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This paper illustrates the use of probability models to study properties of voting rules. In particular, a simple occupancy distribution and its limiting Dlrichlet form are introduced, corresponding to simplifying assumptions about voters' preferences. We use as illustrations the occurrence probability of the Condorcet Paradox, a vintage problem in social choice theory, along with the related concept of Condorcet efficiency, a measure of goodness for voting rules. Further examples include properties of a lottery rule and the vulnerability of certain voting rules to strategic manipulation. Prospects for future work are indicated.

Looks at wages and employment, income distribution, benefits from government expenditure. Also discusses urbanisation and the spatial distribution of economic activity. (SJO)

Since the early 1970s, the South African economy has undergone fundamental structural change with major implications for development prospects, and for the trickle down of the benefits of economic growth. It is argued that a declaration of economic growth, a shift in the balance of power, especially economic power, in South African society and a political crisis, reflecting recognition of the insustainability of the apartheid paradigm were mainly responsible for creating such structural changes in South African economic life. (DÜI-Sen)

THIS ESSAY DISCUSSES THE TWO BASIC MODELS, WHICH ARE WELL KNOWN IN STATISTCAL PHYSICS AND CLASSICAL PROBABILITY UNDER THE NAMES MAXWELL-BOLZMANN AND BOSE-EINSTEIN, RESPECTIVELY. FOR THE CASE OF THREE ALTERNATIVES OR CANDIDATES, WE SHOW IN DETAIL BY MEANS OF EXACT AND ASYMPTOTIC FORMULAS HOW THE TWO MODELS DIFFER WITH RESPECT TO PARADOX PROBABILITIES. IN A SEPARATE SECTION, WE DISCUSS THE CASE OF FOUR ALTERNATIVES. AS A BY-PRODUCT OF OUR ANALYSIS, WE SHOW THAT, CONTRARY TO GEHRLEIN AND FISHBURN'S (1976) CLAIM, IT IS NOT POSSIBLE TO USE MAY'S (1974) CONVENIENT FORMULA FOR COMPUTING PARADOX PROBABILITIES IF THE VOTERS ARE ANONYMOUS.

Reactive sputtering processes are quite complex processes and therefore difficult to understand in detail. However, a number of attempts to clearify the behaviour of reactive sputtering of oxides and nitrides have been made. Several process modelling results for such processes have been published that reasonable well mirrors the actual experimental findings. All of these models indicate that the processes normally exhibit hysteresis effects and that the oxides/nitrides will saturate at the stoichiometric compound values. We therefore call these processes saturated reactive sputtering processes. Carrying out reactive sputtering in a hydrocarbon gas like CH4 instead of in oxygen or nitrogen cannot be described with the previously suggested models for oxide or nitride formations. Decomposition of the CH4 molecule in the plasma may result both in carbide formation with the target metal as well as plasma deposited carbon. Depending on the supply of the CH4 the deposited film composition may vary from 0 to 100% of carbon. In the extreme case of very high supply of CH4 a pure carbon film will be deposited. We expect that similar behaviour will be found when carrying out reactive sputtering in other solid material containing gases like e.g. silane or diborane. We have chosen to call such processes non-saturated reactive sputtering processes. In order to understand the behaviour of non-saturated reactive sputtering processes we have developed a new model that enables the user to find the response to individual processing parameters and thus obtain a tool for process optimization. In order to limit the number of parameters our model is outlined for reactive sputtering of Ti in a mixture of argon and CH4. In this article we report that the simulation results reasonable well correlate with our experimental findings. ; Funding Agencies|Carl Tryggers Foundation [CTS 17:336, CTS 15:219, CTS 14:431]; Swedish Government Strategic Research Area in Materials Science on Advanced Functional Materials at Linkoping University (Faculty Grant SFO-Mat-LiU) [2009-00971]; Knut and Alice Wallenberg FoundationKnut & Alice Wallenberg Foundation [KAW2016.0358]; Swedish Research Council VR Grant [2018-03957]; VINNOVA GrantVinnova [2018-04290]; Carl Tryggers Stiftelse [CTS 17:166]