My understanding of Objectivism is that the ideal government Rand proposed in her writings does not have the power to violate individual rights even if it can be proven that such a violation would benefit the individuals in the state.
Such a thing can never be proven. If it appears that it could, you’re working with a false premise or assumption. For example:
Assuming that a state has limited natural resources and that more people will result in higher prices for these resources (higher demand + limited supply = higher prices), it would benefit everyone if the population were limited by the government.
Natural resources aren’t truly limited. There is no limit to water, wood, air, etc. etc. However, let’s try to think of a resource that is limited. Say oil is actually really running out. It wouldn’t benefit every individual for the government to set a price cap on oil - it would hurt those that run the oil company, supply the oil company, work for the oil company, etc. Furthermore, I’d rather pay higher prices than live under a government that coerces productive citizens to benefit the majority.
Can the ideal government proposed by Rand ever violate individual rights if that violation benefits the individuals in the state?
Such a violation would never benefit the individuals in the state, as illustrated above. Try as hard as you want to think of a counterexample.
If you poke around the forum, you’ll notice that people complain when someone proposes a false hypothetical. This is exactly why. A false hypothetical assumes reality is different. If reality were different, well, Objectivism wouldn’t be Objectivism, because Objectivism is based upon reality as it actually is. So there’s no point in talking about false hypotheticals on an Objectivism forum, unless they’re within the realm of possibility (e.g. if Obama is elected, if McCain is elected, if we run out of oil, etc.).
I really want to know how an objectivist political platform would be distinguishable from the Libertarian Party political platform - limited government and the enshrinement of individual rights, leaving aside the philosophical underpinnings.
That’s a much different question; I’d suggest asking in a new topic or, better yet, try to read up on the issues yourself. In short, though, Objectivism would differ on things like foreign policy, (probably, depending on what Libertarian you’re talking to) abortion, (possibly) “marriage,” etc. And it would lead to different conclusions in a number of more subtle issues, no doubt, because it has different philosophical underpinnings.