منابع مشابه
Voting Paradoxes
The early work of Condorcet in the 18th century, and that of Arrow and others in the 20th century, revealed the complex and interesting mathematical problems that arise in the theory of Social Choice, showing that the simple process of voting leads to strikingly counter-intuitive paradoxes. I will describe some of these, focusing on several recent intriguing examples whose analysis combines com...
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Both in dealing with the semantic paradoxes and in dealing with vagueness and indeterminacy, there is some temptation to weaken classical logic: in particular, to restrict the law of excluded middle. The reasons for doing this are somewhat different in the two cases. In the case of the semantic paradoxes, a weakening of classical logic (presumably involving a restriction of excluded middle) is ...
متن کاملGeometry, Voting, and Paradoxes
What could be easier than “voting?” After all, to vote we just count how many people favor each candidate. What can go wrong with something so elementary as this? Actually, a lot. As mathematicians and others have shown over the last two centuries, once there are at least three candidates—not an atypical situation—the winner need not be whom the voters really want. Such bad outcomes may occur n...
متن کاملPentagrams and Paradoxes
Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and the...
متن کاملOn Newton's paradoxes
Reading the Principia [1] it is easy to realize that Newton, without being aware of the fact, has corrected the law of the fall of bodies formulated by Galilei. In the present paper we examine the consequences of such a fact and show that they affect the entire Celestial Mechanics, being related to the very small 43” per century of the perihelion shift of Mercury as well as to the substantial 5...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2001
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/34/44/317