“The Arrow impossibility theorem and its implications for voting and elections”

Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics, widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions, explain its meaning, explore some of the solutions available to escape its predictions and finally discuss its implications for political voting and elections. I will begin by giving some definitions and presenting the fundamental issue of social choice theory, consisting of the identification of an “ideal” device for preference aggregation, capable of converting individual rankings into collective ones, reflecting each individual’s preference into an optimal societal choice.

Given a finite set of voters having to choose between a finite set of candidates, we call a voting system the function taking as input the voting preferences of each voter and returning as output a collectively valid ranking of the candidates. Majority voting is the voting system requiring that given two alternative options X and Y, X is preferred to Y by the group if the number of group members prefering X to Y exceeds that of members prefering Y to X. When group preferences are rational and transitive, for every pairwise comparison between two options, the group-wide valid outcome obtained applying majority voting is a unique winning alternative, which is said to be the “Condorcet winner”. Sometimes though, group preferences are not rational and for each pairwise comparison a different winner emerges. In such case there is said to be a cycling majority and the situation represents a “Condorcet paradox”.

Named after the distinguished economist and nobel laureate Kenneth Arrow, the “Arrow Impossibility Theorem” was first proposed and demonstrated in his book “Social Choice and Individual Values”, published in 1951. The...

...Courtney Thompson
The Impossibility of Social Choice
Introduction
Social choice theory depends on individual preferences. Kenneth Arrow wrote a book exploring the properties of social choice functions. This book focuses on problems of aggregating individual preferences to maximize social choice functions, or to satisfy some kind of normative criteria given the preferences of the individual voters. This research on optimal methods of aggregation has spurred...

...Original year 11 Advanced English short story written by Aisha Akhtar - copyright users will face severe consequences
The Wrong Arrow (c)
That’s weird thought cupid, ‘I’ve never hit the wrong person like that before’, he sat on a fluffy white cloud and stared down at the world. ‘How’, he thought with a bedazzled look on his face, ‘I was concentrating’. He slightly shuddered and squared his shoulders in an attempt to pull himself back together. ‘Hmm, better go talk to mom...

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Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two...

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Arrow Electonics - distributor of electronic components.
The thing
They recently adquired Eagle semiconductor division, and in the negoatiation they made a deal that Eagle will keep its autonomy when it comes to management.
Concerns to this deal: low inventory accuracy levels reported for Eagle warehouses. (Niveles de precision baja de inventario)
Decicions: allow them to keep operating with several regional warehouses or move the inventory to Arrow´s large...

...bernoulli's theorem
ABSTRACT / SUMMARY
The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus, F1-15. In this experiment, the pressure...

...BINOMIAL THEOREM :
AKSHAY MISHRA
XI A , K V 2 , GWALIOR
In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc, where the coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial...

...The Coase Theorem
In “The Problem of Social Cost,” Ronald Coase introduced a different way of thinking about externalities, private property rights and government intervention. The student will briefly discuss how the Coase Theorem, as it would later become known, provides an alternative to government regulation and provision of services and the importance of private property in his theorem.
In his book The Economics of Welfare, Arthur C. Pigou,...

...pressure dynamics specified by Bernoulli’s Principle to keep their rare wheels on the ground, even while zooming off at high speed. It is successfully employed in mechanism like the carburetor and the atomizer.
The study focuses on Bernoulli’s Theorem in Fluid Application. A fluid is any substance which when acted upon by a shear force, however small, cause a continuous or unlimited deformation, but at a rate proportional to the applied force. As a matter of fact, if a fluid...