In spite of its infinite expectation value, the St. Petersburg game is not only a gamble without supply in the real world, but also one without demand at apparently very reasonable asking prices. We offer a rationalizing explanation of why the St. Petersburg bargain is unattractive on both sides (to both house and player) in the mid-range of prices (finite but upwards of about $4). Our analysis – featuring (1) the already-established fact that the average of finite (...) ensembles of the St. Petersburg game grows with ensemble size but is unbounded, and (2) our own simulation data showing that the debt-to-entry fee ratio rises exponentially – explains why both house and player are quite rational in abstaining from the St. Petersburg game. The house will be unavoidably (and intentionally) exposed to very large ensembles (with very high averages, and so very costly to them), while contrariwise even the well-heeled player is not sufficiently capitalized (as our simulation data reveals) to be able to capture the potential gains from large-ensemble play. (Smaller ensembles, meanwhile, enjoy low means, as others have shown, and so are not worth paying more than $4 to play, even if a merchant were to offer them at such low prices per trial.) Both sides are consequently rational in abstaining from entry into the St. Petersburg market in the mid-range of asking prices. We utilize the concept of capitalization vis-à-vis a gamble to make this case. Classical analyses of this question have paid insufficient attention to the question of the propriety of using expected values to assess the St. Petersburg gamble. And extant analyses have not noted the average-maximum-debt-before-breaking-even figures, and so are incomplete. (shrink)

It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.

By recourse to the fundamentals of preference orderings and their numerical representations through linear utility, we address certain questions raised in Nover and Hájek 2004, Hájek and Nover 2006, and Colyvan 2006. In brief, the Pasadena and Altadena games are well-defined and can be assigned any finite utility values while remaining consistent with preferences between those games having well-defined finite expected value. This is also true for the St Petersburg game. Furthermore, the dominance claimed for the Altadena (...) class='Hi'>game over the Pasadena game, and that would have been claimed for the St Petersburg game over the Altadena, can be contradicted without fear of inconsistency with the axioms of utility theory. However, insistence upon dominance can be made to yield a contradiction of the Archimedean axiom of utility theory. CiteULike Connotea Del.icio.us What's this? (shrink)

In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ. The deduction of those fees is the main result of Section 2. We (...) then propose a Bayesian approach to the problem. When the probability of heads is θ the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in, for in this case there is a paradox. (shrink)

(2012). In Response to “Revisiting Blumberg's ‘The Practice of Law As A Confidence Game’” by Professor Gilbert Geis. Criminal Justice Ethics: Vol. 31, No. 1, pp. 39-41. doi: 10.1080/0731129X.2012.657508.

Among the educative games of Plato’s Cretan city, choral performances have a prominent role. This paper examines the function of play (παιδιά) in the choral education in virtue in Plato’s Laws. I reconstruct the notion of play as it is elaborated throughout this dialogue, and then show how it contributes to solving the problem of virtue acquisition in the Athenian’s account of moral education through songs and dances. I argue that play in the Laws is best understood as an imitative (...) activity that is intrinsically pleasurable, ordered by rules and patterns of repetition, and undertaken for its own sake by a player whose psychic condition is childish. Thus interpreted, we are in a better position to see why choruses must be engaged in playfully. Because the self-likening process (ὁμοίωσις) choral performances aim at requires pleasure and because pleasure normally obtains when there is a concordance between one’s character and the imitations, virtue acquisition is best secured if the imitations of virtue in choruses are performed or spectated playfully. (shrink)

Among the educative games of Plato’s Cretan city, choral performances have a prominent role. This paper examines the function of play (παιδιά) in the choral education in virtue in Plato’s Laws. I reconstruct the notion of play as it is elaborated throughout this dialogue, and then show how it contributes to solving the problem of virtue acquisition in the Athenian’s account of moral education through songs and dances. I argue that play in the Laws is best understood an imitative activity (...) that is intrinsically pleasurable, ordered by rules and patterns of repetition, and undertaken for its own sake by a player whose psychic condition is childish. Thus interpreted, we are in a better position to see why choruses must be engaged in playfully. Because the self-likening (ὁμοίωσις) process choral performances aim at requires pleasure and because pleasure normally obtains when there is a concordance between one’s character and the imitations, virtue acquisition is best secured if the imitations of virtue in choruses are performed playfully. (shrink)

This book is an introduction, entirely by example, to the possibilities of using computer models as tools in phosophical research in general and in philosophical logic in particular. Topics include chaos, fractals, and the semantics of paradox; epistemic dynamics; fractal images of formal systems; the evolution of generosity; real-valued game theory; and computation and undecidability in the spatialized Prisoner's Dilemma.

Adults are skilled at using language to construct/negotiate identity and to signal affiliation with others, but little is known about how these abilities develop in children. Clearly, children mirror statistical patterns in their local environment (e.g., Canadian children using zed instead of zee), but do they flexibly adapt their linguistic choices on the fly in response to the choices of different peers? To address this question, we examined the effect of group membership on 7‐ to 9‐year‐olds' labeling of objects in (...) a trivia game, exploring whether they were more likely to use a particular label (e.g., sofa vs. couch) if members of their “team” also used that label. In a preregistered study, children (N = 72) were assigned to a team (red or green) and were asked during experimental trials to answer questions—which had multiple possible answers (e.g., blackboard or chalkboard)—after hearing two teammates and two opponents respond to the same question. Results showed that children were significantly more likely to produce labels less commonly used by the community (i.e., dispreferred labels) when their teammates had produced those labels. Crucially, this effect was tied to group membership, and could not be explained by children simply repeating the most recently used label. These findings demonstrate how social processes (i.e., group membership) can guide linguistic variation in children. (shrink)

One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.

The principle of Anteriority says that prospects that are identical from the perspective of every possible person’s welfare are equally good overall. The principle enjoys prima facie plausibility, and has been employed for various theoretical purposes. Here it is shown using an analogue of the St Petersburg Paradox that Anteriority is inconsistent with central principles of axiology.

I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.

Written and set on the banks of the Neva, St Petersburg Dialogues is a startlingly relevant analysis of the human prospect in the twenty-first century. As the literary critic George Steiner has remarked, "the age of the Gulag and of Auschwitz, of famine and ubiquitous torture... nuclear threat, the ecological laying waste of our planet, the leap of endemic, possibly pandemic, illness out of the very matrix of libertarian progress" is exactly what Joseph de Maistre foretold. In the Dialogues (...) Maistre addressed a number of topics that are discussed briefly or not at all in his other works already available in English. These include an apologetic for traditional Christian beliefs about providence, reflections on the social role of the public executioner and the "divinity" of war, a critique of John Locke's sensationalist psychology, meditations on prayer and sacrifice, and a mini-course on "illuminism." The literary form is that of the "philosophical conversation" – one that allowed Maistre to be deliberately provocative and to indulge his taste for paradox, a "methodical extravagance" that he judged particularly appropriate for the eighteenth-century salon. Translator and editor Richard Lebrun provides a full scholarly edition of this classic work, complete with an introduction, chronology, critical bibliography, and generous explanatory notes. The Dialogues will be of interest to scholars of literary history as well as the history of ideas. (shrink)

Why does Derek Parfit, a philosopher very much associated with the University of Oxford, use pictures of St. Petersburg on the covers of volumes of On What Matters? Perhaps it is because he regards his agony argument as like something from Russian literature. But I can envisage a response to the argument from such literature.

Written and set on the banks of the Neva, St Petersburg Dialogues is a startlingly relevant analysis of the human prospect at the end of the twentieth century. As the literary critic George Steiner has remarked, "the age of the Gulag and of Auschwitz, of famine and ubiquitous torture,... nuclear threat, the ecological laying waste of our planet, the leap of endemic, possibly pandemic, illness out of the very matrix of libertarian progress" is exactly what Maistre foretold. In the (...) Dialogues Maistre addressed a number of topics which are discussed briefly or not at all in his other works already available in English. These include an apologetic for traditional Christian beliefs about providence, reflections on the social role of the public executioner and the "divinity" of war, a critique of John Locke's sensationalist psychology, meditations on prayer and sacrifice, and a mini-course on "illuminism." The literary form is that of the "philosophical conversation" -- one that allowed Maistre to be deliberately provocative and to indulge his taste for paradox, a "methodical extravagance" that he judged particularly appropriate for the eighteenth-century salon. Translator and editor Richard Lebrun provides a full scholarly edition of this classic work, complete with an introduction, chronology, critical bibliography, and generous explanatory notes. The Dialogues will be of interest to scholars of literary history as well as the history of ideas. (shrink)

Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is (...) another problem associated with the St. Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)

Cumulative Prospect Theory (CPT) does not explain the St. Petersburg Paradox. We show that the solutions related to probability weighting proposed to solve this paradox, (Blavatskyy, Management Science 51:677–678, 2005; Rieger and Wang, Economic Theory 28:665–679, 2006) have to cope with limitations. In that framework, CPT fails to accommodate both gambling and insurance behavior. We suggest replacing the weighting functions generally proposed in the literature by another specification which respects the following properties: (1) to solve the paradox, the slope (...) at zero has to be finite. (2) to account for the fourfold pattern of risk attitudes, the probability weighting has to be strong enough. (shrink)

The image of St. Petersburg is an integral part of Russian art, in particular, in watercolor painting. This article is devoted to the analysis of the work of Russian watercolor artists, identifying the specifics and characteristic features of the image of the city on the Neva in their work. The object of the study is watercolors by Russian artists, the subject is expressive means, techniques and methods through which the image of St. Petersburg is embodied. On the example (...) of watercolor works by E.P. Gau, I.A. Vladimirova, A.S. Vedernikov, A.P. Ostroumova-Lebedeva, P.P. Grigoryants, G.P. Fitingof, A. Ermolaev, V.V. Proshkin, K. Kuzema, V. Kolbasov, O. Litvinenko, etc. the historical transformation of the artistic image of St. Petersburg, its conditionality by cultural and historical factors and the nature of the life of the inhabitants of the city is shown. The study concluded that the image of St. Petersburg is important for Russian artists, as well as a significant variety of its creative interpretations. Each watercolor work demonstrates the subjective attitude of artists to St. Petersburg, thanks to which real urban landscapes acquire spirituality and unique expressiveness. The complex historical fate of this cultural and artistic center of Russia, which was once a magnificent capital, experienced revolutionary events and went through military destruction, determined the versatility of creative approaches to the embodiment of the city, as a result of various turns of history, it lost, then regained its greatness, beauty and attractiveness. Petersburg in watercolors is invariably filled with vitality, lyrical feelings and the love of artists. (shrink)

Khoryev regards Petersburg, a collection of essays by Jarosław Iwaszkiewicz, published in 1976, as a windup of the writer’s complex ties with Russian culture and literature, which he was widely known to have loved and known in depth. It is a book where, through the legendary city on the river Neva, Iwaszkiewicz takes a look at a number of essential issues of Russian history and its ties with the history of Poland and the Polish people. Iwaszkiewicz avoids unequivocal judgments, (...) noticing the antinomian nature of St. Petersburg, seen as a being full of contrast but at the same time the center of revolutions and despotism, a manifestation of imperial power and the highest achievements of sophisticated art. These contrasts reveal, in Khoryev’s opinion, the multi-faceted and fullest picture of St. Petersburg and its individuality: so mysterious, overpowering and unique. (shrink)

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as (...) desirable or undesirable as we want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

The article presents results of an ongoing study of centers of intellectual innovations in post-Soviet Russia. Using the European University at St. Petersburg as the main object of their analysis, the authors demonstrate how new models of academic careers, which became available in the 1980s and 1990s, were eventually institutionalized as new models of knowledge production and educational practices. Supported by American foundations, this private university had to invent a new institutional structure and to position itself within the field (...) of higher education, still mostly dominated by the state. (shrink)

The St. Petersburg Theological Academy was the first of the four academies in the early years of the nineteenth century to undergo a remodeling along the lines of a new charter for the empire’s church-affiliated educational institutions. Instruction in philosophy was mandated, but the academy faced staffing issues at the outset. Courses were taught following Wolffian guidebooks that many found to be antiquated, raising pedagogical dilemmas for the teachers. Nevertheless, a divorce between faith and reason was proscribed, and adherence (...) to a Christianized Plato remained prescribed and seen as central to the Orthodox religion. (shrink)

This paper aims to consider the meaning of the dismal theorem, as presented by Martin Weitzman [(2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91, 1–19]. The theorem states that a standard cost–benefit analysis breaks down if there is a possibility of catastrophes occurring. This result has a significant influence on debates regarding the economics of climate change. In this study, we present an intuitive similarity between the dismal theorem and the St. (...) Petersburg paradox using a simple discrete probability distribution. (shrink)

This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to the (...) St. Petersburg puzzle and related puzzles. The result will be a decision theory that gives a novel, but well-motivated, reason for discounting small probabilities when making decisions. We examine the merits and demerits of such a decision theory. (shrink)

This is the first complete translation of this work of Maistre's into the English language. It also includes Maistre's shorter piece, "Elucidation on Sacrifices," which has traditionally been appended to these philosophical dialogues. Maistre himself had divided his writing into eleven numbered dialogues, each of which formally represents an evening of conversation, as well as a "Sketch of a Final Dialogue," in which the participants say their farewells. The debating figures are called "the Count", "the Senator", and "the Chevalier." There (...) is an elaborate apparatus surrounding the work, consisting of the footnotes and endnotes to each dialogue that Maistre himself had written, as well as explanatory footnotes and endnotes to each dialogue by the translator. Lebrun has traced virtually all of the references Maistre had made, and in some cases has been able to point out slight errors and misstatements in Maistre's own citations. He has also translated into English all the passages in languages other than French, which follow immediately after their appearance in the text in their original tongue. Lebrun has also provided fine supplements to Maistre's writing--a preface, scholarly introductory essay, chronology, critical bibliography, a well as a note on the text. There is also a very fine index, which includes virtually every work and author cited or mentioned in Maistre's text. The quality of Lebrun's translation is excellent indeed, clearly aware of a variety of nuances in Maistre's language, and based squarely on a life-long study of the thinker. (shrink)

RESUMO O artigo discute os princípios fundamentais de elaboração do projeto e anotação de corpora de fala no âmbito da Escola Fonológica de São Petersburgo e fornece os exemplos de utilização de dados de vários corpora na pesquisa em fonética. Um dos princípios fundamentais é analisar as amostras em todos os níveis: desde o segmento até a entoação, incluindo as disfluências da fala. Durante a anotação fonética, sugerimos ouvir cada som isoladamente e confiar nos dados do espectrograma. Na anotação silábica, (...) é crucial considerar a ressilabificação. Durante a anotação prosódica, sugerimos confiar na percepção do ouvinte e analisar as curvas melódicas. Um corpus de fala que segue esses princípios é uma fonte valiosa de dados fonéticos, uma vez que os fatores segmentais e prosódicos estão em constante interação e não se pode analisar as unidades de um nível de anotação sem fazer referência aos outros. (shrink)

The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.

Khoryev regards Petersburg, a collection of essays by Jarosław Iwaszkiewicz, published in 1976, as a windup of the writer’s complex ties with Russian culture and literature, which he was widely known to have loved and known in depth. It is a book where, through the legendary city on the river Neva, Iwaszkiewicz takes a look at a number of essential issues of Russian history and its ties with the history of Poland and the Polish people. Iwaszkiewicz avoids unequivocal judgments, (...) noticing the antinomian nature of St. Petersburg, seen as a being full of contrast but at the same time the center of revolutions and despotism, a manifestation of imperial power and the highest achievements of sophisticated art. These contrasts reveal, in Khoryev’s opinion, the multi-faceted and fullest picture of St. Petersburg and its individuality: so mysterious, overpowering and unique. (shrink)

In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion rather (...) than a positive model of decision making processes. (shrink)

The art historian Alessandro Giovanardi has recently published a monograph on one of the important representatives of the Russian religious-philosophical renaissance of the beginning of 20th century – Vladimir Nikolayevich Zabugin. This volume, written in Italian, aims to provide a comprehensive overview of Zabugin's intellectual biography, philosophical and aesthetic ideas and opens up a completely unknown corpus of the author’s works as well as the history of the reception of his heritage. The monograph underlines the contribution of Vladimir Zabugin in (...) Italian and European humanitarian culture and defines his heritage as a rare synthesis of the finest erudition and Christian spirituality. (shrink)

In our 2004, we introduced two games in the spirit of the St Petersburg game, the Pasadena and Altadena games. As these latter games lack an expectation, we argued that they pose a paradox for decision theory. Terrence Fine has shown that any finite valuations for the Pasadena, Altadena, and St Petersburg games are consistent with the standard decision-theoretic axioms. In particular, one can value the Pasadena game above the other two, a result that conflicts with (...) both our intuitions and dominance reasoning. We argue that this result, far from resolving the Pasadena paradox, should serve as a reductio of the standard theory, and we consequently make a plea for new axioms for a revised theory. We also discuss a proposal by Kenny Easwaran that a gamble should be valued according to its 'weak expectation', a generalization of the usual notion of expectation. (shrink)

Standard decision theory has trouble handling cases involving acts without finite expected values. This paper has two aims. First, building on earlier work by Colyvan (2008), Easwaran (2014), and Lauwers and Vallentyne (2016), it develops a proposal for dealing with such cases, Difference Minimizing Theory. Difference Minimizing Theory provides satisfactory verdicts in a broader range of cases than its predecessors. And it vindicates two highly plausible principles of standard decision theory, Stochastic Equivalence and Stochastic Dominance. The second aim is to (...) assess some recent arguments against Stochastic Equivalence and Stochastic Dominance. If successful, these arguments refute Difference Minimizing Theory. This paper contends that these arguments are not successful. (shrink)

This paper revisits the Pasadena game (Nover and Háyek 2004), a St Petersburg-like game whose expectation is undefined. We discuss serveral respects in which the Pasadena game is even more troublesome for decision theory than the St Petersburg game. Colyvan (2006) argues that the decision problem of whether or not to play the Pasadena game is ‘ill-posed’. He goes on to advocate a ‘pluralism’ regarding decision rules, which embraces dominance reasoning as well as (...) maximizing expected utility. We rebut Colyvan’s argument, offering several considerations in favour of the Pasadena decision problem being well posed. To be sure, current decision theory, which is underpinned by various preference axioms, leaves indeterminate how one should value the Pasadena game. But we suggest that determinacy might be achieved by adding further preference axioms. We conclude by opening the door to a far greater plurality of decision rules. We suggest how the goal of unifying these rules might guide future research. (shrink)

How much would you pay to play a lottery with an “infinite expected payoff?” In the case of the century old, St. Petersburg Paradox, the answer is that the vast majority of people would only pay a small amount. The authors seek to understand this paradox by providing an explanation consistent with a broad, process‐level model of human decision‐making under risk.

The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up (with high probability) poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.

With the foundation of the journal,,Evrejskaja Starina" in 1909, the Jewish Historical-Ethnographic Society of St. Petersburg wanted to create a forum for the study of the history of Jews in Russia and Poland. This article investigates whether the journal was able to live up to its goal, and to which extent,,Evrejskaja Starina" served as a basis for the further development of a Russian-Jewish historiography.

In their paper, “Vexing Expectations,” Nover and Hájek (2004) present an allegedly paradoxical betting scenario which they call the Pasadena Game (PG). They argue that the silence of standard decision theory concerning the value of playing PG poses a serious problem. This paper provides a threefold response. First, I argue that the real problem is not that decision theory is “silent” concerning PG, but that it delivers multiple conflicting verdicts. Second, I offer a diagnosis of the problem based on (...) the insight that standard decision theory is, rightly, sensitive to order. Third, I describe a new betting scenario—the Alternating St. Petersburg Game—which is genuinely paradoxical. Standard decision theory is silent on the value of playing this game even if restrictions are placed on the order in which the various alternative payoffs are summed. †To contact the author, please write to: Department of Philosophy, Swarthmore College, Swarthmore, PA 19081; e-mail: [email protected]. (shrink)