Mown said ultimately makes more sense since everything balances out eventually. Course that being said, I'd find it hilarious if that character went to extremes to track everything in his sphere of influence and committed both good and evil acts to maintain the balance no matter the cost.

"Yesterday I saw someone save children from drowning. Tonight I must do the unspeakable in order to preserve the balance." And then the murders started.

He doesn't necessarily believe that they cancel out, so he believes he is increasing the overall good in the world and speeding the cosmic process up. His argument of course falls flat to reasonable logic, but his self delusion keeps him from being ax crazy-crazy.

"that character went to extremes to track everything in his sphere of influence and committed both good and evil acts to maintain the balance no matter the cost."

Which is pretty much what his cult does.

More good = good. More bad= I dunno, I'm crazy.
"Speeding the cosmic process up" so he believes that he's helping the world grow/develop/end by putting more good and evil into it?