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Topic: Apportionment paradox

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	Paradox (Site not responding. Last check: 2007-10-29)
		A paradox is an apparently true statement that seems to lead to an illogical contradiction, or to a situation that contradicts common intuition.
		Put simply, a paradox is 'the opposite of what one thinks to be true.' The identification of a paradox based on seemingly simple and reasonable concepts has often led to significant advances in science, philosophy and mathematics.
		The etymology of paradox can be traced back to texts appearing at the dawn of the renaissance, a period of accelerated scientific thought in Europe and Asia sometime after the year 1500 AD.
	www.factsite.co.uk /en/wikipedia/p/pa/paradox.html (1809 words)

	Paradox - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-29)
		A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition.
		Simpson's paradox: An association in sub-populations may be reversed in the population.
		Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
	www.encyclopedia-online.info /Paradox (1790 words)

	Apportionment paradox -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-29)
		To apportion is to divide into parts according to some rule, the rule typically being one of (The quotient obtained when the magnitude of a part is divided by the magnitude of the whole) proportion.
		In some, such as the case of the dying farmer and his horses (one of the (additional info and facts about horse paradox) horse paradoxes), the resolution is simple—the farmer didn't apportion all of his horses.
		The method for apportionment used during this period (put forth by (A port city in southeastern Ontario at the western end of Lake Ontario) Hamilton) was as follows: first, the fair share of each state is computed (the fair share is the share that the state would get if fractional values are allowed).
	www.absoluteastronomy.com /encyclopedia/a/ap/apportionment_paradox.htm (379 words)

	Encyclopedia
		Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context (or language) to lose their paradox quality.
		Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.
		Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest
	www.stylokna.pl /wikipedia/index.php?title=paradox (2302 words)

	Alabama paradox - Wikipedia, the free encyclopedia
		The Alabama paradox was the first of the apportionment paradoxes to be discovered.
		Census Office, computed apportionments for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300.
		In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares.
	en.wikipedia.org /wiki/Alabama_paradox (219 words)

	Paradox Article, Paradox Information (Site not responding. Last check: 2007-10-29)
		A paradox is an apparently true statement or group of statements thatseems to lead to a contradiction or to a situation that defies intuition.The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics.
		Paradoxes which are not based on a hidden error generally happen atthe fringes of context or language, andrequire extending the context (or language) to lose their paradox quality.
		Paradox of hedonism : When one pursues happiness itself,one is miserable; but, when one pursues something else, one achieves happiness.
	www.anoca.org /paradoxes/one/paradox.html (1831 words)

	Paradox (Site not responding. Last check: 2007-10-29)
		The identification of a paradox based on seemingly simple and reasonable concepts has often led to significant advances in science, philosophy and mathematics.
		Grandfather paradox: You travel back in time and kill your grandfather before he meets your grandmother, resulting in you never being conceived.
		Olbers' paradox: If the universe is infinite, the sky should be entirely bright because there's a star in every direction.
	www.enlightenweb.net /p/pa/paradox.html (1300 words)

	Paradox (Site not responding. Last check: 2007-10-29)
		Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise.
		Carroll's paradox: the angular momentum of a stick should be zero, but is not.
		Twin paradox: When the travelling twin returns, he is younger and older than his brother who stayed put.
	www.tocatch.info /en/Paradox.htm (2389 words)

	The Constitution and Paradoxes
		One exhibiting inexplicable or contradictory aspects: “You have the paradox of a Celt being the smooth Oxonian” (Anthony Burgess).
		Close to 1900 Hamilton's method was shown to lead to the Population paradox and in 1907, on the occasion of Oklahoma joining the Union, the New-States paradox was also detected.
		The population paradox occurs when a state with a higher grows rate loses a seat to a state with a lower growth rate, when the apportionment is recalculated on the basis of new figures.
	www.cut-the-knot.org /ctk/Democracy.shtml (1981 words)

	Apportionment Paradoxes (Site not responding. Last check: 2007-10-29)
		An increase in the total number of seats to be apportioned causes a state to lose a seat.
		The Population Paradox was discovered around 1900, when it was shown that a state could lose seats in the House of Representatives as a result of an increase in its population.
		However, when the apportionment was mathematically recalculated, Maine gained a seat (4 instead of 3) and New York lost a seat (from 38 to 37).
	www.ctl.ua.edu /math103/apportionment/paradoxs.htm (288 words)

	Most Math 131 class notes and homework assignments, Fall 05 (Site not responding. Last check: 2007-10-29)
		Balinski and Young showed that there is NO apportionment method that always stays within the quota and does not have instances of the paradoxes.
		apportionment is one where no switch of one seat from state to another state can get us closer to the quotas over all states.
		apportionment is one where no switch of one seat from state to another state can make the smallest district larger.
	www.csun.edu /~hcmth007/m131f05cn.htm (1219 words)

	paradox information (Site not responding. Last check: 2007-10-29)
		A falsidical paradox establishes a result that not only appears false but actually is false; there is a fallacy inthe supposed demonstration.
		A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properlyapplying accepted ways of reasoning.
		Nihilist paradox : iftruth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect.
	www.vsearchmedia.com /paradox.html (1836 words)

	thirty-thousand.org -- Neubauer-Zeitlin Analysis
		The reasons for this method of apportionment of the EC members are rooted in the Connecticut Compromise of 1787 (Kelly, Harbinson, and Belz 1970; Koppell 2000).
		We apportioned a hypothetical House with 830 members and, using the official results of the 2000 presidential election from all 50 states and the District of Columbia, added up the electoral votes for Bush and Gore under this scenario.
		Though apportionment appears at first sight to be a straightforward problem that should allow for a satisfactory answer, the real story is quite a bit more complex.
	www.thirty-thousand.org /pages/Neubauer-Zeitlin.htm (3601 words)

	Apportionment: Hamilton's method
		The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but was subsequently vetoed by president Washington - in the very first exercise of the veto power by President of the United States.
		The given total number of seats (23 in the applet) is to be apportioned between several (3 at the ouset) states proportionally to their populations.
		This is probably the most controversial method of apportionment that leads to the so called paradoxes: Alabama paradox, population paradox, new-state paradox.
	www.cut-the-knot.org /Curriculum/SocialScience/AHamilton.shtml (204 words)

	Paradox (Site not responding. Last check: 2007-10-29)
		's self-flowing flask fills itself in this diagram, but perpetual motion machines don't exist.]] A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition, such as "This statement is false".
		The word paradox is often used indifferently with contradiction; but where a contradiction by definition cannot be true, many paradoxes do allow of resolution, though many remain unresolved or only contentiously resolved (such as Curry's paradox)..
		St. Petersburg paradox: People will only offer a modest fee for a reward of infinite value.
	www.33beat.com /Paradox.html (1947 words)

	paradox
		A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition.
		This might be termed an ethical dilemma; another example is the conflict between an injuction not to steal and one to care for a family that you cannot afford to feed except with stolen money.
		The various proofs that 1 = 2 are classic examples, generally relying on a hidden division by zero.
	www.fact-library.com /paradox.html (1340 words)

	iqexpand.com (Site not responding. Last check: 2007-10-29)
		Known for being an innovative research and development company, Paradox Security Systems is a recognized worldwide force in the security industry.
		The paradox arises within naive set theory by considering the...
		where a paradox is an unintuitive outcome of economic theory.
	paradox.iqexpand.com (2348 words)

	Apportionment paradox - TheBestLinks.com - Mathematics, Maine, Oklahoma, Paradox, ... (Site not responding. Last check: 2007-10-29)
		Apportionment paradox - TheBestLinks.com - Mathematics, Maine, Oklahoma, Paradox,...
		Apportionment paradox, Mathematics, Maine, Oklahoma, Paradox, Virginia, 1900s...
		You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page.
	www.thebestlinks.com /Apportionment_paradox.html (495 words)

	Paradox - Wikpedia (Site not responding. Last check: 2007-10-29)
		For other meanings of "Paradox", see Paradox (disambiguation).
		A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition, such as "This statement is false".
		Bertrand's paradox (probability): Different common-sense defintions of randomness give quite different results.
	www.bostoncoop.net /~tpryor/wiki/index.php?title=Paradox (2227 words)

	Re: Population paradox
		In Europe, where there is an apportionment problem for allocating seats to parties in elections there are similar noisy details of "applied mathematics" mirroring the American problem of having to give each state one seat.
		Again - and as a caveat to some conclusions one might draw from the paper - there are various viewpoints on just which criteria and measures thereof are most important to optimize.
		For me, the preferred apportionment should maximize, for ones chosen convex utility function, the sum over all persons of each persons utility value for her per-cap representation level.
	www.mail-archive.com /election-methods-list@eskimo.com/msg09039.html (426 words)

	ipedia.com: United States Congressional Apportionment Article (Site not responding. Last check: 2007-10-29)
		The method first assigns one seat to each state, as required by the Constitution, and then assigns additional seats based upon a "priority ranking," calculated by dividing the population of each state by the geometric mean of its current and next seats.
		The Equal Proportions method has been the fifth distinct method of determining congressional apportionment since the adoption of the United States Constitution.
		The size of the Congressional delegations from the thirteen original states were assigned by the Constitution for use until the completion of the first U.S. Census.
	www.ipedia.com /united_states_congressional_apportionment.html (576 words)

	dictionary - Paradox
		Socratic Paradox : One can never knowingly choose the lesser good or willingly do the wrong thing.
		Cursed Friend : If one is cursed into hurting one’s friends by just being with them, can one still be a friend and seek the other's company?
		Paradox of Denial : How can one accept oneself as one is, if one is not the way one thinks one should be?
	www.medicalrace.com /dictionary/Paradox (2195 words)

	Calculus Proposal Level Two Module
		reproduce and implement algorithms for calculating the Hamilton method of apportionment
		apply the Webster and other divisor methods of apportionment
		use the Apportionment Impossibility Theorem to describe deficiencies of various apportionment methods
	www.dist.maricopa.edu /m2c/teams/results/calctwomodule-part2.html (278 words)

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