St Petersburg paradox

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	St. Petersburg paradox - Wikipedia, the free encyclopedia
		The St. Petersburg paradox is a classical situation where a naive decision theory (which takes only the expected value into account) would recommend a course of action that no (real) rational person would be willing to take.
		Under this restriction, it has been proved that the St. Petersburg paradox disappears as long as the utility function is concave, which translates into the assumption that people are (at least for high stakes) risk averse.
		In some of these new theories, as in Cumulative Prospect Theory, the St. Petersburg paradox again appears in certain cases, even when the utility function is concave, but not if it is bounded [Rieger and Wang, 2006].
	en.wikipedia.org /wiki/St._Petersburg_paradox (1591 words)

	St. Petersburg Paradox
		"From the mathematical and logical point of view," observes Resnick, "the St. Petersburg paradox is impeccable." But this is the point of view to be taken when evaluating a theory per se (though not the only point of view ever to be taken).
		This problem, discovered by the Swiss eighteenth-century mathematician Daniel Bernoulli (1954) is the St. Petersburg paradox.
		Petersburg paradox "is to grant that the paradox is not an antinomy." He may mean that the difficulty posed by the game is a result of a factual assumption that utility is unbounded (and not merely by its logical features), and can be removed by rejecting that assumption.
	www.science.uva.nl /~seop/archives/spr1999/entries/paradox-stpetersburg (6108 words)

	EconLog, St. Petersburg Paradox, Arnold Kling: Library of Economics and Liberty
		St Petersburg's Paradox is purely based upon mathematics, which in the end simply is a reoccurrence of what has been already preceded.
		I have argued in a recent article 'Solving the St Petersburg Paradox-the paradox which is not and never was' SAJEMS 6 (2) 2003 that the St Petersburg game does not lead to a paradox at all.
		Will Baude brings up the St. Petersburg Paradox, in which a bet with an infinite expected payoff is rejected by the typical individual.
	econlog.econlib.org /archives/2003/11/st_petersburg_p.html (1262 words)

	The St. Petersburg Two-Envelope Paradox
		The St. Petersburg two-envelope paradox (taking C = A, and D = B-A, where A and B are the amounts in the two envelopes, and allowing infinite positive and negative expected values) shows that this principle is false.
		The St. Petersburg two-envelope paradox (taking C as the value in envelope A, and A and B as the respective choices) shows us that this principle is false.
		Apart from the illustration provided by the St. Petersburg two-envelope paradox, most of the issues discussed here have been discussed elsewhere: Dreier (forthcoming) discusses the breakdown of dominance reasoning; Norton (1998) discusses matters in the vicinity of the false probabilistic principle, and Clark and Shackel (2000) discuss the role of absolute convergence.
	consc.net /papers/stpete.html (1067 words)

	EconPort - Handbook - Decision-Making Under Uncertainty - The St. Petersburg Paradox
		Daniel Bernoulli and the St. Petersburg Paradox: Soshichi Uchii, Kyoto University
		Note: If you are curious about the St. Petersburg paradox in real life, you can see the section on an experimental discussion of the St. Petersburg Paradox.
		This puzzle,which has now become famous as the St. Petersburg Paradox, deeply troubled Swiss mathematician Nicholas Bernoulli, so in 1738 he asked his cousin, Daniel Bernoulli, an even more illustrious mathematician, how it could be explained.
	www.econport.org /econport/request?page=man_ru_basics2 (578 words)

	Choice Paradoxes
		The St. Petersburg paradox, in which people prefer a small sum of money rather than play a gamble with infinite expected value, was explained in 1738 by Daniel Bernoulli, who theorized that utility of money is nonlinear.
		Petersburg Paradox refutes EV The St. Petersburg paradox presents a case where scholars insisted that they would and should prefer a small amount of cash to a gamble with much higher EV.
		The EV of this St. Petersburg gamble is infinite,
	psych.fullerton.edu /mbirnbaum/paradox/paradoxes12.htm (2915 words)

	South(west)paw: paradoxes in decision science
		The St. Petersburg paradox has the same relationship to expected value theory that the Allais and Ellsberg paradoxes have to expected utility theory.
		The Allais and Ellsberg paradoxes debunk expected utility theory in the same way the St. Petersburg paradox debunks expected value theory.
		Petersburg paradox” using the concept of diminishing marginal utility.
	debfrisch.com /archives/000268.html (1177 words)

	Deinonychus antirrhopus: St. Petersburg Paradox
		Arnold Kling has an interesting post on the St. Petersburg Paradox (also worth checking out is this link Arnold provides that discusses the paradox).
		The problem with St. Petersburg Paradox is that the expected payoff is infinite.
		Basically this is a paradox because there is an unstated assumption that no matter what the final payoff is, it will be met.
	www.steveverdon.com /archives/statistics/000670.html (454 words)

	The world's top st petersburg paradox websites
		Petersburg paradox is a paradox that exhibits a random variable whose value is probably very small, and yet has an infinite expected value.
		Encounter with the paradox leads to a deeper understanding of a variety of issues in economics and decision theory, in particular:
		In probability theory and decision theory the St.
	www.websbiggest.com /dir-wiki.cfm?cat=st__petersburg_paradox&tab=edit (515 words)

	St. Petersburg (disambiguation) - Wikipedia, the free encyclopedia
		Petersburg paradox, a paradox by which a participant will only pay a modest fee for an infinite expected value
		The Treaty of Saint Petersburg, signed in 1875 between Japan and Russia
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/St._Petersburg_(disambiguation) (104 words)

	The Expected Utility Hypothesis - Introduction
		The expected utility hypothesis stems from Daniel Bernoulli's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli).
		Channelled by Gossen (1854), Bernoulli's idea of diminishing marginal utility of wealth became a centerpiece in the Marginalist Revolution of 1871-4 in the work of Jevons (1871), Menger (1871) and Walras (1874).
		The Paradox challenges the old idea that people value random ventures according to its expected return.
	cepa.newschool.edu /het/essays/uncert/bernoulhyp.htm (457 words)

	The St. Petersburg Paradox
		Professor Carl Hempel, who invented this paradox, believes that a purple cow actually does slightly increase the probability that all crows are black.
		It's easy to find millions of non-black objects that are not crows, therefore strongly confirming the law.
		The problem with Hempel's Paradox is finding the catch.
	www.geocities.com /CapitolHill/Lobby/3022/hempel.html (238 words)

	Introduction
		(But his solution doesn't eliminate the paradox because every utility function which is unbounded above, including log, has a modified version of the St. Petersburg Paradox.) The utility function was revisited by J.L. Kelly (1956) where he showed that it had some remarkable properties.
		It has been of interest at least since the eighteenth century discussion of the St. Petersburg Paradox (Feller, 1966) by Daniel Bernoulli.
		Daniel Bernoulli used the utility function to ``solve'' the St.
	www.bjmath.com /bjmath/thorp/paper1.htm (440 words)

	Daniel Bernoulli, Note
		In his paper on probability and expectation, published in 1738 (but written much earlier) by St. Petersburg Academy, he discussed a paradox now known as the "St. Petersburg Paradox".
		However, it must be pointed out that the same paradox reappears as soon as we make payments of the gamble in terms of your utility, instead of yen (or dollars or whatever).
		Despite Johann's objections Daniel became a mathematician himself, and Daniel spent several years in St. Petersburg, as a professor of mathematics.
	www.bun.kyoto-u.ac.jp /phisci/Gallery/D.bernoulli_note.html (906 words)

	Complexity Digest - The St. Petersburg Paradox And The Crash Of High-Tech Stocks In 2000
		The St. Petersburg Paradox And The Crash Of High-Tech Stocks In 2000, Ameri.
		We recount a remarkable article by Durand in which the valuation of growth stocks is related to the St. Petersburg paradox.
		Our conclusion is that the run-up in stock prices in the late 1990s and the subsequent declines in 2000 could have been avoided by an analysis and application of the St. Petersburg paradox.
	www.comdig.org /article.php?id_article=18018 (164 words)

	The Utility of Infinite Menus
		It is sometimes concluded from the St. Petersburg paradox that von Neumann-Morgenstern utility functions must be bounded.
	www.derivativesmath.com /Infinite.html (84 words)

	The St. Petersburg Paradox
		In the St. Petersburg Paradox, which is more of a gambling game than a paradox, a balanced coin is tossed fairly until the first head appears.
		The gambler's winnings are based on the number of tosses that are made before the game ends.
		What price would you be willing to pay to play this game?
	www.geocities.com /CapitolHill/Lobby/3022/stpete.html (222 words)

	CoFES: Center for Computational Finance and Economic Systems: Events and Seminars
		Finally, we will see how the St. Petersburg paradox easily predicted the crash of U.S. high-tech stocks in 2000.
		The St. Petersburg Paradox and the Crash of High-Tech Stocks in 2000
		This game, the classic example of a St. Petersburg game, was first described in 1713 by Nicolaus Bernoulli in a letter to Remond de Montmort.
	cohesion.rice.edu /engineering/cofes/events.cfm?EventRecord=6318 (180 words)

	Petersburg Paradox
		The paradox is that this disagrees with your experience to loose.
		Whatever entrance fee you would pay, you would win.
	www.mathematik.com /Petersburg/Petersburg.html (99 words)

	Deinonychus antirrhopus: November 2003 Archives
		That paradox is that even though health care resources are decreasing, infant mortality is also declining which on the surface appears to be a paradox.
		For there to be a paradox the amount of medical resources allocated towards infanats would have to decline and infnat mortality would also have to decline.
		There does not have to be a paradox.
	www.steveverdon.com /archives/2003_11.html (15678 words)

	Dr. T's EconLinks.com: Glossary: St. Petersburg Paradox
		Petersburg paradox refers to a lottery that pays $2
		The paradox is used to make the point that rational agents make decisions based on expected utility, rather than on expected value.
		Check the Stock Evaluation page to get a second opinion now!
	www.econlinks.com /glossary/st_petersburg_paradox.php (122 words)

	EUT.htm
		In the Ellsberg paradox, this tendency violates the __________ axiom
		Bernoulli argued that the paradox is due to ________________________________ for money.
		Prefer to bet on the option with _______ likelihood to win
	www.rci.rutgers.edu /~gbc/RPDM/EUT.htm (349 words)

	St Petersburg paradox ; Petersburg paradox ; Petersburg game
		St Petersburg paradox ; Petersburg paradox ; Petersburg game
		paradoxa de Sant Petersburg ; paradoxa de Petersburg ; joc de Petersburg
		This Glossary may not be copied, reproduced or retained in any form whatsoever without the express permission of the ISI.
	isi.cbs.nl /glossary/term3117.htm (83 words)

	Back to the St. Petersburg Paradox?
		Conventional parameterizations of cumulative prospect theory do not explain the St. Petersburg paradox.
		Keywords: EUT; Cumulative prospect theory; St. Petersburg paradox; Power utility; Probability ; Weighting.
		To do so, the power coefficient of an individual's utility function must be lower than the power coefficient of an individual's probability weighting function.
	ideas.repec.org /p/cer/papers/wp227.html (208 words)

	Statistics All Topics Homework Help
		This is a two part problem that expands on the St Petersburg Paradox.
		I have already figured out the paradoxical nature of this part of the problem.
		I have attempted this problem and ca not seem to arrive at the answers given in my book.
	www.brainmass.com /homeworkhelp/statistics/alltopics/9526 (150 words)

	Is St. Petersburg Paradox properly defined?
		to settle this little paradox once and for all.
		I would say that this is not a "real life paradox" because
		Buffon's needle problem and Bertrand's Paradox come to mind.
	www.groupsrv.com /hobby/post-775978.html (2120 words)

	Wiley::Encyclopedia of Statistical Sciences, Volume 8, Regressograms to St. Petersburg, Paradox, The
		Wiley::Encyclopedia of Statistical Sciences, Volume 8, Regressograms to St. Petersburg, Paradox, The
		Encyclopedia of Statistical Sciences, Volume 8, Regressograms to St. Petersburg, Paradox, The
		Wiley > Mathematics & Statistics > Statistics Text & Reference > Encyclopedia of Statistical Sciences, Volume 8, Regressograms to St. Petersburg, Paradox, The
	eu.wiley.com /WileyCDA/WileyTitle/productCd-0471055565.html (240 words)

	Daniel Bernoulli
		Bernoulli and the St. Petersburg Paradox by Soshichi Uchii - (also portrait)
		"The St. Petersburg Paradox" at Stanford Encyclopedia of Philosophy
	cepa.newschool.edu /het/profiles/bernoulli.htm (72 words)

	Earliest Known Uses of Some of the Words of Mathematics (S)
		B'} both under the additional condition C and under the complement C' of that condition." ("On Simpson's Paradox and the Sure-Thing Principle", Journal of the American Statistical Association, 67, (1972), p.
		SQUARE MATRIX was used by Arthur Cayley in 1858 in "A Memoir on the Theory of Matrices" Coll Math Papers, I, 475-96: "The term matrix might be used in a more general sense, but in the present memoir I consider only square or rectangular matrices" p.
		Rather Hamilton used "set" to mean what we would call an "n-tuple" or "vector," that is, a set of numbers which could be used as a coordinate in n-dimensional analytic geometry [James A. Landau].
	members.aol.com /jeff570/s.html (12636 words)

	Worldandnation: From paradise to paradox in Aruba
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		Impact killed all on Cypriot jet, coroner says
	www.sptimes.com /2005/08/22/Worldandnation/From_paradise_to_para.shtml (1741 words)

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In the News (Fri 18 Dec 09)