Where does power lie and who controls policy? This is a key question within political science, and one with much disagreement over. One group is the pluralists. Pluralists argue that power is distributed among competing interest groups striving to control policy, either mediated by the state or with the state as its own autonomous entity in this fight. Pluralists argue that, through this competition of interest groups, the will of the people can be expressed. In contrast, class theorists argue that it there are stratified classes within society and that those in the upper classes control policy, but have to contend with the lower classes through class conflict. This is the analysis of Marx and many class theorists are marxian theorists, though not always marxists.
Then there is elite theory. According to elite theory, there are a small number of "elites" who control policy and the state. These elites can be government officials, people of prestigious families, leaders within corporations, or people with powerful social influence, such as preachers. Usually, they are more than one of those. For example, Ted Kennedy was a US Senator for nearly 50 years (making him a governmental official) and was a member of the Kennedy family (making him a member of a prestigious family). While people can rise to join the elite, such as, to continue the running example of the Kennedy family, P J Kennedy, grandfather of JFK, Robert Kennedy, and Ted Kennedy, managed to rise from obscurity to become a US Representative then later US Senator and became adept at playing the internal politics of Boston, those who are already the elite or have family within the elite can more easily gain and use power thanks to greater education, more money, family and personal connections, and education of the inner workings of the state and other bodies of power, often since an early age. While the elite do not necessarily agree, they are the only ones with power and they are the ones who control the system. In fact, the masses are often excluded entirely from the decision making.
Now, this does not mean there is some conspiracy of elites who are necessarily in cahoots with each other and control things in secret. Indeed, oftentimes the elites exert their influence openly. In addition, the elites are not necessarily unified.
This also does not mean that the excluded group can never exert any influence. Indeed, elite theory recognizes the existence of "counter-elites" through whom the disenfranchised can negotiate with the elites. However, the excluded group do not have any power nor do they participate in the making of policy.
Elite theorists see the US, and other western nations claiming to be democracies, as not truly democratic because the people don't have true influence on who is in power or policy making. While this may seem to deny the existence of voting for public officials or more direct democratic initiatives where the people themselves vote for policy. However, elite theorists argue that the choices that the voters have are limited. When we choose between two senators, both of them are "pre-screened" by the elite and the choices are limited to those who the elites want or are at least ok with. This often means that the voter is choosing between two elites themselves or just between two people who can be controlled by elites. On occasion, one of the choices will be rising elites, like P J Kennedy in 1884 when he successfully ran for the House of Representatives. With direct democratic initiatives, they are written by or at least approved by the elite. The choices become remaining in the status quo, which, while not necessarily in the interests of the elite, definitely preserving the power of the elite, or choosing something the elite want or don't mind. This is not the same as having power or choices.
Now, one might wonder why sometimes policies which don't benefit the elites or actively hurt the elites can happen if the elites truly control policy. This is a complicated issue and one without a single answer. There are many reasons why this might happen.
One obvious reason is that the policy might actually benefit the elite, and it's only perceived as not benefitting the elite. One example I can think of is a progressive income tax. While the progressive income tax appears to hurt the elite, since the vast majority of the elite are rich and a progressive taxation system taxes the rich more than the poor, it actually comes with benefits to the elite. If we were to switch to a flat tax or a sales tax, both of which disproportionately hurt the poor, the rich benefit from a functioning state, and flat or sales taxes makes it more difficult to continue having a functioning state, so the progressive income tax helps them by keeping the state functioning.
Another reason is that the elite aren't perfectly rational and don't necessarily want what is in their best interests. In addition, sometimes the elites don't know what is in their best interests, so they fight for a solution that hurts them.
Still another reason is that the elite aren't homogeneous and don't have one voice and one interest. What might hurt one elite helps another. A high progressive income tax clearly helps a senator who's salary depends on a functioning state more than the CEO of a corporation.
Finally, there is the existence of counter-elites and threats from the masses. One of the key examples of this is the New Deal. The Great Depression hurt the masses greatly, and negative feelings arose among them. Many were radicalised and a radical sentiment grew within the masses. There was a growing danger that the elite would be taken out of power through a revolution similar to what happened in Russia. Because of this danger, FDR, who was a member of the elites as a member of the Roosevelt family, growing up in a monied atmosphere, married to a member of the Roosevelt family (far enough removed that there was no danger of anything bad related to incest) who was the niece of former president Teddy Roosevelt, and a former senator and governor. However, he recognized the danger of a communist revolution, and, in his desire to save capitalism, he instituted the New Deal. The New Deal helped the masses immensely. While the Great Depression wasn't completely ended by it (that would be the almost corporatist economics instituted during World War II), it did alleviate many of the ill affects to the poor and helped lessen it at the expense of the elites. Not all elites recognized the importance of this to their power, and many called him a class traitor. However, the power of the elites was maintained.
Now, there are surely other ways for such policies to happen, but all of them must eventually go through the elite and happen because the elite want them to happen.
Now, the power of the elites can crumble. This often happens in revolutions. In the French Revolution, the aristocracy lost its power thanks to the masses rising up and killing them or kicking them out of the country. This didn't lead to an end to elites, though, and new elites soon cropped up. These destruction of the power of the elites almost always comes from below, and sometimes through the counter-elites, though they often benefit from the current structure since it gives them power, too, even if they don't have any actual control over policy.
But what does this all mean for anarchism?
The most important thing about this is that the power of elites and hierarchy in general cannot be destroyed from within. The elites are the ones benefiting from their power and from hierarchy, and they are the ones who control the system. They are not, or will very rarely, willingly give up that power. This is why revolution is necessary.
The other lesson from this is that we need to be cautious of the rise of elites and design whatever society we create from the shell of the old in such a way that elites cannot form.