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Here is an example which will illustrate the flaw in the Single Transferable Vote (STV) system used in the Presidential...
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Here is an example which will illustrate the flaw in the Single Transferable Vote (STV) system used in the Presidential elections in the US and India. Consider what happens when there are five Presidential candidates A, B, C, D, E and the electoral college consists of 501 electors. Suppose 251 electors have given their preference order as ABCDE (A preferred most and E preferred least) and the remaining 250 electors have their preference as BCDEA. Most people would agree that B should be elected President, since he has been chosen by everyone as either the first preference or the second preference, and almost half (250 out of 501) have given him the first preference. Also, A is preferred least by almost half the electorate (250 out of 501), which should neutralize the 251 first preference votes in his favor. While common sense suggests that B is the right choice, the system of STV would choose A as the President. Arrow's paradox asserts that this kind of anomalies are inevitable if the input to a voting system is a preference order.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
May 18, 2009
Date Modified:
May 18, 2009
Peer Review for material titled "Saving Democracy from Arrow's Paradox (youtube video)"
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Godel has proved that there are formulas in Elementary Arithmetic, which will introduce contradictions, irrespective of...
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Godel has proved that there are formulas in Elementary Arithmetic, which will introduce contradictions, irrespective of whether we assume the formula itself or its negation. His proof is in metalanguage. Sentient Arithmetic (SA) adds three more derivation rules to EA and shows that the proof for incompleteness of SA can be given in SA itself without using any metalanguage.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
Jun 25, 2001
Date Modified:
Apr 14, 2010
Peer Review for material titled "Sentient Arithmetic and Godel's Theorems"
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A complete analysis of Shannon's telegraph channel is given, making use of matrices with elements from a division ring. A...
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A complete analysis of Shannon's telegraph channel is given, making use of matrices with elements from a division ring. A notation is developed for representing the set of signals of a communication channel.
Material Type:
Simulation
Author:
Kannan Nambiar
Date Added:
Nov 07, 2001
Date Modified:
Dec 20, 2005
Peer Review for material titled "Shannon's Communication Channels and Word Spaces"
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The most popular format for publishing mathematics on the Web is the PDF, and HyperLaTeX is the program which allows us to...
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The most popular format for publishing mathematics on the Web is the PDF, and HyperLaTeX is the program which allows us to introduce hyper references in the PDF documents. This paper is a tutorial on using HyperLaTeX to produce PDF files.
Material Type:
Tutorial
Author:
Kannan Nambiar
Date Added:
Nov 30, 2001
Date Modified:
Dec 20, 2005
Peer Review for material titled "The Ecstasy of HyperLaTeX"
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Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to...
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Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does not appear, nonLebesgue measurable sets are not possible, and the unit interval splits into a set of infinitesimals.
Material Type:
Reference Material
Author:
Kannan Nambiar
Date Added:
Nov 03, 2001
Date Modified:
Dec 20, 2005
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