Now that we know the basic properties of stars, we look at how the laws of physics determine those properties, and then how stars change with time – how they evolve. Stars go through a recurring full life cycle. They are born, they live through middle age, and they die. In their death, they distribute material into interstellar space to be incorporated into the next generation of stars.

In describing the life cycle, we can start anywhere in the process. In Chapter 9, we discuss the most stable part of their life cycle, life on the main sequence – stellar middle age. In Chapters 10, 11 and 12 we will look at the deaths of different types of stars. After discussing the interstellar medium in Chapter 14, we will look at star formation in Chapter 15.

Brightness of starlight

When we look at the sky, we note that some stars appear brighter than others. At this point we are not concerned with what causes these brightness differences. (They may result from stars actually having different power outputs, or from stars being at different distances.) All we know at first glance is that stars appear to have different brightnesses.

We would like to have some way of quantifying the observed brightnesses of stars. When we speak loosely of brightness, we are really talking about the energy flux, f, which is the energy per unit area per unit time received from the star. This can be measured with current instruments (as we will discuss in Chapter 4). However, the study of stellar brightness started long before such instruments, or even telescopes, were available. Ancient astronomers made naked eye estimates of brightness. Hipparchus, the Greek astronomer, and later Ptolemy, a Greek living in Alexandria, Egypt, around 150 BC, divided stars into six classes of brightness. These classes were called magnitudes. This was an ordinal arrangement, with first-magnitude stars being the brightest and sixth-magnitude stars being the faintest.

When quantitative measurements were made, it was found that each jump of one magnitude corresponded to a fixed flux ratio, not a flux difference. Because of this, the magnitude scale is essentially a logarithmic one. This is not too surprising, since the eye is approximately logarithmic in its response to light.

Aristotle, observing the Greeks in the fourth century b.c., thought that man's natural proclivities were toward discourse and political activity. Adam Smith, observing the Scots in the eighteenth century a.d., saw instead a propensity to engage in economic exchange. From the observations of these two intellectual giants, two separate fields in the social sciences have developed: the science of politics and the science of economics.

Traditionally, these two fields have been separated by the types of questions they ask, the assumptions they make about individual motivation, and the methodologies they employ. Political science has studied man's behavior in the public arena; economics has studied man in the marketplace. Political science has often assumed that political man pursues the public interest.

The Bergson-Samuelson SWF has been constructed analogously to the individual's utility function. Just as the individual chooses bundles of commodities to maximize his utility, society must choose an allocation of commodities across individuals to maximize its welfare. That consumers make choices to maximize their utility follows almost tautologically from the definition of rationality. In extending the idea of maximizing an objective function to the level of society, however, more is involved than just rationality. Embedded in the characteristics of the welfare function and the nature of the data fed into it are the value judgments that give the SWF its normative content, as the discussions of Bergson (1938) and Samuelson (1947, ch. 8) make clear.

An alternative way of analyzing individual behavior from assuming that individuals maximize their utility is to assume various postulates about individual rationality that suffice to define a preference ordering, and allow one to predict which bundle an individual will choose from any environment. Again by analogy, one can make various postulates about social decision making and analyze society's decisions in terms of social preference orderings.

Two views of representation

Several alternatives to the majority rule have been proposed down through the years. Three of the newest and most complicated of these are presented in Chapter 8. Here we discuss some of the simpler proposals.

These voting procedures are usually not considered a means of revealing preferences on a public good issue, but a means of choosing a candidate for a given office. All issues cannot be chosen simultaneously. Only one of them can be. Although such choices are perhaps most easily envisaged in terms of a list of candidates for a vacant public office, the procedures might be thought of as being applied to a choice from among any set of mutually exclusive alternatives – such as points along the Pareto-possibility frontier.

The alternative voting procedures defined

In Part III we examine the properties of the different institutions of representative government that have been devised to supplement or replace direct democracy as a means of representing individual preferences. We begin with the United States's contribution to the evolution of representative government – federalism – because it is in some ways related to the theory of clubs reviewed in the preceding chapter.

Majority rule and redistribution

As Chapter 4 indicated, a committee concerned only with providing public goods and correcting for externalities might nevertheless choose as its voting rule the simple majority rule, if it placed enough weight on saving time. But speed is not the only property that majority rule possesses. Indeed, once issues can pass with less than unanimous agreement, the distinction between allocative efficiency and redistribution becomes blurred. Some individuals are inevitably worse off under the chosen outcome than they would be were some other outcome selected, and there is in effect a redistribution from those who are worse off because the issue has passed to those who are better off.

To see this point more clearly, consider Figure 5.1. The ordinal utilities of two groups of voters, the rich and the poor, are depicted on the vertical and horizontal axes. All of the members of both groups are assumed to have identical preference functions. In the absence of the provision of any public good, representative individuals from each group experience utility levels represented by S and T. The point of initial endowment on the Pareto-possibility frontier with only private good production is E. The provision of the public good can by assumption improve the utilities of both individuals.

With large numbers of voters and issues, direct democracy is impossible. Even in polities sufficiently small so that all individuals can actually come together to debate and decide issues – say, a polity of 500 – it is impossible for all individuals to present their own views, even rather briefly, on every issue. Thus the “chairman's problem” is to select individuals to represent the various positions most members of the polity are likely to hold (de Jouvenal, 1961). When the polity is too large to assemble together, representatives must be selected by some means.

The public choice literature has focused on three aspects of representative democracy: the behavior of representatives both during the campaign to be elected and while in office; the behavior of voters in choosing representatives; and the characteristics of the outcomes under representative democracy. The public choice approach assumes that representatives, like voters, are rational economic actors bent on maximizing their utilities. Although it is natural to assume that voters' utilities are functions of the baskets of public goods and services they consume, the “natural assumption” concerning what maximizes a representative's utility is not as easily made.

In this part of the book we present four applications of the public choice approach to explaining real-world phenomena. The first application tries to explain the macroeconomic policies of governments. To what extent are these determined by the competitive struggle for votes? To what extent do voters take into account the macroeconomic performance of a government when deciding how to vote? These questions have elicited a variety of theoretical models to explain governmental macroeconomic policies and a gigantic number of empirical studies. Indeed, probably no other area of public choice has witnessed as much empirical testing of its propositions as this area of politico-macroeconomic models. Alas, as too often happens with empirical work, not all authors reach the same conclusions as to what “the data show,” and the literature is therefore filled with often spirited exchanges. We shall not attempt to resolve all of the outstanding disagreements, but will try instead to give the reader a feel for the nature of the debate on various issues and the weight of the empirical support on each side of a question. We begin with the question that Harold Wilson obviously considered an established fact. Does the state of the economy affect how voters vote?

In Chapter 26 we illustrated why individuals might choose to define certain rights to act in the constitution. The existence of these sorts of constitutionally protected rights is often regarded as an essential prerequisite for a free society. Such rights protect the liberty of all citizens and are associated with classic definitions of liberalism as put forward by John Stuart Mill (1859). In a short note published in 1970, Nobel prize-winner Amartya Sen (1970b) explored the notion of liberalism from a public/social choice perspective. This note proved yet another impossibility theorem of the Arrow variety, and precipitated a lengthy and often vigorous debate over both the implications of the theorem and the concept of liberalism itself.

In the previous chapter we documented how governments have grown around the world – until in Europe; they now generally absorb half the national income or more. What have been the consequences of this growth for the welfare of the citizens of these countries? What have been the consequences for the economic performance of the countries? The first question is, of course, the most relevant one. Since the end of World War II, the United States has spent over $8 trillion on defense. If these expenditures prevented a third world war, led to the collapse of Communism in East Europe and the Soviet Union, and thereby preserved democracy and freedom in the West, most Americans would probably say that the money was well spent. But if the same events would have transpired if the United States had spent only a tenth as much on defense, then more than $7 trillion would have been wasted, and Americans are that much worse off as a result.

The very “nonmarket” nature of many of the goods and services government supplies makes it difficult to measure their effects on welfare.

Public goods and prisoners' dilemmas

Probably the most important accomplishment of economics is the demonstration that individuals with purely selfish motives can mutually benefit from exchange. If A raises cattle and B corn, both may improve their welfare by exchanging cattle for corn. With the help of the price system, the process can be extended to accommodate a wide variety of goods and services.

Although often depicted as the perfect example of the beneficial outcome of purely private, individualistic activity in the absence of government, the invisible hand theorem presumes a system of collective choice comparable in sophistication and complexity to the market system it governs. For the choices facing A and B are not merely to trade or not, as implicitly suggested.

The cycling problem has haunted the public choice literature since its inception. Cycling introduces a degree of indeterminacy and inconsistency into the political process that hampers the observer's ability to predict outcomes, and clouds the normative properties of the outcomes achieved. The median voter theorem offers a way out of this morass of indeterminateness, a way out that numerous empirically minded researchers have seized. But the median voter equilibrium remains an “artifact” of the assumption that issue spaces have a single dimension (Hinich, 1977). If candidates can compete along two or more dimensions, the equilibrium disappears and with it the predictive power of the econometric models that rely on this equilibrium concept.