There are innumerable definitions of the state, all of which are substantially different.
In practical terms, this definition is not very good. It isn't clear that states in general operate in favor of the people's will or rule by any kind of majority. This sounds like a description of a liberal democracy, rather than a state.
A definition of "state" must be applicable to all states. Try to find examples where your definition doesn't apply. My first thought is about states like Turkmenistan - a dictatorship consistently ranked as the worst in the world. It's hard to see how that state embodies the public will. Overtly there is no mechanism of majority rule.
There is also a problem with the idea of "equality of all humans before the law". That would prevent every government currently existing from being a state! In America, people can't vote until they are 18 - which is an example of legal inequality. Other countries have similar restrictions.
Finally, the governments we have today almost never decide purely on the basis of the "benefit of any activity" (unless you define "benefit" in a very broad way). Politics often happens: Legislators have to decide what proposals are likely to be successful, how members of their own (and other) parties will react, whether their constituents will appreciate the proposal, whether the groups funding their campaigns will approve, etc. Legislators are also people, and they have human emotions and viewpoints which color their world. This is all just to say that they are far from utilitarian, even though in some cases they try to be.
Since this was tagged political-theory, I suspect you might intend this to be a moral or ethical description of the state. It's not a bad starting place - it's reminiscent of the work of French philosopher Jean-Jacques Rousseau. One significant difference is that Rousseau is describing the ideal form of government, not setting a definition.
To further develop your thoughts on a philosophy-styled definition, here are a few questions you might consider:
- How does the state know what the people's Will is? Can it ever be mistaken? If it is mistaken, does it cease to be a state?
- The minority of people will have a different opinion than the majority. Is it just or fair to impose the majority's will on them? This could include imprisonment or death. What rights does the minority have against the majority?
- If the state is empowered by the people's Will, is there any limit on what it can do?
A Proposed Definition
Like I said, there are a lot of definitions. Here is one from the world of international relations. I think it will give you a better starting point:
According to the Montevideo Convention, a state is:
The state as a person of international law should possess the following qualifications:
a ) a permanent population;
b ) a defined territory;
c ) government; and
d) capacity to enter into relations with the other states.
If an organization governs a piece of territory with a permanent population and this ability to govern is recognized by other states, then the organization is a state.