The Policy Making Process and Models for Public Policy Analysis
Giovanni E. Reyes
University of Pittsburgh
Graduate School of Public and International Affairs
1. Introduction (4)
2. The Nature of Public Policy Problems (5)
2.2. Public and private problems
2.3. Political forces within public problems
2.4. Political systems and problem identification
2.5. A list of major issue-areas
2.6. Issues and events
3. The Policy Making Process (10)
3.1. General features
3.2. Conceptual approaches to study the methodology of policy process
3.3. Defining policy
3.4. A policy process framework
3.4. Theoretical approaches to study the policy making process and main political actors -rationalists, technicians, incrementalists, reformists-.
4. Major Models for Public Policy Analysis (18)
4.1. General Considerations
4.2. Difference Equations
4.2.1. Description and illustrations
4.2.2. General form of a difference equation
4.2.3. Difference equations of higher order
4.2.4. The use of difference equations in modeling
4.3. Queuing or ranking method
4.3.1. General features
4.3.2. Probabilistic queuing models
4.4. Simulation and non-lineal methods
4.4.1. General features
4.4.2. Macroeconomic simulation
4.4.3. Simulation as an analytical tool
4.5. Markov chains
4.5.1. Markov chains: An example
4.5.2. Main properties of a transition matrix
4.5.3. Regular, absorbing and cyclical chains
4.6. Cost-Benefit Analysis
4.6.1. Cost-benefit analysis and project evaluation
4.6.2. The procedure
4.7. Linear programming
4.7.1. The elements of a linear programming problem
4.7.2. The limitations of linear programming
5. Public Policy Analysis: A General Methodology to Apply (36)
5.1. Establishing the context
5.2. Determining alternatives
5.3. Establishing the consequences
5.4. Valuing the outcomes
5.5. Determining a choice
6. Bibliography (40)
The main objective of this document is to present a summary about two major topics: a) the process to formulate public policy decisions, and b) the principal methods to evaluate the impact and effects of a public policy. Both areas constitute core aspects of public policy analysis. Here I present their major characteristics followed by a brief discussion concerning their social implications and methodology.
The term government is consider here from a Weberian perspective, that it is the main social institution which gives national social units its coherence, representation, and a leading role. Its power is based either on a) tradition; or b) on charismatic features of leaders; or c) on a law and rationalistic basis. From this perspective, bureaucracy plays an important role in being a fundamental part of the public sphere, and its main "technostructural" column. Bureaucratic power is mainly evident in the stages of implementing and evaluating public policy. 
This document has three main parts. At the beginning we are going to focus on the nature of public problems, how these problems are different from the private sector problems, and what are their main repercussions. A good understanding of this section is pertinent to the comprehension of the next chapters, and the main sections of this exposition.
The middle section is devoted to the discussion of the process to formulate public policies. Here it is important to keep in mind the influence from the real powers in society, namely the business sector, the international interest, and also some institutions, such as political organizations, especial interest groups, churches, universities, and the armed forces. Complementary it is also important to be aware of the processes derived from the formal powers in society, namely national officials which are elected to represent society as a whole in a democratic nation.
The final section will focus on the main methods to study the impact from public policy decisions. We do not expect to cover all the methods, but at least to present the fundamental methodologies and their main features. References respect to the implementation process for public policy making is presented at the end of this document. I will finish with a general presentation concerning the methodology for a public policy analysis situation. In this last part the objective is to synthesize the analytical aspects discussed in the other chapter of this document.
2. The Nature of Public Policy Problems
To understand many of the most important features of public problems, it is necessary to clarify terms in order to set the context of both the political and social conditions for public policy analysis. Several of the most commonly used terms are the following:
a) Events: Human and natural acts perceived to have social consequences.
b) Problems: Human needs, however identified, that cannot be met privately.
c) Issues: Controversial public problems.
d) Issue areas: Bundles of controversial public problems. 
Events naturally vary immensely in effect. Wars and natural disasters touch millions of lives. Inventions like the internal combustion engine have altered our life-style dramatically. A new family in the neighborhood, however, normally has only limited consequences.
Events may cause problems to emerge and set the conditions for resolving them. Whether this happens depends on how observers perceive events. Those directly affected by a zoning variance that permits construction of a new shopping center and apartment complex, for example, may identify specific needs created by this event; others affected may not identify any particular resulting needs. Still others, perhaps a group of environmentalists not directly affected, may identify a need for those living in the area and oppose the variance. Congruity in identifying and acting on needs is by no means guaranteed, and therefore many problems may result from the same event. Conflict among problem definitions creates an issue.
2.2. Public and Private Problems
If a problem can be resolved without making demands on the people that are not immediately affected, then it is private in nature. John Dewey explains it thus:
"We take then our point of departure from the objective fact that human acts have consequences upon others, that some of these consequences are perceived, and that their perception leads to subsequent effort to control action so as to secure some consequences and avoid others. Following this clew, we are led to remark that the consequences are of two kinds, those which affect the persons directly engaged in a transaction, and those which affect others beyond those immediately concerned. In this distinction, we find the germ of the distinction between the private and the public."
A particular and essential feature of a public problem is the following: Human acts have consequences on others, and some of these are perceived to create needs to the extent that relief is sought. If the transaction to control consequences (regulating needs) is relatively restricted in effect, it is private. If the transaction has a broad effect, it is public. According to Dewey, "the public consists of all those who are affected by the indirect consequences of transactions to such an extent that it is deemed necessary to have those consequences systematically cared for."
People take actions or propose actions to control their environments: to meet their needs, to solve their problems. Sometimes these actions have consequences for others. When these consequences are perceived by others and considered to be significant enough to be controlled, we are facing a public problem. As David G. Smith explains: "That which intervenes between the perceived problem and the governmental outcome is a public, a group of affected parties-aroused, engaged in conjoint activity, growing conscious of itself, organizing and seeking to influence officials."
In a more economic sense oriented, public problems, on the other hand, frequently involved the production and use of public goods, such as national defense, the national road system, and the general structure of the academic pensa. Conversely, private problems involved production and consumption of private goods. Public goods are goods -and in a broad sense services- that can be used by many people at the same time. Private goods have as a fundamental feature, the fact that it is not possible for two persons to use the same private good at the same time, i.e. personal cloths.
2.3. Political Forces Within Public Problems
This concept of a public is important for these deliberations. Just as we have made a distinction between public and private problems, so too we can distinguish between public problems that have a supporting public and those public problems that do not. The first type of problem is characterized by a group of concerned and organized citizens who intend to get action; the second is acknowledged as a problem that cannot be solved privately, but it lacks organized and active support.
This distinction is critical for understanding the complex processes by which some problems reach government and others do not. The objective verification that a public problem exists (e.g., the many problems of the poor in most of the more developed nations) is no guarantee that a public will emerge to press for relief. As it is evident in many cases in the United States, "Public problems may lack a supporting public among those directly affected." Yet the government may act due to the demands of others. "Policy makers sometimes define problems for people who have not defined problems for themselves." This last condition can present several concrete opportunities for politicians especially during the political campaign and elections.
Not only are problems private and public supported and non supported, this discussion shows that a whole bundle of issues may be associated with any one event-for example, the Arab oil embargo; the hostage crisis in Iran; the rapid growth, then decline, of the school population; the deregulation of the airlines. For this reason it is important to introduce the term issue area. What are often referred to as public problems-education, energy, mass transportation, housing-are in reality various conflicting demands for relieving several sets of needs among the persons within society. Complicating matters even more is the fact that needs and demands, and therefore conflicts and priorities, are constantly changing; issues therefore require almost continual definition and redefinition.
2.4. Political Systems and Problem Identification
One can distinguish one political system from another by examining the characteristics of problem identification processes. In a democratic system problem identification is intended to be more subjective; in an authoritarian system it is intended to be more objective. In objectively defining problems an effort is made to employ scientific measures of the effects of events on people (this says nothing about the success of these measures, of course). 
There is little or no reliance on how the people interpret effects of events. Subjective processes, on the other hand, place a great deal of reliance on how those affected by an event interpret their needs. Elections and other representative processes presumably tap the public's subjective views. Both objective and subjective measures are, if fact, relied on by all political systems.
2.5. A List of Major Issue Areas
One of the many advantages of an open society -in which a democratic political systems works, and civil society has an important and permanent influence on national issues-, is that evaluations of social progress come from a variety of sources. We do not have to await the announcement of a five-year plan to determine what should be done, like in the former soviet-socialist countries. We get frequent private and public assessments. 
Often presidents' national discourses and economic and budget messages, counter programs and messages from legislative branches, all constitute official evaluations of where we are and what we must do. In addition we in this kind of open societies, can see any number of critical and analytical reviews from private agencies and interest groups. In United States, for example, the Brooking Institution, an independent organization devoted to nonpartisan research, has for the past several years offered an analysis of the president's budget that has become a justly respected document. Groups like Common Cause, a citizen lobby, and the Ralph Nader Center for Study of Responsive Law are devoted to a kind of government watchdog function, and their reports naturally become source of information on public problems. 
While admittedly not altruistic in their endeavors, many national interest groups also performs similar functions as they search for policies, problems, and events that may affect their clienteles. Finally, some groups can provide data on what problems the general public judges to be important at any one time.
Taken together these various sources suggest a number of issue-area categories, that is, broad classifications of "bundles of controversial public problems." As a minimum these would include: 
Issue-Areas for Public Policy Analysis
Relations with nations (individually and in alliances)
Security cooperation with other nations
Arms special dispositions and treaties
Human resources, including health, education, welfare and job training
Physical and natural resources
Social control and internal security
Source: Based on Stokey, E. Public Policy Analysis, Ob.Cit. p.10-12; and Jones, Ch. Study of Public Policy Analysis, Ob.Cit. p. 43.
National budgets in different nations reflect one catalog of needs and how those needs are interpreted as priorities. However, the accelerated growth of certain budget items, combined with a stagnating economy, has reduced the capacity of governments to respond to new problems. Some people, including many in the Reagan administration in United States, conclude that the biggest problem of all is the rejuvenation of the economy, and that can occur only with a reduction in government spending and influence -neoliberal social and economic perspective-.
Others doubt that this solution will work and call for increased government control of the economy -Keynesian, and Neokeynesian option-. It is apparent that the two groups are in agreement on one point at least: that certain major problems are not being solved by governments. Of both sides the budget is not the best inventory of major issue areas, a conclusion that has placed the budget front and center in the national policy-making system.
2.6. Issues and Events
What events have created the needs leading to major national issues? Again the discussion must be conducted at a general level and must be designed primarily to explain contemporary trends. According to Charles O. Jones, there are five broad categories of events influential in shaping issues: events of discovery, development, communication, conflict, and control. Broadly speaking, these events constitute what John Dewey calls the "human acts" that "have consequences upon others." They are the starting points for tracing the policy process for any one issue. 
3. The Policy Making Process
3.1. General Features
A common dictionary definition of process is "a series of actions or
operations definitely conducting to an end." Obviously
process is associated with all forms of social behavior.
Political scientists traditionally have been interested in institutional processed,
that is, those "series of actions or operations" associated with legislatures,
executives, bureaucracies, courts, political parties, and other political institutions. Many, if not most, political science courses focus
on these processes: what they are, how they work, what they produce, and how they connect. Generalizations are developed about such
processes as budget making, administrative rule making, congressional voting, priority
setting, making appointments, reorganization, and committee decision making. More often than not, these generalizations cut
across substantive issues. 
Focusing on group processes is also popular. In this approach it is assumed that groups are absolutely crucial in political decision making. One studies the role of interest groups but also looks for groups within political institutions. The latter groups may not always coincide with the organizational framework of the institution. 
The focus here is on public problems and how they are acted on in government. It is assumed that problems themselves help to shape the structure and organization of government, and that often cross-institutional and intergovernmental connections will emerge to treat these problems. Generalizations are developed about issues or issue areas as well as the activities associated with resolving them.
3.2. Conceptual Approaches to Study the Methodology of Policy Process
There are several conceptual process approaches to study policy making processes. They differ in terms of the focus of analysis and the nature of the generalizations. Examples of the more frequently used approaches are: a) focus on real social powers and institutions; b) formal elected officials as primary axis of representations; c) dynamics of different and relevant groups of pressure; d) historical social conditions and trend of political needs; and e) the external and internal political and economic conditions as social domestic factors. 
None of them is one more legitimate than the others; rather, each contributes to a fuller understanding of the others. Each is an effort to describe and analyze reality: for example, committees as institutional groups are real; interactions among outside formal groups are real; public problems are very real. Finally, each emphasis may reveal an aspect of the political or decision-making system that is obscured by the others.
These conceptual approaches need to deal with the concrete conditions in which a particular policy making process is carried out. For example, they must take into account who participates and interacts with whom in a particular matter. It may well be, for example, that not all members of a congressional committee participate in exploring solutions to a problem, whereas lobbyists, bureaucrats, and private consultants do. The student of group processes attempts to identify this cross-institutional participation and generalize about its nature. Various elite theories propose that decisions are actually make by small groups that may or may not communicate with their publics. In this view the group process is really an elite process. 
Some people are primarily interested in the substance of issues; that is, in the nature of the problems and how they can be solved. For example, they want to understand the essential elements of inflation, unemployment, or trade imbalances in order to identify alternative courses of action for solving these problems. Their expertise is related to these substantive issues, for example, as labor, economic, education, or trade specialists.
Many political scientists are more interested in process than substance. For them substance (e.g. inflation and actions to curb it) is merely a way to study process. Their expertise develops out of knowledge about the organization, routines, and decisions of government and other public agencies. 
3.3. Defining Policy
Those studying the policy process do not have the advantage of a common reference. A definition is required to determine what to look for in "policy". The definition I favor is offered by Heinz Eulau and Kenneth Prewitt: "Policy is defined as a "standing decision" characterized by behavioral consistency and repetitiveness on the part of both those who make it and those who abide by it. 
This definition leaves us with the problems of determining how long a decision must stand, what constitutes behavioral consistency and repetitiveness, and who actually constitutes the population of policy makers and policy abiders, but it does identify some of the components of public policy.
Here then are two broad uses of the term policy: one as a word substitute or shorthand where common understanding is assumed; another as a set of characteristics to be specified and then identified through research. Clearly the second is more applicable to the present objective. For the purpose here is to encourage study of public policy and how it is made. We do not plan to conduct research on policy questions as such. The plan is rather to provide a basis for understanding the "behavioral consistency and repetitiveness" associated with efforts in and through government to resolve public problems. Used in this way, policy is a highly dynamic term.
As Eulau and Prewitt point out, "What the observer sees when he identifies policy at any one point in time is at most a stage or phase in a sequence of events that constitute policy development." To put it another way, we freeze the action for purposes of analysis. Whatever we learn must be specified in terms of the questions we seek to answer, the time frame within which our research is conducted, and the institutional units being studied.
Therefore any reference to "defense policy," "farm policy," or "social security policy" should lead us to ask, What do you mean by that? Are you speaking of national goals? Current statutes? Recent decisions? Or are you characterizing certain behavioral consistencies by decision makers? The point of asking these questions is not to enforce one particular definition of the term policy, but rather to clarify meanings and thereby improve understanding.
One important observation is that, Eulau and Prewitt also observe that "policy is distinguished from policy goals, policy intentions, and policy choices." What this suggests is that it is helpful to distinguish the several components of public policy. For example:
a) Intentions: The true purposes of an action
b) Goals: The stated ends to be achieved
c) Plans or proposals: Specified means for achieving the goals
d) Programs: Authorized means for achieving goals
e) Decisions or choices: Specific actions taken to set goals, develop plans, implement and evaluate programs.
f) Effects: The measurable impacts of programs (intended and unintended; primary and secondary)
One can reasonably use the term policy as an adjective with each of these components, but it does become somewhat confusing if the term is used interchangeably with all of them. We should also note the more legal terms associated with public policy making: legislation, laws, statutes, executive orders, regulations, legal opinions. these too are often called policy. For our purposes, however, they are simply the formal ingredients or legal expressions of programs and decisions. 
3.4. A Policy Process Framework
The following table shows a synthesis of the main activities and particular questions often confronted in the policy making process, at its different levels of decisions.
Activities and Questions for Public Policy Analysis
Perception / definition
What is the problem related with the proposal?
How many people think it is an important problem?
How well organized and power have these people?
What is the access to decision makers?
How and how establishes the agenda topics?
What is the proposed solution?
Who supports the main decisions? Any groups of power?
What is the financial condition?
Who administers the budget?
Who judges the achievements and based on what criteria?
Adjustment / termination
What adjustments have been made and what adjustments it is possible to predict?
Source: Jones, Ch. Ob.Cit. p. 27-28; Dunn, W. Public Policy Analysis. (New Jersey: Prentice Hall, 1994). p. 15-19.
The policy activities listed can be grouped in sequence of government action. The first five are associated with getting the problem to government and the next three with direct action by the government to develop and fund a program. Implementation is really the government returning to the problem, and the last two activities (evaluation and adjustment/termination) can be thought of as returning the program to government (for review and possible change).
Each activity may also be thought of as yielding a product that often contributes to the next activity. For example, perception and definition can result in a clearly specified problem; formulation in a definite proposal or plan.
3.5. Theoretical Approaches to Study the Policy Making Process and the Political Foundations of Main Actors
Participants vary in how they view the policy process and in what they seek to gain from it. At a minimum we can identify rationalists, technicians, incrementalists, and reformists. All four types of actors will typically be involved in any complex issue. However, at any one time or for any one issue, one or more of the groups may dominate. The four types of participants vary in the roles they play in the policy process, the values they seek to promote, the source of goals for each, and their operating styles. 
"The main characteristic of rationalists is that they involve reasoned choices about the desirability of adopting different courses of action to resolve public problems." This process of reasoned choice 1) identifies the problem, 2) defines and ranks goals, 3) identifies all policy alternatives, 4) forecasts consequences of each alternative, 5) compares consequences in relationship with goals, and 6) chooses the best alternative. This approach is associated with the role of the planner and professional policy analyst, whose training stresses rational methods in treating public problems.
Often the methods themselves are valued by the rationalist and therefore are promoted. It is assumed that goals are discoverable in advance and that "perfect information" is available. The operating style tends to be that of the comprehensive planner; that is, one who seeks to analyze all aspects of the issue and test all possible alternatives by their effects and contribution to the stated goals. Most readers probably find this approach appealing. It strikes one as commonsensical to be as comprehensive as possible. Unfortunately, both institutional and political characteristics frequently interfere with the realization of so-called rational goals.
A technician is really a type of rationalist, one engaged in the specialized work associated with the several stages of decision making. Technicians may well have discretion, but only within a limited sphere. They normally work on projects that require their expertise but are defined by others. The role they play is that of the specialist of expert called in for a particular assignment. The values they promote are those associated with their professional training, for example, as engineers, physicists, immunologists, or statisticians. Goals are typically set by others, perhaps any of the other three types identified here (or a mix of them). the operating style of the technician tends to be abstracted from that on the rationalist (who tends to be comprehensive). The technician displays confidence within the limits of training and experience but considerable discomfort if called upon to make more extensive judgments. 
Charles Jones associates incrementalism with politicians in our policy system. Politicians tend to be critical of or impatient with planners and technicians, though, dependent on what they produce. Incrementalists doubt that comprehensiveness and rationality are possible in this most imperfect world. They see policy development and implementation as a "serial process of constant adjustment to the outcomes (proximate and long-range) of action."
For incrementalists, information and knowledge are never sufficient to produce a complete policy program. They tend to be satisfied with increments, with building on the base, with working at the margins. The values associated with this approach are those of the past or of the status quo. Policy for incrementalists tends to be a gradual unfolding. Goals emerge as a consequence of demands, either for doing something new or, more typically, for making adjustments in what is already on the books. Finally, the operating style of incrementalists is that of the bargainer-constantly hearing demands, testing intensities, and proposing compromises. 
Reformists are like incrementalists in accepting the limits of available information and knowledge in the policy process, but are quite different in the conclusions they draw. Incrementalists judge that these limits dictate great caution in making policy moves. As David Braybrooke and Charles Lindblom note, "Only those policies are considered whose known or expected consequences differ incrementally from the status quo."
This approach is much too conservative for reformists who, by nature, want to see social change. They would agree with David Easton that "we need to accept the validity of addressing ourselves directly to the problems of the day to obtain quick, short-run answers with the tools and generalizations currently available, however inadequate they may be." The emphasis is on acting now because of the urgency of problems. This is the approach taken by self-styled citizen lobbyists. The values are those related to social change, sometimes for its own sake but more often associated with the special interests of particular groups. Goals are set within the group by various processes, including the personal belief that the present outcomes of government action are just plain wrong. The operating style of reformists has become very activist, often involving demonstrations and confrontation.
Given the striking differences among these four types of participants it is not surprising that each group in highly critical of the others. It is alleged, for example, that rationalists simply do not understand human nature. Braybrooke and Lindblom state that the rationalist's "ideal is not adapted to man's limited problem-solving capacities." Technicians are criticized for their narrowness. Incrementalists rely too much on the status quo and fail to evaluate their own decisions. Reformists are indicted for their unrealistic demands and uncompromising nature.
Different eras do appear to evoke different perspectives: the incrementalism of the 1950s, the reformism of the 1960s and 1970s, the rationalism of the late 1970s and the early 1980s (particularly in energy, environmental, and economic planning). But in every era our politics is characterized by a mix of participants within and among the institutions. Thus each group is forced at some point to deal with or encounter the others. The product may favor one perspective at a given stage of the policy process, but the multiplicity of institutions, governments, and decision making insures a melding over time.
Four Perspectives in Public Policy Analysis
Roles Values Goals Style
Failure to acknowledge limits
Expert / Specialist
Training / Expertise
Set by others
Set by new demands
Citizen / Lobbyist
Set by substantive concerns
Source: Jones, Ch. Ob.Cit. p. 32.
4. Principal Models for Public Policy Analysis
4.1. General Considerations
The core decision in economics is "What do we want and what can we get?. Ordinarily we want more than we can get, and because our capabilities are limited and the resources available to us scarce, choices must be made among our competing desires. The Port Authority would like to expand airport operations and at the same time reduce noise levels. It cannot do both; as headlines testify, the choice is difficult. How choices should be made-the whole problem of allocating scarce resources among competing ends-is the stuff of economics and the subject of this book. 
In public policy analysis we focus on choices in the public sector, on how decisions should be made by governments at all levels and by nonprofit institutions. As we are by now all well aware, the government is not a business, and in many respects it cannot be run like a business. Its goals are different and it operates under different constraints. Yet the basic elements of good decisions are the same in all arenas, and the methods for making them set forth here are applicable for all decision makers, public and private.
Our starting point is a fundamental model of choice. We have seen that a model is a simplified representation of some aspect of the real world, a deliberate distillation of reality to extract the essential features of a situation. The fundamental choice model is particularly valuable because it offers a universal yet succinct way of looking at problems in terms of the two primary elements of any act of choice: 
1. The alternatives available to the decision maker; and
2. His preferences among these alternatives.
The model forces the decision maker to express the alternatives he faces and his preferences among them in comparable units. You will see from our examples that the alternatives may sometimes be described in tangible terms, actual outputs that can be seen and counted, such as electricity and water, or allergy tests and electrocardiograms. At other times the outputs of the alternative choices will be described in terms of intangible attributes such as intelligence and beauty, or taste and nutrition, or safety and speed. Some of these intangibles can be measured more or less objectively; others cannot. The model is flexible; it easily handles all types of attributes, whether described by hard numbers or paragraphs of prose, so long as the decision maker's preferences are expressed in the same terms as the alternatives.
In terms of alternatives available to the decision maker, the first element of the basic model describes the alternatives available to the decision maker. If this were a standard economics text, we would introduce you to apples and oranges and ask you to consider the plight of the grocery shopper who must allocate his fruit budget between those two goods. But this is a document about public decisions, so we ask you instead to play the part of a public official who must choose among several alternative dam projects. These projects are identical in every respect-costs, environmental consequences, and so on-except two: they produce different amounts of electric power and water for irrigation. In other words, the decision maker faces a certain number of alternative quantities of power and water. 
A main general concept about public policy analysis is the marginal analysis tool. This concept includes the discussion of marginal rates of transformation and substitution is only one example of the type of analysis that forms the core of traditional microeconomics theory. In a nutshell, in order to achieve an optimal result, the allocation of scarce resources among competing uses must satisfy certain marginal equalities. For example, the consumer should allocate his budget so that he gets the same satisfaction from the last dollar he spends on orange juice and the last dollar he spends on going to the ballet. And a rational consumer will do just that, even though he will rarely do so consciously. A farmer or the manager of a pencil factory should expand production just to the point where his last dollar of sales costs him exactly $1. Producing more diminishes his profit, producing less means that he forgoes some of the profit he might have reaped. Similarly, a public decision maker-a mayor, for example should allocate spending on park maintenance and on fire protection so that the last dollar spent on each is equally satisfying to the society he represents. 
The model of choice to develop public policy analysis requires that preferences be expressed in the same units as the outcomes of the various alternatives proposed. Thus, if the decision maker is offered a choice among assorted combinations of apples and oranges, his preferences must be expressed also in terms of apples and oranges. Conversely, if he is to choose a mix of strange fruit whose attributes are a mystery to him, although he knows his preferences for, say, vitamins and juiciness, the outcomes of the various possible choices must be expressed not as bundles of fruit but as combinations of these attributes. In other words, he must be able to measure these fruits in terms of the characteristics he understands, cares about, and can work with.
The following sections will address discussions concerning the most frequently models used to carry out public policy analysis.
4.2. Difference Equations
This method is more useful when the features of the phenomenon under study are quantitative variables. Difference equations have the significant advantage to allow us to take into account the dynamic change in the variables, and thus the possibility to identify possible trends of the variables.
4.2.1. A General Description and Illustrations
There are two ways we can represent dynamic processes. We can view things as changing continuously over
time, which is in fact generally the case, or we can break in on a process or system at
specified time intervals and see where things are.
Difference equations take the period-by-period or discrete approach: they relate the value of a variable in a given time period to its values in periods past. They are an essential feature of the financial world; indeed the compound interest model that we used is a simple difference equation:
S1 = (1 + r ) So
Here S1, the sum of money in a savings bank account at the end of a year, is related to the initial sum So; r is the rate of interest. For example, this equation is valid whether r is 5 percent, 7 percent, or 100 percent. Note the use of subscripts, numbers or letters written to the right of and a little below the symbol for the variable, to indicate the specific time at which a variable is being valued. They are typical of difference equations: using the variables So and S1 rather than completely different symbols such as A and B for the variables serves to remind us that we are talking about a particular chunk of money, even though the exact sum in question is different at different times. 
Listed below are a few illustrations of the many sorts of situations in which difference equation models are useful:
1. A couple wishes to set aside money to supplement Social Security when they retire in twenty years. They want to know what their savings will be when they retire if they invest $2000 per year at 7 percent interest, and how long those savings will last if after retirement they withdraw $5000 per year, continuing to earn 7 percent on the balance left in their account.
2. A school district has overcrowded classrooms. There is pressure to relieve this overcrowding, either by building a new school or by renting temporary facilities. In order to decide between these two alternatives, the school board needs projections of the school-age population in the district over the next two decades.
3. The president of a university is concerned about its ability to fund ongoing programs. He needs projections of income and expenses over the next 10 years to help him decide what policies to follow with respect to tuition, scholarship aid, and faculty hiring.
4. A state department of public health is considering a new program to detect and treat hypertensives. It has guesstimates of how many new hypertensives would be discovered every month, what proportion would then enter treatment, and what the attrition rate from the program would be. In order to put together a budget, the department needs estimates of the number of people in treatment during the first two years of the program.
5. The 1970 Clear Air Act mandates stepped reduction in the permissible level of pollutants emitted by new cars. The possibility of requiring the owners of older cars to add pollution control devices has been discussed. Given the rates at which older cars go out of service, how much difference would such a policy make in the total amount of auto emissions?
6. A mosquito control district is considering several alternative spraying programs, all of which have the same dollar cost. It needs a model of mosquito reproduction and of the effects of different spraying programs in order to determine the most effective plan. 
An extremely important aspect of difference equations is the choice of the appropriate time interval-the amount of time that elapses between time 0 and time 1-to use in a difference equation depends on the particular problem at hand. If we were examining the growth of a flu epidemic, for instance, days or weeks might be appropriate, whereas for the growth of world population we would be more likely to look at years or decades.
4.2.2. The General Form of a Difference Equation
Thus far our difference equations have modeled changes for specific periods of time, an initial period (0) and one period later (1). Usually we are more interested in a general statement that relates the value of the variable in any time period to its value in the preceding period. In the compound interest model, it would be useful to have an expression for Sn, the sum at the nth period, in terms of what S was in period (n-1). This of course offers greater flexibility in applying the formula. In this case it is clear what that formula must be; we simply write:
Sn = (1 + r ) Sn-1
For all n ³ 1
Where Sn-1 is the sum on deposit at the end of the (n-1) period. This equation is called the general form of the difference equation, because it holds in general and not just for specific values of n. It is a first-order difference equation because the variable Sn can be determined from its value in the one preceding period only. 
4.2.3. Difference Equations of Higher Order
Consider the following statement:
The Bonex Company prefers, earnings permitting, to pay dividends according to the following rule: The dividend on a share of common stock should be equal to 90 percent of last year's dividend plus one and one-half times the previous year's change in dividend.
This exercise is designed to illustrate a situation slightly more complicated than those previously encountered. Here we are concerned with a dividend, D, that depends on its value not only in the last period but also in the period before last. The general difference equation is:
This is presented only as an example, the difference equations in this case is of higher order, since the value of n must be equal or higher than 2.
4.2.4. The Use of Difference Equations in Modeling
Ordinarily we expect to see difference equations used as sub models, to predict parts of a system rather than the system as a whole. This is not to downgrade the importance of difference equations. Indeed, few people would view predictions about the future availability of oil as unimportant. In constructing their models, policy analysts rely on the existing age structure and predictions as to the future behavior of variables such as age-specific birth rates, death rates, migration rates, percent of the population gainfully employed, retirement age, wage rates, and the like, with difference equations playing a central role.
In this part we have discussed the use of difference equations primarily as a vehicle for introducing a variety of concepts and techniques. We must keep in mind that our main goal in developing these models is better predictions of the outcomes of policy alternatives.
4.3. Queuing or Ranking Method
4.3.1. General Features
Problems of public policy analysis in which it is possible to apply queuing or ranking methods, are characterized by the fact that a service facility is too limited to provide instantaneous service to all of its customers on all occasions. We do not want that people wait for services, but on the other hand, installing additional service capacity is too expensive. Queuing problems arise whenever a service facility is too limited to provide instantaneous service to all of its customers on all occasions. When the customers arrive more swiftly than they can be serviced, lines or queues will develop. Waiting is costly; frequently we would pay to avoid it.
It is, of course, impossible to eliminate waiting altogether; the costs would be prohibitive. A fire engine for every house in a rural area would protect against the one in a trillion possibility that all the engines will be needed at the same time, but it would obviously be undesirable. This is a straightforward matter of tradeoffs: the shorter we wish waiting time to be, the more facilities we must have available. To be more specific, the model can tell us how the waiting time for service will respond to the level of facilities that is made available. How much, for example, can the local Social Security office shorten clients' waiting times by opening another window? Occasionally it is also possible to change the time required for service; what would be the result of improving procedures so as to cut service time by two minutes?
Studying the way queues behave is important for public policy because the relationship between waiting times and service capacity is far from obvious, while the cost of providing extra capacity is likely to be large. Even simple models can help us grasp the essence of a great variety of real-world situations, and the results are often surprising.
4.3.2. Probabilistic Queuing Models
When customers arrive for service at a regular and predictable rate, as we assumed they did at the toll bridge, long lines may develop as a result of sheer numbers; expected arrivals may exceed the service capacity. A deterministic model that pays no attention to uncertainties can then predict directly the effects of adding or subtracting stations. Most queuing problems are not so tractable; customers usually arrive at irregular rates. Take the case of a facility that can serve up to 12 people per hour if they arrive at regular intervals. One day 3 people may arrive during the first hour and 18 during the next hour. As a result, people must queue up even when there is, on average, enough service capacity. In other words, a facility may be able on paper to serve a given number of customers per day provided they arrive regularly. But if they arrive irregularly, as a practical matter the facility will serve far fewer than its theoretical capacity. As the average number demanding service each day rises, waiting times will become intolerable.
In the real world, queuing systems are of course likely to be much more complex and to involve several different kinds of random events. In principle the problem is still likely to be straightforward, although programming the computer may become more of a chore. It's useful to keep in mind a checklist of the types of random events and complications that can occur in a queuing system. These fall under three main aspects:
1. Arrivals. Arrival intervals may be independent of one another, or the fact of one arrival may influence the probability as to when the next occurs. The latter will true whenever customers are likely to arrive in groups, as at an airport customs station. The arrivals in the Registry of Motor Vehicles example were independent, on the assumption that a driver's license expires on the holder's birthday. In contrast, 20 percent of the hypertension clinic patients arrived in groups of two or more, reflecting the greater likelihood that people would choose to make joint trips to the facility. It is also possible that the arrival pattern might vary with the time of day, or with the number of people waiting for service. So if we wished to make the model more sophisticated, we could relate patient arrival frequencies to the number of patients waiting. We might, for example, use one frequency distribution when fewer than 5 people are waiting, another when 5 to 10 are waiting, and so on. In this way we would recognize the influence of service characteristics on arrival behavior. It's more work to program the computer for the fancier model, but conceptually the problem is no more difficult.
2. Service times. Different people may require different service times. Further, the service time for on person may be affected by the number waiting of by the nature of the services rendered those who preceded him. Again, such variations on the basic model make the programming more burdensome, and it would be necessary to develop data on the frequency distribution for service times. But no fundamental changes in the model are required.
3. The "queue discipline." The way in which the queue forms and moves may not be a straightforward one right after the other straight line process. There may be more than one line; line jumping may be permitted; perhaps people who receive service must then get in another queue for a second service. With the hypertension clinic's lunch breaks, we introduced the possibility of a variable number of service stations. There may be bumping or other priority procedures.
Note that changes in the quality of service will show up as changes in queuing behavior only if arrival or service times of the queue discipline are affected. Service quality as such need not appear independently in the model.
4.4. Simulation and Non-Lineal Methods
4.4.1. General Features
The policy arena, the true world of affairs, is not always compatible to the straightforward use of analytic methods. The analyst may be confronted with problems that are too intricate to solve directly. He can write down equations that describe the workings of a system, and this may be a useful discipline in itself. But given the complex interactions within the system, even modern mathematical techniques are not powerful enough to predict the consequences of any policy choice.
In such a case, we can try to construct a laboratory model of the system. The model can be physical; frequently ship or plane designs are tested on scale models in water tanks or wind tunnels. It may be highly abstract; military strategies are sometimes tested by reproducing battlefield conditions on what is essentially a game board. If alternative predictions are made as to how individual encounters between elements of the opposing forces will be resolved, the board representation enables army strategists to consider the overall outcome of many simultaneous encounters. 
Models of this sort are also helpful to transportation planners who must predict traffic flows, say to determine the benefits of a new bypass. Behavioral equations are employed to predict , for instance, how motorists' decisions will respond to traffic density-how they will change the timing of their trips, or the routes, or the destinations. A simulation method thus attempts to reproduce a system in what is the equivalent of a laboratory setting, in many occasions we need to conclude using concepts of chaos theory in order to represent the main factors, the more important limitations concerning the phenomenon under study, and the more probable trends of results.
Sometimes we wish to examine the histories that may result from alternative policy choices. For example, suppose a number of different pollutants are discharged into a river at several places along it. A model can be constructed to relate water conditions at various points downstream to the levels of these discharges. This model of the river basin could then be used for studying the effects of regulatory discharge levels. Any number of policy choices in the form of possible combinations of discharge levels may be investigated, and their performance assessed.
At other times we wish to investigate the implications of changes in certain key parameters. A river, for example, has an extraordinary ability to cleanse itself-provided pollution does not exceed certain levels. Even though it is polluted over an upstream stretch, the river may be relatively free of pollution at its mouth. Perhaps the volume of municipal sewage discharges is critical for this regenerative capacity. 
Simulations directed to random situations, such as those usually encountered in queuing problems, generally run through a great number of histories to provide a feel for the frequency distribution of outcomes.
4.4.2. Macroeconomic Simulation
In the last quarter century, simulations of national economies and of the world economy have come into increasing prominence. These models use large numbers of data to predict the behavior of key variables in the economy-investment, consumption, employment, imports and exports, government expenditures, and the like-over the next few quarters or years. A typical model might relate consumption in year t, for example, to wages and profits in the same year, and investment in year t to profits in years t and (t-1). Government economists trying to determine the optimal level of government spending and corporate planners trying to determine the optimal level of investment rely on them. To a degree, the models build in an element of self-fulfillment as decision makers respond to their predictions. Similar macroeconomic models are now used to try to predict future world use of certain vital resources, especially oil. 
4.4.3. Simulation as an Analytic Tool
Analysts recognize that there are many problems in formulating informative simulations and usually employ them only as a last resort. The difficulties encountered in building the model can be formidable; frequently independent verification of the accuracy of the model is impossible. In addition, probabilistic output, the usual output of a simulation, is susceptible to misuse, particularly if some of the information is not presented.
For example, suppose the average epidemic for a population of 100 people turns out to be 5 cases. This average could have resulted from epidemic sizes of 4, 7, 3, 5, 6, and so on, year after year. Or it could conceivably conceal the fact that no epidemic occurs 19 years out of 20, but then everyone is laid low at once; the average epidemic is still 5 cases. Obviously this information could be misleading; as a precaution, the analyst should insist on seeing a sampling of complete runs as well as the final averages. Despite these risks, in many situations informative simulation is the appropriate recourse for the analyst. Used wisely, it is an indispensable tool for predicting the outcomes of alternative policies.
4.5. Markov Chains
Simple models sometimes yield compelling conclusions. Such models are worthy of study if their basic elements reappear in a variety of situations. Markov models are among these models; an understanding of them yields insights into a number of policy issues. Pollutants moving through the biosphere, mentally ill individuals moving from one level of functional capability to another, heroin users moving from addiction to treatment to abstention and back again-all can be illuminated by casting them in a Markov framework.
Consider the following situation,  which we will describe with the aid of a Markov model. New Kent has a labor force of 10,000 people. In any month, each of these 10,000 people is either employed (E) or unemployed (U). At present, 3000 are unemployed. As things now stand, 90 percent of those employed in one y ear are still employed the following year, while 40 percent of the unemployed find jobs and are employed in the next year. These proportions hold true year after year. New Kent's employment situation is summarized in the following table or matrix. This type of matrix is called a transition matrix because it describes how changes take place from one period to another.
E .90 .10
U .40 .60
E = employed
U = unemployed
The first row of numbers tells us what proportion of the people who are employed in the first period will still be employed in the next, and what proportion will be unemployed. Thus the .90 in row E, column E. means that of the people who are employed in the first period, .90 or 90 percent will be employed in the next period. The second row gives us the same information about those who are unemployed in the first period. We might also have labeled the two periods "y" and "y+1," since it is stipulated that the proportions don't change from year to year.
We could have used a set of difference equations to set forth the information contained in the transition matrix:
E2 = .90E1 + .40U1
U2 = .10E1 + .60U1
The main advantage of the matrix notation is its simplicity, in writing and especially in manipulation. This becomes much more important as the number of different categories increases.
The situation we have just examined is an example of a Markov system. In this case we have considered movements within an entire population, New Kent's labor force, from employed or unemployed in one period to employed or unemployed in the next period. When we observe the probabilistic movements of a single individual, the process is called a Markov chain. The arithmetic for the two situation is identical.
4.5.1. Markov Chains: An Example
Let's consider an individual-we'll call him Smith-who is either well (W) or sick (S). Moreover, if Smith is well one day, he has an 80 percent chance of being well the next day. If he is sick, he has a 50 percent chance of being well the next day. These probabilities depend only on his condition today, an assumption that is crucial; his previous history doesn't matter. Smith's health is completely described by the following transition matrix, which defines a Markov chain:
W .80 .20
S .50 .50
Customarily we assign a label, let us call it P, to this matrix and write it simply as
These probabilities for the state of Smith's health hold for any two consecutive periods.
4.5.2. Main Properties of a Transition Matrix
The main properties of a transition matrix that define a finite Markov chain, taking into account the aforementioned example are:
First, there must be a finite number of well-defined categories or states, such that the individual falls in one and only one state in each period; the mathematician's phrase is mutually exclusive and collectively exhaustive. This means that the system is closed-the individual always stays within it and does not move to some state outside the system, which is equivalent to stating that the numbers in each row of the matrix must add up to 1. Sometimes this inclusiveness requirement may be satisfied by enlarging the matrix, in other words by adding states so that all possibilities are accounted for. For example, suppose Smith, when he is well, has an 80 percent chance of remaining well and a 15 percent chance or being sick in the following period. He also has a 5 percent chance of dying and hence moving out of the two-state system. We may keep him in the system by adding "dead" as a third state.
A second property is that the probabilities in the transition matrix must be the same for any tow consecutive periods.
A third property is the so-called Markov condition: the probabilities must have no memory. It doesn't matter whether Smith was well or sick yesterday; the probability of his being well tomorrow depends only on how he is today. Suppose you find that the probability of his being well tomorrow, given that he is sick today, depends on how long he has been sick, and not just on whether he's well or sick in this period. Perhaps that probability is 50 percent if he has been sick one day, but only 30 percent if he has been sick longer. At first glance this presents insurmountable difficulties, but if only a few periods of history matter we can cope with the situation. In this particular set of circumstances, we replace the state "sick" with two states, "sick for one day" (S1) and "sick for two days or longer" (S2). The matrix Q would then represent a Markov chain:
W S1 S2
W .80 .20 0
Period 1 S1 .50 0 .50 = Q
S2 .30 0 .70
W = well
S1 = sick for one day
S2 = sick for two days or longer
If the number of states that the chain "remembers" is finite, it is possible to satisfy the Markov requirement by redefining the states in this manner.
A fourth property of a Markov chain is that time periods must be uniform in length. This may seem to be a superfluous requirement , as here they are automatically defined that way. But now and then it can give trouble. Generations, for example, are a very difficult time unit to work with. Moreover, with longer periods we have to pay attention to moves out of and back into a state within a single period. If these conditions-inclusive states, constant and memory-less probabilities, and uniform period lengths-are satisfied, then we have a Markov chain.
4.5.3. Regular, Absorbing, and Cyclical Chains
With regular Markov chains we may draw two conclusions about the long-run probabilities: (1) for the long run, the probability of being in a particular state approaches an equilibrium value that is independent of the state that the individual is in initially; (2) these equilibrium probabilities may be interpreted as the percent of time spent in each state over the very long run.
With absorbing chains, the equilibrium is frequently uninteresting. We are more likely to want to know how many periods an individual can be expected to spend in each state before he is absorbed, or how quickly he is likely to get trapped. If there is more than one absorbing state, we may be interested in knowing what the probability is that the individual lands in each.
The fully cyclical chains tell us no more than what is intuitively obvious. The rotation continues perpetually, and where you are at any particular time depends on where you started and how many periods have passed. with a partially cyclical chain, the individual will become trapped in the rotation eventually, but if we know where he started, we will at least be able to estimate the expected number of periods that will pass before he is caught up in the rotation.
Finally, it is important to specify how the long run is in term of Markov chains. The answer is, "It all depends." If there is very little movement between states and if there are a large number of states, the system will be slow to converge toward its equilibrium probabilities. For example, consider the following well-sick transition matrix:
W .99999 .00001
S .00003 .99997
W = well
The equilibrium probabilities for this system are .75 and .25 for well and sick. But this is scant comfort for a sick man, whose chances of getting well quickly are slim. Contrast this with our earlier well-sick matrix, where the long-run probabilities weren't quite as favorable (.714 and .286), but which converged to the equilibrium probabilities much more rapidly. If there are a large number of states, rather than just two, and period length is , say, one week, the system may take years to come close to equilibrium.
4.6. Cost-Benefit Method
Benefit-cost analysis is one of the principal analytical framework used to evaluate public expenditure decisions. This approach requires systematic enumeration of all benefits and all costs, tangible and intangible, whether readily quantifiable or difficult to measure, that will affect to all members of society if a particular project is adopted.
Benefit-cost analysis is sometimes described as the public household's version of a profit and loss statement. The analogy is strained; benefit-cost analysis examines all impacts of a project, internal and external, whereas a private business is presumed to look only at those that affect its own welfare, that its cost-benefit analysis must take into consideration externalities of a program, project, action or activity. 
The rationale for benefit-cost analysis is economic efficiency; it aims to ensure that resources are put to their most valuable use, including the significant possibility of leaving them in private hands. As a practical matter, benefit-cost analysis is most helpful in assessing well-defined projects. It would be of great assistance in choosing among alternative pollution-control systems for a particular river system, or in deciding whether road repairs in a community should be made with a new, more weather-resistant asphalt.
4.6.1. Cost-Benefit Analysis and Project Evaluations
For many analysts the core approach to benefit-cost analysis is positive and enthusiastic. But it would be unfair to praise the merits of project evaluation techniques without identifying their liabilities as well. Benefit-cost analysis is especially vulnerable to misapplication through carelessness, naiveté, or outright deception. The techniques are potentially dangerous to the extent that they convey an aura of precision and objectivity. Logically they can be no more precise than the assumptions and valuations that they employ; frequently, through the compounding of error, they may be less so. Deception is quite a different matter, involving submerged assumptions, unfairly chosen valuations, and purposeful misestimates. 
Bureaucratic agencies, for example, have powerful incentives to underestimate the costs of proposed projects. Any procedure for making policy choices, from divine guidance to computer algorithms, can be manipulated unfairly. Since project evaluation techniques have been widely used in the past, it is no surprise that they have also been misapplied in some circumstances. But they are also somewhat less susceptible to manipulation than the more informal approaches to decision making, for they are designed to highlight the ingredients that go into a choice. If presented in a professional manner, they lend themselves to the introduction of alternative sets of assumptions that enable the policy maker and his critics to see whether different conclusions would emerge. Thus an important contribution of benefit-cost analysis is the information it provides to the political process.
Project evaluation techniques have proven themselves in a variety of arenas. Recently, benefit-cost and cost-effectiveness studies have been applied to a wide range of medical procedures, helping doctors to determine, for example, which patients should be routinely screened for hypertension and how they should be treated.
4.6.2. The Procedure
In principle, the procedure followed in a benefit-cost analysis consists of five steps.
1. The project or projects to be analyzed are identified.
2. All the impacts, both favorable and unfavorable, present and future, on all of society are determined.
3. Values, usually in dollars, are assigned to these impacts. Favorable impacts will be registered as benefits, unfavorable ones as costs.
4. The net benefit (total benefit minus total cost) is calculated.
5. The choice is made. Criteria for making this decision are discussed in a later section of
Benefit-cost analysis is a tool, indeed a most sophisticated set of tools. The mechanical elements of benefit-cost analysis are decision rules to determine whether a project or projects should be undertaken, and if so at what scale of activity. These decision rules do not spring into existence by some magical process; rather they are carefully designed to ensure that public decisions accurately reflect what it is that the society wants to accomplish. 
The formal rules for benefit-cost analysis use as inputs estimates of the benefits and costs of the projects. But a knowledge of these rules is only the beginning of wisdom for the decision maker. He must confront such matters as:
1. Deciding which rule is appropriate for use in any particular circumstance;
2. Placing a complex problem in a benefit-cost framework;
3. Computing estimates of benefits and costs; and
4. Deciding at what level of detail and sophistication an analysis should be conducted.
4.7. Linear Programming
Of the various types of operations research, mathematical programming, and linear programming in particular, is the most highly developed and widely used. Programming is a means of optimizing; i.e., it is concerned with choosing the best levels for various activities in situations where these activities compete for scarce resources, or with choosing the minimum-cost method of producing required outputs.
There are situations where mathematical programming, whether used as a formal technique or as a guide to thinking, is enormously helpful. In some cases it can give us an outright solution, say an assignment of the police officers. In others it offers a solution only if we are able to make certain value judgments; perhaps we can assign weights to the cases the legal aid office might handle. At still other times no immediate answers are forthcoming, but greater insights may be gained by trying to structure the problem in a programming format by thinking carefully about the limited inputs available, the outputs desired, and the relationships among them. With such a problem we are still a long way from a decision, but at least we are asking better questions. 
4.7.1. The Elements of a Linear Programming Problem
The linear case assumes, first, that all relations between variables are proportional. If we double the inputs, we will double the outputs as well. Thus, if we need 1 widget and 2 gadgets to make 1 bobbin, we will need 2 widgets and 4 gadgets to make 2 bobbins. Economists refer to his property as "constant returns to scale." Second, we assume that all variable inputs and all outputs are infinitely divisible: fractional bobbins and gadgets cause us no problems. Third, we also assume that processes can be added together.
Anyone who understands linear programming can readily comprehend the basic ideas behind the more complicated types of mathematical programming. Our assumptions of constant returns, divisibility, and additivity are purely for expository reasons; none is critical for the kind of use that we wish to make of mathematical programming.
Political, economic, social, and institutional constraints usually place direct limits on levels at which the activities may be used. For example, in the diet problem we might wish to achieve a taste balance as well as a nutritional balance. A typical set of budget constraints for an institution might require that no program receive less than last year, nor more than a 10 percent increase over last year. Or it might specify that the ratio of the amounts expended on two programs remain within certain limits. In all these cases we are, in a sense, establishing subsidiary objectives for certain activities.
4.7.2. The Limitations of Linear Programming
First, some of the relationships may be nonlinear, and some of the variables may take only integral values.
Second, the constraints are such that no feasible solution yields acceptable score on the objective function. In that case, one possibility is merely too do the best we can with the onerous set of constraints. Alternatively, we can go back and see if the original problem can be re specified. Perhaps when the lack of acceptability of outcomes is pointed out to the individuals or agencies that imposed the constraints.
5. Public Policy Analysis: A General Methodology to Apply
The public decision maker has a difficult task.
He confronts all the problems of an individual choosing for himself and, because he
is acting on behalf of others, many additional problems as well. The environment in which he makes his choices is
restricted in a multitude of ways. Resources-whether
tax dollars, available space, or talented personnel-are scarce, and their effective
allocation may be constrained by political considerations or the limited capabilities of
sluggish bureaucracies. Nevertheless, the
essence of the public decision problem is that described in the model of choice. There we shoed, with the aid of a simple diagram,
how effective choices can be made when two essential ingredients can be identified: (1)
the alternatives that are available, including a description of the attributes, and (2)
the decision maker's preferences among alternative combinations of those attributes. General steps to apply the methodology for public
analysis is presented here.
The public decision maker has a difficult task. He confronts all the problems of an individual choosing for himself and, because he is acting on behalf of others, many additional problems as well. The environment in which he makes his choices is restricted in a multitude of ways. Resources-whether tax dollars, available space, or talented personnel-are scarce, and their effective allocation may be constrained by political considerations or the limited capabilities of sluggish bureaucracies. Nevertheless, the essence of the public decision problem is that described in the model of choice. There we shoed, with the aid of a simple diagram, how effective choices can be made when two essential ingredients can be identified: (1) the alternatives that are available, including a description of the attributes, and (2) the decision maker's preferences among alternative combinations of those attributes. General steps to apply the methodology for public analysis is presented here.
5.1. Establishing the Context
Usually the most frequently questions asked are: What is the underlying problem that must be dealt with? When contemplating action in any policy area, the first step is to determine whether and why there is a problem at all. In a market-oriented society, the question becomes: Is the market performing satisfactorily in this area, and if not, why not?
Considering the context and in social and economic terms, the range of possible explanations for unsatisfactory market performance are:
1. Information is not shared costlessly among all prospective participants in the market.
2. Transactions costs significantly impede the conduct of beneficial trades.
3. The relevant markets do not exist.
4. Some of the participants in the market exercise market power.
5. Externalities are present, so that the actions of one individual (whether a person or an organization) affect the welfare of another.
6. The commodity involved in the policy choice is a public good.
Under any of these conditions, or if a compelling distributional objective will be served, government intervention may be appropriate. A policy analysis is then merited. 
5.2. Determining Alternatives
With the context of the problem clearly in mind, we can proceed to the second step: What are the alternative courses of action? The alternatives for policy choice are often much broader than they first seem. Government intervention can take many forms; in any particular situation it is important to determine which type is most appropriate.
Can the alternative courses of action be designed so as to take advantage of additional information as it becomes available? A flexible decision process will enable the decision maker to change his course of action as he learns more about the real world in which he must operate. 
5.3. Establishing the Consequences
Once the problem is well-defined and the alternative courses of action delineated, the policy analyst must try to predict what will happen. What are the consequences of each of the alternative actions? Occasionally, mere reflection will be sufficient to trace the course from actions to outcomes. In some situations, the model will serve as little more than an intellectual guide.
Especially in this point we need to keep in mind the political and social role of actors and institutions. Since the public policy analysis is going to be useful as a tool, to produce results, the repercussions in form of predictable scenarios are crucial to consider. In this aspect the consideration of non lineal models are indispensable.
5.4. Valuing the Outcomes
An individual making a personal decision can define his preferences through introspection. The policy analyst's task is more complicated. Because one of his primary responsibilities is to help the decision maker define his preference function, a substantial part of this document has been devoted to methods for carrying out this task.
Some valuation problems, particularly those that involve intangibles, do not lend themselves to quantification. In such a case, analysis can address the issue descriptively. Perhaps a proposed welfare program is perceived as damaging the dignity of the recipients; that fact should be included in the analysis as one output of the program, just as the total dollar cost would be. Identifying the key intangibles is as much a part of the analyst's job. In any case, values must be assigned openly and explicitly.
Recognizing that an alternative will inevitably be superior with respect to certain objectives and inferior with respect to others, how should different combinations of valued objectives be compared with one another? Assigning values to specific attributes is only a small part of the difficulty in defining preferences. In almost every serious policy choice, painful tradeoffs must be made among valued attributes. 
5.5. Determining a Choice
When all aspects of the analysis are drawn together, what is the preferred course of action? The last step in policy analysis is a most satisfying one, for the sole objective of that analysis has been to make a better decision. Having struggled hard with defining the problem, specifying the objectives, constructing the necessary models, and valuing the alternative outcomes, the policy maker now pulls everything together to make the preferred choice. The situation may be so straightforward he can simply look at the consequences predicted for each alternative and select the one that is best. At the opposite extreme, it may be so complex that he will have to rely on a computer to keep track of what the options are, how the world will behave in response to the possible choices, and what his preferences are among possible outcomes.
One critical lesson is obvious:
the purpose of all this work is to help make
a better decision. Yet we all know that
countless policy studies have led nowhere. Sometimes
the fault lies with the public decision makers who don't bother to take advantage of
readily accessible information. More often,
it is the producers of the analysis who are to blame. Many policy analyses are gathering
dust because they are too long or too hard to understand.
Remember that the world will never beat a pathway to your door just because you
build a better model; analysis is worthless if it can't be communicated to others. The watchword, therefore, is: "Keep it
simple." The purpose is to inform the
decision maker, not to overwhelm him. Analysis should be presented in such a way that the
essential points can be readily grasped and, if necessary, debated.
One critical lesson is obvious: the purpose of all this work is to help make a better decision. Yet we all know that countless policy studies have led nowhere. Sometimes the fault lies with the public decision makers who don't bother to take advantage of readily accessible information. More often, it is the producers of the analysis who are to blame. Many policy analyses are gathering dust because they are too long or too hard to understand. Remember that the world will never beat a pathway to your door just because you build a better model; analysis is worthless if it can't be communicated to others. The watchword, therefore, is: "Keep it simple." The purpose is to inform the decision maker, not to overwhelm him. Analysis should be presented in such a way that the essential points can be readily grasped and, if necessary, debated.
The choice among competing policy alternatives in never easy, for the future is always uncertain and the inescapable tradeoffs painful. The methods set forth here cannot eliminate these difficulties, but they can help us manage them. By improving our ability to predict the consequences of alternative policies, and providing a framework for valuing those consequences, the techniques of policy analysis lead us toward better decisions.
Pittsburgh, July 2001
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Dewey, J. The Public and Its Problems. (New York: Holt and Winston Publish., 1987).
Dunn, W. Publlic Policy Analysis. (New Jersey: Prentice Hall, 1994).
Etzioni, A. The Active Society. (New York: Free Press, 1989).
Eulau, H; Prewitt, K. Labyrinths of Democracy. (Indianapolis: Merrill, 1989).
Frohok, M. Public Policy, Scope and Logic. (New Jersey: Prentice Hall, 1979).
Greenberger, M. Models in Policy Process. (New York: Russell Found., 1986).
Hochman, H. Redestribution through Public Choice. (New York: Columbia Univ. Press, 1976).
Jones, Ch. The Study of Public Policy. (Monterrey: Brooks, 1990).
Lasswell, H. A Preview of Policy Sciences. ( New York: Elsevier, 1992).
Nagel, S. Enclycopedia of Policy Studies. (New York: Marcel Dekker, 1991).
Ochaeta R. Procesos de Politica Publlica. (Guatemala: INAP, 1993).
Olson, M. The Logic of Collective Action. (Cambridge: Harvard University Press, 1991).
Orellana, E. Introduccion y Aplicaciones de la Teoria de Caos. (Mexico: LIMUSA, 1989).
Raymond A. Study of Policy Formation. (New York: Free Press, 1992).
Raymond, A. Public Policy Process. (New York: Free Press, 1988).
Rothenberg, J. The Measurement of Social Welfare. (New Jersey: Prentice-Hall, 1982).
Russell L. Ackoff and Maurice W. Sasieni, Fundamentals of Operations Research (New
Samayoa A. Aplicaciones del Analisis de Costo-Beneficio. (Guatemala, USAC, 1987).
Samuelson, P. Economics. (Boston: MIT, 1993).
Schultze, Ch. The Public Use of Private Interest. (Washington, D.C.: The Brookings Institution,
Smith, D. Pragmatism and the Group Theory of Politics. (New York: BCB, 1988).
Stokey, E. A Primer for Public Policy. (London: Norton, 1991).
Tobin, J. Introduccion a las Ecuaciones Diferenciales. (Bogota: McGraw-Hill, 1990).
Torres-Rivas Edelberto. Interpretacion
del Desarrollo Social Centroamericano. (San Jose: EDUCA,
Truman, D. The Govermental Process (New York: Knopf, 1992).
Weber, M. Economia y Sociedad. (Mexico: Fondo de Cultura Economica, 1991)
Wright, M. The Power Elite. (New York: Oxford University Press, 1989)
 See Weber, M. Economia y Sociedad. (Mexico: Fondo de Cultura Economica, 1991). p. 12-34.
 See Torres-Rivas Edelberto. Interpretacion del Desarrollo Social Centroamericano. (San Jose: EDUCA, 1988). p. 35-42.
 Raymond A. Study of Policy Formation. (New York: Free Press, 1992). p. 15-23.
 Ibid. p. 25.
 Dewey, J. The Public and Its Problems. (New York: Holt and Winston Publish., 1987) p. 17.
 Smith, D. Pragmatism and the Group Theory of Politics. (New York: BCB, 1988). p. 32.
 Samuelson, P. Economics. (Boston: MIT, 1993), p. 23-25; 45-53.
 Hochman, H. Redestribution through Public Choice. (New York: Columbia University Press, 1976). p. 34-36.
 Ibid. p. 44.
 Stokey, E. A Primer for Public Policy. (London: Norton, 1991). p. 12.
 Jones, Ch. The Study of Public Policy. (Monterrey: Brooks, 1990). p.17-19
 Ibid. p. 21
 Ibid. p. 43.
 Nagel, S. Enclycopedia of Policy Studies. (New York: Marcel Dekker, 1991) . p. 55.
 Jones, Ch. Ob.Cit. p. 54.
 Lasswell, H. A Preview of Policy Sciences. ( New York: Elsevier, 1992), p. 54-58.
 Truman, D. The Govermental Process (New York: Knopf, 1992), p. 66.
 Ochaeta R. Procesos de Politica Publlica. (Guatemala: Instituto Nacional de Administracion Publica, 1993), p. 45-48.
 Wright, M. The Power Elite. (New York: Oxford University Press, 1989)
 Ochaeta R. Ob. Cit. p. 71
 Eulau, H; Prewitt, K. Labyrinths of Democracy. (Indianapolis: Merrill, 1989). p. 41.
 Ibid. p. 473.
 Stokey, E. Ob. Cit. 11.
 Jones, Ch. Ob. Cit. p. 30-33.
 Dunn, W. Publlic Policy Analysis. (New Jersey: Prentice Hall, 1994). p. 226.
 Frohok, M. Public Policy, Scope and Logic. (New Jersey: Prentice Hall, 1979). p. 45.
Jones, Ch. Ob.Cit. p. 30-31.
Ibid. p. 31.
 Etzioni, A. The Active Society. (New York: Free Press, 1989). Chapter 12.
Braybrooke, D. A Strategy of Decision. (New York: Free Press, 1983). p. 77-85
Ibid. p. 87.
 See Raymond, B. The Study of Policy Formation. (New York: Free Press, 1988).
 Stokey, E. Ob. Cit. p. 26-28.
 Ibid. p. 31.
 Olson, M. The Logic of Collective Action. (Cambridge: Harvard University Press, 1991). p.55.
 Stokey E. Ob. Cit. p. 36.
 Correa, H. Multivariate Analysis. (Pittsburgh: GSPIA, 1994). p. 18-23.
 Stokey, E. Ob.Cit.p. 48-49.
 Ibid. p. 50.
 Schultze, Ch. The Public Use of Private Interest. (Washington, D.C.: The Brookings Institution, 1992). p.33.
 Ibid. p. 42.
 Tobin, J. Introduccion a las Ecuaciones Diferenciales. (Bogota: McGraw-Hill, 1990). p. 23-34.
 Stankey, E. Ob.Cit. p. 76.
 Ibid. 80-81.
 See for example, Russell L. Ackoff and Maurice W. Sasieni, Fundamentals of Operations Research (New York:Wiley, 1968).
 Orellana, E. Introduccion y Aplicaciones de la Teoria de Caos. (Mexico: LIMUSA, 1989). p.18-24.
 Ibid. p. 33.
 Aguilar, M. Tratado de Economia. (Mexico: Aguilar Eds., 1987).p.57.
 Stokey, E. Ob.Cit.p.97.
 Ibid. p. 101.
 Ibid.p. 104-105; Orellana, E. Ob.Cit. p. 65.; and Tobin, J. Ob.Cit.p.88.
 Stakey, E. Ob.Cit. p.107.
 Greenberger, M. Models in Policy Process. (New York: Russell Found., 1986).
 Stakey, E. Ob. Cit. p.156.
 Samayoa A. Aplicaciones del Analisis de Costo-Beneficio. (Guatemala, USAC, 1987).p.43-47
 Stakey, E. Ob.Cit. p.154.
Ibid. p. 156.
 Jones, Ch. Ob.Cit. p. 233-238; Stakey, E. Ob.Cit. p.321.
 Jones, Ch. Ob.Cit. p. 239.
 Stakey, Ob.Cit. p.324.
 Ibid, p. 325.; and Rothenberg, J. The Measurement of Social Welfare. (New Jersey: Prentice-Hall, 1982).p.56.
 Stakey, Ob.Cit. p.327-329.
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