I think that AJ gave a good enough answer, but I want to add a few things.
Natural rights people are just confused, indirect consequentialists. People came up with “natural rights” based on the consequences of holding those beliefs, but I don’t think that much of it was conscious.
Half of what we call “morality” is what our subconsciousness tells us about how we should treat other people. We think of a situation in which we have a number of options of how to treat other people, and then we feel either a positive emotion or a negative emotion about each of them. We might think of a situation in which somebody is drowning, conclude that we could either try to save them or just leave, feel a positive emotion about the former, a negative emotion about the latter, and then decide that the former is the “moral” thing to do, and the latter is the “immoral” thing to do. This sort of “morality” could be called our “moral feelings”, and biologically evolved just like anything else giving us advice, such as taste, happiness, and so on.
The other half of what we call “morality” is what our consciousness tells us about how we should treat other people. We think of a situation in which we have a number of option of how to treat other people, and then we perform a conscious cost-benefit analysis about the options. We might think of a situation in which somebody is drowning, conclude that we could either try to save them or just leave, think that saving them would be beneficial to us for some reasons, such as social capital from other people who hear about it, the fact that you like the person and would like to be able to hang out with them, or whatever, and think that letting them drown would be the opposite, and then decide that the former is the correct thing to do, and the latter is the incorrect thing to do.
When people sit down and try to spin out what is moral and what isn’t in the first sense, they just try to think of a situation in which they have more than one option of how to treat somebody, and then consult their subconsciousness to see what its advice is. But, when people sit down and try to spin out what is moral and what isn’t in the second sense, they try to consciously figure out what the consequences would be of each option, and for that you often need economics.
Both of the methods are cost-benefit analyses. To put it simply, but a bit superficially, the only difference is that one is conscious, and therefore driven by cultural evolution, and the other one is subconscious, and thereby driven by biological evolution. We should in my opinion use both methods, but always keep in mind that they are both cost-benefit analyses. We shouldn’t think of the former as a sort of cold, sober way of looking at things, and the latter as a sort of romantic, mystical way of looking at things. We should consult both of them, but just realize that they both are of the nexus of means and ends.
(By the way, we can use economics to find out why we evolved those subconscious feelings about how we should treat other people, and why they spit out the advice that they do. To put it simply, dividing labor is more productive than not dividing labor, and anyone in the division of labor, no matter how far away they are, are to some extent helping you out. We feel compassion for other people, and want to help them out, because them being active in the division of labor helps us out in the long term.)
Taste is the best example of something else where we have subconscious advice in the form of feelings, but also conscious thoughts about it. Our taste tells us whether it would be a good idea to keep eating something. A bad taste is our subconsciousness advising us to stop eating what we are eating, and a good taste is our subconsciousness advising us to continue eating what we are eating. But we can also think about whether something is a good thing to eat. We might decide that ice cream isn’t a good thing to eat based on research studies linking it to a disease or something.
Why is our taste so wrong so often? Why do people so often want to eat something that they know in their thoughts is unhealthy, but do so just because it tastes so good? Why would our two senses, our feelings about what foods to eat, and our thoughts about what foods to eat, be so against each other? Well, the problem is this. Our sense of taste evolved around certain inputs. Our taste evolved only needing to deal with giving output about a small number of inputs. But we have in the modern world many more things that our sense of taste didn’t have to deal with when it was evolving. To give you a quick example, maybe one of the parameters was basically “the denser the food the better”, which would have worked when the densest thing that we could find were nuts and seeds, which we might not have found very often. But we have in the modern world the ability to make things artificially dense, so our sense of taste rewards us even though it didn’t evolve to even appraise anything as dense as that. Maybe, if it did have to appraise things as dense as that, it would have developed a more nuanced set of parameters.
Now, could our moral thoughts and moral feelings also be in conflict like that? Of course, and I actually think that they are. We apparently lived in small tribes of mostly people of our extended family during the time when most people consider our biology to have reached pretty close to where it is right now. But the way that the economy worked in small tribes like that was different. Price gouging would be evil, simply because we would have bought the thing that we were selling from the same person that we are trying to sell to after they find out that they need it after all. Walter Block, among others, has talked about this. He thinks that a lot of the tendencies of most people to embrace socialism and whatever are just fueled by the fact that our biology is basically the same as those people who lived in small tribes of most people of your extended family, where mild socialism actually makes sense. But now we live in a huge, integrated society, where we divide labor with complete strangers across the world, and which is much different, which means that, contrary to a lot of our moral feelings, socialism doesn’t really make any sense. Foreign aid packages are a good example. They sound great, and average people might call you selfish or something if you tell them that we shouldn’t be sending foreign aid packages. But we know through our moral thoughts that foreign aid packages might sound good, but they mess up the people who are getting them in the long term, whether anyone involved knows or not.
So my conclusion is that I think that both the moral thoughts, and the moral feelings, are important, but that, just like with taste, we need to be very wary of the advice of the moral feelings, because the input that it evolved around is a lot different than the input that it gets nowadays.
I am against statism because of what my very limited economic knowledge tells me are the consequences, because of the fact that my very limited economic knowledge tells me that it isn’t a good means to our ends, not because of a mystical thing like natural rights.
Natural rights are just where people consult their moral feelings about certain things, consult their moral thoughts about those things, and then give an answer to what is moral, pretending that they didn’t ever consult their moral thoughts. I don’t think that anyone ever spins out anything that is purely just moral feelings, and I don’t even think that is possible, because I know that our thoughts about the healthiness of food can affect what our subconsciousness tells us, though not very much. So, if they pretend that they aren’t also consulting their moral thoughts, and that they are just spinning out something from their “conscience” or something, they are just replacing what could be explicit, systematic investigation, with implicit, unsystematic investigation.
For further reading, and restatements of the same sorts of things, see this post and the links in it.