The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities."

I. Until about a dozen years ago, the economic analysis of the relationship between political preferences and political demands was a rather straightforward, if dull, subject. The most common assumption was that the only political instrument available to citizens was the vote. Given this assumption, the analyst could express the outcome of the voting process in one of two ways. One possibility was to make the heroic assumptions necessary to obtain the median voter theorem, in which case, the political demands of the citizenry are simply the preferences of the median voter. The alternative was to make Arrow's Impossibility Theorem in which case even though individual preferences are well ordered, no collective preference function exists. On either of these approaches, institutions such as interest groups, political parties, or the structures ofpolitical representation played no role in the analysis. The work of "Chicago" scholars especially George Stigler, Gary Becker and Sam Peltzman took a different approach and emphasized the importanceoforganizationinmakingpoliticaldemandseffective, shifting thefocus from voting topolitical "pressure" byinterestgroups. However, in these models, voting as an instrument of political action simply disappears and the relationship between interest group pressures and electoral processes has never been clarified.

G. Galeotti* and M. Marrelli** *Universita di Perugia **Universita di Napoli 1. The economic analysis of optimal taxation has permitted considerable steps to be taken towards the understanding of a number of problems: the appropriate degree of progression, the balance between different taxes, the equity-efficiency trade-off etc .. Though at times considered as abstract and of little use in policy design, the issues it addresses are real ones and very much on the agenda of many countries. As usual in scientific debate, criticisms have contributed to the correct understanding of the theoretical problems involved and made clear that, at the present state of the art, definitive conclusions may be premature. A first well-taken criticism addresses the assumption, underlying optimal taxation models, of a competitive economy with perfect information on the part of individual agents and full market clearing. Once we leave the Arrow-Debreu world, it is no longer necessarily the case that taxes and transfers introduce distortions on otherwise efficient allocations.

I. Until about a dozen years ago, the economic analysis of the relationship between political preferences and political demands was a rather straightforward, if dull, subject. The most common assumption was that the only political instrument available to citizens was the vote. Given this assumption, the analyst could express the outcome of the voting process in one of two ways. One possibility was to make the heroic assumptions necessary to obtain the median voter theorem, in which case, the political demands of the citizenry are simply the preferences of the median voter. The alternative was to make Arrow's Impossibility Theorem in which case even though individual preferences are well ordered, no collective preference function exists. On either of these approaches, institutions such as interest groups, political parties, or the structures ofpolitical representation played no role in the analysis. The work of "Chicago" scholars especially George Stigler, Gary Becker and Sam Peltzman took a different approach and emphasized the importanceoforganizationinmakingpoliticaldemandseffective, shifting thefocus from voting topolitical "pressure" byinterestgroups. However, in these models, voting as an instrument of political action simply disappears and the relationship between interest group pressures and electoral processes has never been clarified.

P. de Bernardis, S. Masi , G. Moreno Dipartimento di Fisica, Universita' "La Sapienza" 00184 Roma Italy ABSTRACT. Anisotropy measurement techniques and results are reviewed, with special attention given to experimental problems. The cosmological relevance of the dipole anisotropy, the only anisotropy truly detected in the Cosmic Background Radiation, is discussed. 1. INTRODUCTION Anisotropy of the Cosmic Background Radiation at 2.7 K (CBR hereafter) is a cosmological topic with a wide range of applications. In order to define anisotropy let us consider fig. 1 a, where the celestial sphere is shown with two beams A and B, with beamwidth 0 and angular separation e. We define the anisotropy of CBR at angular scale e in terms of the difference i'2,1 between the CBR flux I(ex,u) measured in the two beams. At small angular scales (e ) a "stochastic" approach is preferred, and the anisotropy is defined as .cJ I = GBP (1) I e where the brackets indicate averages over the whole celestial sphere. At large angular scales e>l a deterministic approach is preferred, and the CBR flux I(ex, S) is expressed as a sum of spherical harmonics (2) I (ex, S) = I ~ aIm Y (ex, S) lm I,m The alm coefficients give the dipole, quadrupole and higher order components of the anisotropy. 257 P. Galeotti and D. N. Schramm (eds.), Gauge Theory and the Early Universe, 257-282.

This volwne is the proceedings of the third school in particle astrophysics that Schramm and Galeotti have organized at Erice. The focus of thirs third school was the Generation of Cosmological Large-Scale Structure. It was held in November of 1996. The fIrst school in the series was on "Gauge Theory and the Early Universe" in May 1986, the second was on "Dark Matter in the Universe" in May 1988. All three schools have been successful under the auspices of the NATO Advanced Study Institute. This volume is thus the third in the series of the proceedings of these schools. The choice of the topic for this third school was natural, since the problem of generating a large-scale structure has become the most pressing problem in cosmology today. In particular, it is this generation of structure that is the interface between astronomical observations and particle models for the early universe. To date, all models for generating structures inevitably require new fundamental physics beyond the standard, SU x SU X U , model of high energy physics. The 3 2 I seeds for generating structures usually invoke unifIcation physics, and the matter needed to clump and form them seems to require particle properties that have not been seen in laboratories to date.

The second Erice course in the school of Particle-Astrophysics was held in May, 1988. The topic choosen was Dark Matter. This is one of the most exciting top ics at the interface of particle physics and astrophysics. It is developing rapidly now due to a coming together not only of the theoretical concepts from the early universe with the theoretical concepts of galaxy formation, but also the coming to gether of the theorists, experimentalists and observers. It is with Dark Matter, the combined interrelated topics of galaxy formation and the generation of large scale structure that we see a confrontation of the exotic ideas from the early universe, such as phase transitions and unification, coming face to face with the realities of traditional observational cosmology. These realities have recently been heightened by the tremendous number of new observations, demonstrating that large scale structure of the universe is far more complex than anybody had suspected. In particular, we now see large scale foam, apparent large scale velocity fields, indicating devations from the Hubble flow, large scales of the order 100 Mpc, and galaxy formation occurring at high red shifts much greater than unity. We also see an apparent correlation of clusters of galaxies that may even exceed the c- relation of galaxies despite their being on much larger scales with lower average densities."

I. The concept of competition played a central role in the very first attempts to apply the tools of economics to the analysis of politics. Adopting Hotelling's (1929) industrial organization model of imperfect competition in markets in which space has a predominant role, Downs (1957), following on some perceptive insights of Schumpeter (1942), was able to formulate a model of electoral competition in which political parties, seeking the support of citizens, compete against each other in offering policies designed to elicit their vote. Downs' model and the numerous variants to which it gave birth soon became the major component of what was to become Public Choice Theory. The enormous efforts of the last 30 years devoted to modelling electoral competition have helped improve our understanding of politics and have contributed a basic element that undoubtedly will remain essential to any reasonably complete theory of politics. But whatever may have been early expectations, it is now clear that electoral competition will only be one such element. More recently, the idea of competition has been used to model interest-group behavior. Becker (1983), building on earlier work by Bentley (1908), Truman (1958), Olson (1965), Stigler (1971) and Peltzman (1976), applied the Public Finance analysis of the excess-burden of taxes and subsidies - to which, incidentally, Hotelling (1938) had made pioneering contribution- to produce a model in which competition between interest groups determines an equilibrium distribution of income.

G. Galeotti* and M. Marrelli** *Universita di Perugia **Universita di Napoli 1. The economic analysis of optimal taxation has permitted considerable steps to be taken towards the understanding of a number of problems: the appropriate degree of progression, the balance between different taxes, the equity-efficiency trade-off etc .. Though at times considered as abstract and of little use in policy design, the issues it addresses are real ones and very much on the agenda of many countries. As usual in scientific debate, criticisms have contributed to the correct understanding of the theoretical problems involved and made clear that, at the present state of the art, definitive conclusions may be premature. A first well-taken criticism addresses the assumption, underlying optimal taxation models, of a competitive economy with perfect information on the part of individual agents and full market clearing. Once we leave the Arrow-Debreu world, it is no longer necessarily the case that taxes and transfers introduce distortions on otherwise efficient allocations.