The "Political Systems Theory" is another descriptive model which treats the government like an organism which responds to inputs and stimuli and creates outputs. The inputs are demands and support. These go through a filter, enter the government system, are processed into public policy and then the results feedback as an input.
This theory does contain a few prediction capabilities from the fact that this model implies that the purpose of government is to survive. Yet it treats government like a box, that simply processes inputs neutrally, implying that all of the important decisions and bargaining happen outside of government in the environment. Thus, the "Policy Process Theory" is a much better descriptive model of how policymaking occurs.
There are a few models which have much better explanatory power, and allow for much more prediction. Yet they all have their flaws, and must be used carefully when used to make predictions.
"Group theory" (pluralists) assumes the following is true for public policymaking: (1) most demands and supports for policy are manifest through organized groups; (2) no single group can monopolize power; (3) the most influential group will be decided by the amount of competition and the qualities of the competing groups; (4) policy results from compromise; (5) political actors are objective referees who state which group won.
However, this theory overstates the importance of groups and ignores the role that public officials play in policymaking. Some policies are made by judges (with no dominant group winning), and the President has great influence over what policy areas are given attention. Additionally, not all interests are represented by groups and a few groups do monopolize the influence over some policy areas (for example, the American Medical Association).
Thus, many of the premises of "Group Theory" can be challenged, yet the model does focus attention on the importance of interest groups in the policy process. It also allows for predicting policy outcomes by evaluating the groups involved. For example, if a policy on the agenda is supported by a well-organized, well-lead interest group with little competition, this theory says that that policy has a good chance of being approved.
Another explanatory theory is the "Elite Theory" which says that society is stratified with the masses at the bottom and a ruling-class elite at the top. These elites are the rich and well-educated, who share common beliefs and use their influence to dictate public policies. The most serious flaw in this theory is that no such ruling-class can be identified. Yet, if this class could be found, then any policy which went against this class could be predicted to fail. This theory also focuses attention on the role of leadership in policymaking.
Rational-choice theory argues that policymakers pursue their own self-interest instead of any national-interest. They also vote based upon their own goals instead of for any other reason. Anderson gives the example of a politician who will approve of an agency which will trouble his constituents so that he can help them out and get re-elected. This model alerts us to the importance of self-interest in policymaking. If voting for a policy will hurt a politician on election day, then this model allows us to predict that the politician will not vote for it.
The principal-agent theory was originally used to show the relationship between management (the principal) and labor (the agent). This theory can also be applied to political situations. This theory rests upon a number of assumptions:  there is a conflict of interests;  there is unobservable behavior;  there is a "moral hazard" (loopholes in contracts), and "adverse selection" (some workers will cheat and be incompetent);  cheating and deception are everywhere.
By comparing the ultimate goals of those involved in a policy-making process, we can immediately see where the conflict is going to occur. The problem with this theory is that it is overly pessimistic - not all policies are confrontational in nature.
The next three models discussed are really decision-making models instead of public policy models, but the two activities are closely related. The three models are the rational-comprehensive theory, the incremental theory, and mixed scanning.
The rational-comprehensive theory is a very well thought-out, step-by-step map to making good public policy decisions. The steps involved in this theory are:  identify the problem and define it;  decide on the goals to be reached to solve the problem;  identify all of the alternatives to reaching this goal;  evaluate the consequences of each of the alternatives;  compare the alternatives and their consequences and choose the one which best reaches the goal with the least adverse consequences.
As logical as the model sounds, it, too, has many problems. First, it assumes that there is a best way to solve a problem and that decision makers are able to define the problem. It also assumes that the goals of the policy are clear before it is implemented, though, when you cannot define the problem, it's hard to set goals to reach the resolution of the problem. This model also assumes that the policymakers can foresee the consequences of all the alternatives. And, finally, this model ignores the politics of policymaking, and the sunk costs from prior policy implementation. Yet, despite these shortfalls, this model has the positive feature of focusing on goals in policymaking.
The near opposite of the rational-comprehensive theory is the incremental theory. Many political scientists take issue with incrementalism pointing out that it is not the way a government should be ran. Yet, it is still highly touted as the way that officials actually do make decisions. This theory makes the opposite assumptions of the rational-comprehensive theory. Incrementalism assumes:  the goals are unclear;  the problem, goals and implementation are intertwined and will evolve;  alternatives and goals are formed as learned;  policymakers are not free to choose the best alternatives because they must consider the feasibility and acceptability of possible policies.
This model basically means that instead of jumping straight to a goal, as the rational-comprehensive theory suggests, that one take tiny steps toward a goal until the goal becomes more clear. But one of the harshest criticisms of this model is that it does not allow movement toward a goal. Goal setting is really nowhere to be found, just small changes from year to year.
Each of these models would answer the question, who's in control, differently. The group theorist would say that groups control; the elite theorists would say that there is some group of elites at the top of the hierarchy pulling the strings; the rational-choice theorists would say that the politicians are ruled by their own self-interests.
When it comes to which of these public policy models is closest to what empirically is happening, I would have to say that the theory of incrementalism is the most accurate picture of reality. This is especially evident when we look at the bureaucracy. Giant policy changes are rarely seen in the typical agency, but the policies change often a little bit at a time. Implementation of a controversial policy is also often broken into tiny steps to "soften the blow" (e.g. the way minimum wage was raised a little each year). Even legislation of policy seems to be incremental, with the bill going from one committee to another, taking one more step towards authorization.
As far as normatively which model should be the model used, I would have to say that some combination of the rational-comprehensive and incremental model should be used. When these two models are combined, you end up with the Mixed Scanning model of decision making. Mixed scanning permits decision-makers to utilize both the rational-comprehensive and incremental theories in different situations, it is a kind of "compromise" approach. The implementation is incremental for a while, but once enough information is acquired about how the policy could cause problems and whether it is feasible to continue, the agency involved should jump right to the goal. The agency could switch between incremental and rational approaches based upon the nature of the decisions to be made.
What people need is "flexible stability." You cannot have a nation run by a government that makes huge jumps from A to point B (rational-comprehensive model), it should only take such actions in time of crisis. Yet the government cannot be so stable that it does not respond to demands for change. Current public policy is static, freezing in time the political culture of the time the policy was made; as the culture changes, the policy should evolve. Yet, a pure incremental model does not seem to strive for a goal - the goal changes as the policy is implemented. In other words, the incremental method of policymaking does not strive to reach any goal.
The incremental model needs to be modified to allow for searching for alternatives and striving for goals. If an altered incremental model (similar to the mixed scanning model) could be implemented, it should be the model to pattern government after.