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The dataset generation failed because of a cast error

Error code:   DatasetGenerationCastError
Exception:    DatasetGenerationCastError
Message:      An error occurred while generating the dataset

All the data files must have the same columns, but at some point there are 1 new columns ({'text'}) and 4 missing columns ({'num_embeddings', 'embedding_offset', 'passage_offset', 'num_passages'}).

This happened while the json dataset builder was generating data using

hf://datasets/forcemultiplier/diverse_subjects_nov13/colbert/indexes/pdf_files_index/collection.json (at revision 71885d6a36bc82e9dc30ba65e58681d1384ac230)

Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback:    Traceback (most recent call last):
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1870, in _prepare_split_single
                  writer.write_table(table)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 622, in write_table
                  pa_table = table_cast(pa_table, self._schema)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2292, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2240, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              text: string
              -- schema metadata --
              pandas: '{"index_columns": [], "column_indexes": [], "columns": [{"name":' + 192
              to
              {'passage_offset': Value(dtype='int64', id=None), 'num_passages': Value(dtype='int64', id=None), 'num_embeddings': Value(dtype='int64', id=None), 'embedding_offset': Value(dtype='int64', id=None)}
              because column names don't match
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1417, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1049, in convert_to_parquet
                  builder.download_and_prepare(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 924, in download_and_prepare
                  self._download_and_prepare(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1000, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1741, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1872, in _prepare_split_single
                  raise DatasetGenerationCastError.from_cast_error(
              datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
              
              All the data files must have the same columns, but at some point there are 1 new columns ({'text'}) and 4 missing columns ({'num_embeddings', 'embedding_offset', 'passage_offset', 'num_passages'}).
              
              This happened while the json dataset builder was generating data using
              
              hf://datasets/forcemultiplier/diverse_subjects_nov13/colbert/indexes/pdf_files_index/collection.json (at revision 71885d6a36bc82e9dc30ba65e58681d1384ac230)
              
              Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)

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passage_offset int64	num_passages int64	num_embeddings int64	embedding_offset int64	text string
0	22,909	6,115,434	0	null
null	null	null	null	AN INTRODUCTION TO BOUNDARY LAYER METEOROLOGY
null	null	null	null	ROLAND B. STULL Atmospheric Science Programme, Department of Geography The University of British Columbia, Vancouver, Canada. An Introduction to Boundary Layer Meteorology KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
null	null	null	null	Libfary 01 Congress Cataloging in Publication Data SIUI I. RolinG S .. 1950- An ,n'"OOuct lon to b. "n alrY loy," • • ' "O"OlogV " o," 'V! ~. CI. -- (AUos~~or,c Hllne U ' Rollno e. 5'ul'. IncluUS O'O II .G""O~ '" Ona I na ... ISIIN,'3: 918-9().2n·2769-5 ,. Bou nOlry I IY", ' MIII.ralcgv...
null	null	null	null	H~t publislled 1999 RCIlO"inted 1989. 199 1. 1993. 1994 Reprinted with cITata 1991 R""rintoo 1999. 2001. 2003 Printtd on acid-fru paptr All Rights Reserved © t 988 by Kh./We, ACademic Publishers SoftOOvef reprint of the hardoover tst edition t988 No part 01 the material protected by this copyrig...
null	null	null	null	C!oo[co[s Preface XI Mean Boundary Layer Characteristics Turbulent transport Taylor's hypothesis 1.1 A bowlCjary-layer definition 1.2 Wind and flow 1.3 1.4 l.5 Virtual potential temperature 1.6 Boundary layer depth and slructure 1.7 Micrometeorology 1.8 1.9 General references 1.10 Referenc...
null	null	null	null	vi 3 4 5 BOUNDARYLAYER~OROLOGY Application or the Governing Equations to Turbulent Flow 75 Simplifications, approximations, and scaling arguments 3.1 Methodology 3.2 Basic governing equations 3.3 3.4 Equations for mean variables in a turbulent flow 3.5 Summary of equations, with simplifi...
null	null	null	null	3 Local closure - 6.4 Local closure - 6.5 Local closure - 6.6 Local closure - 6.7 Local closure - 6.8 Nonlocal closure - 6.9 Nonlocal closure - 6.10 References 6.11 Exercises zero and half order first order one-and·a·half order second order third order transilient turbulence theory spectral diffusivi...
null	null	null	null	COmENTS vii 7 8 Boundary Conditions and External Forcings 251 7.1 Effective surface turbulent flux 7.2 Heat budget at the surface 7.3 Radiation budget 7.4 Auxes at interfaces 7.5 Partitioning of flux into sensible and latent portions 7.6 Aux 10 and from the ground 7.7 References 7.8 Ex...
null	null	null	null	viii BOUNDARY LAYER MmTEOROLOGY 10 Measurement and Simulation Techniques 405 Instrument platforms 10.1 Sensor and measurement categories 10.2 Sensor lists 10.3 Active remote sensor observations of morphology 10.4 10.5 Field experiments 10.6 Simulation methods 10.7 Analysis methods 10.8 Refe...
null	null	null	null	14 Geographic Effects 14.1 Geographically generated local winds 14.2 Geographically modified flow 14.3 Urban heat island 14.4 References 14.5 Exercises Appendices Scaling variables and dimensionless groups A. B. Notation C. Useful constants, parameters and conversion factors D. Derivation of vi...
null	null	null	null	Preface Part of the excitement of boundary-layer meteorology is the challenge in :;tudying and one of the unsolved problems of classical physics. understanding turbulent flow - Additional excitement stems from the rich diversity of topics and research methods that we collect under the umbrella of boundary-...
null	null	null	null	By excluding a few chapters, instructors can easily fit the remaining material into a one-semester course. With supplemental readings, the book can serve as a two-semester sequence in atmospheric turbulence and boundary-layer meteorology. Notational diversity proved to be the greatest difficulty. Each ...
null	null	null	null	~ BOUNDARYLAYER~OROLOGY I certainly cannot claim to be an expert in all the myriad subdisciplines of boundary layer meteorology. yet I knew the book should be comprehensive to be useful. My interest and enthusiasm in writing this book motivated many trips to the library. and stimulated ...
null	null	null	null	Bob Murphy. Ruwim Berkowicz. Peter Hildebrand. Don Lenschow. and others. Eric Nelson proofread the manuscript. and helped with the list of notation. Sam Zhang compiled the index. Some of the equations were typeset by Camille Riner and Michelle Vlllldall (her name keeps reappearing). Four years of...
null	null	null	null	Z (m) 1000 500 0 (a) z (m) 500 250 o (b) 1000 Range from lidar (km) Range from lidar (km) Frontispiece lidar images of the aerosol-laden boundary layer, obtained during the FIFE field experiment in Kansas. (a) Convective mixed layer observed at 1030 local time on 1 July 1987, when...
null	null	null	null	Claude V. Palisca HUMANISM IN ITALIAN RENAISSANCE MUSICAL THOUGHT Yale University Press New Haven and London
null	null	null	null	Humanism in Italian Renaissance Musical Thought
null	null	null	null	To tile memory of my motller Gisella Fleisch/lacker Palisca (1895-1944) I'ublishcd wilh .1SsUtanCr from the Louis 51t'", Memori;al Fund. Copyright 4) 1985 by Yale UniversilY. All righls reserved. This book may 1101 br reproduced. in whole or in pUI. ill ;any form (beyolld Ih;al copy ill...
null	null	null	null	I. Music-haly-15th century-History ;and criticism. 2. Music h.:aly-16th cmlury-History .and crilicism. 3. nen;aissance-haly. 4. Humanism. I. Tide. ML2'JeI.2.1)34 1985781.745 as-8ICJO ISDN 0-300-03302-8 The paprr in Ihis book meets thr guidelincs for permanence and du rability of the Committee on ...
null	null	null	null	Contents Preface ONE Introduction: An Italian Renaissance in Music? TWO The Rediscovery of the Ancient Sources THREE The Earliest Musical Humanists: Pietro d'Abano FOUR The Earliest Musical Humanists: Giorgio Valla FIVE The Earliest Musical Humanists: Carlo Valgulio The Proem to...
null	null	null	null	Contents TWELVE A Natural New Alliance of the Arts Grammar Mei on tonic accent Pietro Bembo THIRTEEN The Poetics of Music Music as Poetry Vincenzo Galilci The Poetics of Imitation The Case against Mimesis: Francesco Patrizi Expressing the Affections FOURTEEN Theory of Dramatic Music ...
null	null	null	null	Preface Music historians have long been aware of a link between the revival of ancient learning and the changes in musical style and theory that occurred during the Renaissance. But the ties to antiquity have been hard to pin down. because ancient music could not be recreated as...
null	null	null	null	PaulO. Kristeller. Nino Pirrotta, Leo Schrade, D. P. Walker. and Edith Weber, for I have learned enormously from them. In general the field has been dominated by the hunt for parallels between musical manifestations and those in other ans and humanities that show a strong reliance on ancient model...
null	null	null	null	Preface xiii University. enriched and enhanced this book in many ways. by lending me microfilms of Greek manuscripts that once belonged to Giorgio Valla. by letting me use some of the information in the catalog of Greek manuscripts of music theory he is preparing for the RepertOire imernationale...
null	null	null	null	limiting myself to those connections between music and ancient thought that we know existed in the minds of Renaissance men because they are recorded in writing. These considerations. too. explain why I have not allocated much space to past literature on musical humanism. As a conseque...
null	null	null	null	The Whitney Griswold Fund of Yale University aided the preparation of the manuscript. And. of course. the Yale libraries. p~r ticularly the Music Library and the Beinecke: Rare Book and Manuscnpt Library. provided a solid home base for my investigations. Several of my students at Yal...
null	null	null	null	It ONE Introduction: An Italian Renaissance in Music? istorians generally view the Renaissance as a movement that began in Italy and spread northward. Music histo rians. however. have habitually begun the study of music in the Renaissance with composers associated with France Jnd the Low ...
null	null	null	null	but it is dis concerting when applied to cultural historiography. If history in general has a proverbial "problem of the Renaissance." how much more acute it is in music history! Heinrich Besseler. reflecting on his own work in Renaissance studies since I. Gustave: R.e:rse. MIlS;( ;11 IlIr RtI...
null	null	null	null	Game Theory
null	null	null	null	GAME THEORY Analysis of Conflict ROGER B. MYERSON HARVARD UNIVERSITY PRESS Cambridge, Massachusetts London, England
null	null	null	null	Copyright © 1991 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America First Harvard University Press paperback edition, 1997 Library of Congress Cataloging-in-Publication Data Myerson, Roger B. Game theory : analysis of conflict / Roger B. Myerson. p. (c...
null	null	null	null	For Gina, Daniel, and Rebecca With the hope that a better understanding of conflict may help create a safer and more peaceful world
null	null	null	null	Contents Preface (cid:9) 1 Decision-Theoretic Foundations (cid:9) 1.1 (cid:9) Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 5 1.3 Axioms 9 1.4 The Expected-Utility Maximization Theorem 12 1.5 (cid:9) 1.6 Bayesian Conditional-Probability Systems 21 1.7 Limitations of the B...
null	null	null	null	viii (cid:9) Contents 3.3 Computing Nash Equilibria 99 3.4 Significance of Nash Equilibria 105 3.5 The Focal-Point Effect 108 3.6 The Decision-Analytic Approach to Games 114 3.7 Evolution, Resistance, and Risk Dominance 117 3.8 Two-Person Zero-Sum Games 122 3.9 (cid:9) 3.10 Purification of Randomized Stra...
null	null	null	null	5 (cid:9) 5.6 (cid:9) 5.7 Generic Properties 239 5.8 Conclusions 240 Exercises 242 6 Games with Communication (cid:9) 244 Contracts and Correlated Strategies 244 6.1 (cid:9) 6.2 Correlated Equilibria 249 6.3 Bayesian Games with Communication 258 6.4 Bayesian Collective-Choice Problems and Bayesian Bar...
null	null	null	null	Contents (cid:9) ix 6.5 Trading Problems with Linear Utility 271 6.6 General Participation Constraints for Bayesian Games with Contracts 281 6.7 Sender-Receiver Games 283 6.8 Acceptable and Predominant Correlated Equilibria 288 6.9 Communication in Extensive-Form and Multistage Games 294 Exercises 299...
null	null	null	null	1 (cid:9) 9.2 Characteristic Functions with Transferable Utility 422 9.3 The Core 427 9.4 The Shapley Value 436 9.5 Values with Cooperation Structures 444 9.6 Other Solution Concepts 452 9.7 Coalitional Games with Nontransferable Utility 456
null	null	null	null	x (cid:9) Contents 9.8 Cores without Transferable Utility 462 9.9 Values without Transferable Utility 468 Exercises 478 Bibliographic Note 481 10 Cooperation under Uncertainty (cid:9) 483 10.1 Introduction 483 10.2 Concepts of Efficiency 485 10.3 An Example 489 10.4 Ex Post Inefficiency and Subseque...
null	null	null	null	Preface Game theory has a very general scope, encompassing questions that are basic to all of the social sciences. It can offer insights into any economic, political, or social situation that involves individuals who have different goals or preferences. However, there is a fundamental unity and co- herent methodol...
null	null	null	null	xii (cid:9) Preface In every chapter, there are some topics of a more advanced or spe- cialized nature that may be omitted without loss of subsequent compre- hension. I have not tried to "star" such sections or paragraphs. Instead, I have provided cross-references to enable a reader to skim or pass over sections t...
null	null	null	null	Myrna Wooders, Robert Marshall, Dov Mon- derer, Gregory Pollock, Leo Simon, Michael Chwe, Gordon Green, Akihiko Matsui, Scott Page, and Eun Soo Park read parts of the manu- script and gave many valuable comments. In writing the book, I have also benefited from the advice and suggestions of Lawrence Ausubel, Raymond ...
null	null	null	null	Preface (cid:9) xiii Foundation, and by grants from the National Science Foundation and the Dispute Resolution Research Center at Northwestern University. Last but most, I must acknowledge the steady encouragement of my wife, my children, and my parents, all of whom expressed a continual faith in a writing proje...
null	null	null	null	Game Theory
null	null	null	null	1 Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. Game theory provides general mathematical techniques for analyzing situations in which two or ...
null	null	null	null	2 (cid:9) 1 • Decision-Theoretic Foundations behavior in conflict. Thus, it may be natural to hope that advances in the most fundamental and theoretical branches of the social sciences might be able to provide the understanding that we need to match our great advances in the physical sciences. This hope is one of...
null	null	null	null	The idea that a rational decision-maker should make decisions that will maximize his expected utility payoff goes back at least to Bernoulli (1738), but the modern justification of this idea is due to von Neumann and Morgenstern (1947). Using remarkably weak as- sumptions about how a rational decision-maker should b...
null	null	null	null	1.1 Rationality and Intelligence (cid:9) 3 his expected utility. We call this result the expected-utility maximization theorem. It should be emphasized here that the logical axioms that justify the expected-utility maximization theorem are weak consistency assump- tions. In derivations of this theorem, the key ...
null	null	null	null	More gener- ally, the utility payoff of an individual may depend on many variables besides his own monetary worth (including even the monetary worths of other people for whom he feels some sympathy or antipathy). When there is uncertainty, expected utilities can be defined and com- puted only if all relevant uncert...
null	null	null	null	4 (cid:9) 1 • Decision-Theoretic Foundations which quantitatively measure the likelihood of each event. Ramsey (1926) and Savage (1954) showed that, even where objective probabili- ties cannot be assigned to some events, a rational decision-maker should be able to assess all the subjective probability numbers that...
null	null	null	null	For an example of a theory that assumes rationality but not intelli- gence, consider price theory in economics. In the general equilibrium model of price theory, it is assumed that every individual is a rational utility-maximizing decision-maker, but it is not assumed that individuals understand the whole structure ...
null	null	null	null	1.2 • Basic Concepts (cid:9) 5 Of course, the assumption that all individuals are perfectly rational and intelligent may never be satisfied in any real-life situation. On the other hand, we should be suspicious of theories and predictions that are not consistent with this assumption. If a theory predicts that som...
null	null	null	null	There is a vast literature on axiomatic derivations of the subjective probability, expected-utility maximization, and Bayes's formula, begin- ning with Ramsey (1926), von Neumann and Morgenstern (1947), and Savage (1954). Other notable derivations of these results have been offered by Herstein and Milnor (1953), Luc...
null	null	null	null	6 (cid:9) 1 • Decision-Theoretic Foundations scombe and Aumann (1963), and Pratt, Raiffa, and Schlaiffer (1964); for a general overview, see Fishburn (1968). The axioms used here are mainly borrowed from these earlier papers in the literature, and no attempt is made to achieve a logically minimal set of axioms. (...
null	null	null	null	On the other hand, many events do not have obvious probabilities; the result of a future sports event or the future course of the stock market are good examples. We refer to such events as subjective un- knowns. Gambles that depend on subjective unknowns correspond to the "horse lotteries" of Anscombe and Aumann (...
null	null	null	null	1.2 Basic Concepts (cid:9) 7 the prize may depend on both objective unknowns (which may be di- rectly described by probabilities) and subjective unknowns (which must be described by a state variable). (In the terminology of Fishburn, 1970, we are allowing extraneous probabilities in our model.) Let us now develo...
null	null	null	null	(Following common probability notation, "1" in parentheses may be interpreted here to mean "given.") For this interpretation to make sense, the state must be defined broadly enough to summarize all subjective unknowns that might influence the prize to be received. Then, once a state has been specified, only objecti...
null	null	null	null	• • 8 (cid:9) 1 Decision-Theoretic Foundations prize in X represents a complete specification of all aspects that the decision-maker cares about in the situation resulting from his decisions. Thus, the decision-maker should be able to assess a preference ordering over the set of lotteries, given any informat...
null	null	null	null	We may write >, and — for >n, and —n, respectively. That is, when no conditioning event is mentioned, it should be assumed that we are referring to prior preferences before any states in ft are ruled out by observations. Notice the assumption here that the decision-maker would have well- defined preferences over ...
null	null	null	null	1.3 • Axioms (cid:9) 9 (af + (1 — a)g)(x1t) = af(x1t) + (1 — a)g(x1t), Vx E X, Vt E To interpret this definition, suppose that a ball is going to be drawn from an urn in which a is the proportion of black balls and 1 — a is the proportion of white balls. Suppose that if the ball is black then the decision...
null	null	null	null	AXIOM 1. 1A (COMPLETENESS). f g or g s f. AXIOM 1. 1B (TRANSITIVITY). If f zs g and g (cid:9) h then f -?-s h. It is straightforward to check that Axiom 1.1B implies a number of other transitivity results, such as if f — s g and g — s h then f— s h; and if f >s g and g h then f>, h. Axiom 1.2 a...
null	null	null	null	10 (cid:9) 1 • Decision-Theoretic Foundations AXIOM 1.3 (MONOTONICITY). If f >s h and 0 5_ 13<a51, then of + (1 — a)h >s I3f + ( 1 — (3)h. Building on Axiom 1.3, Axiom 1.4 asserts that -yf + (1 — y)h gets better in a continuous manner as y increases, so any lottery that is ranked between f and h is j...
null	null	null	null	In Axioms 1.6A and 1.6B, these events are subjective unknowns, subsets of f/. AXIOM 1.5A (OBJECTIVE SUBSTITUTION). If e f and g >s h and 0 s a (cid:9) 1, then ae + (1 — a)g (cid:9) of + (1 — a)h. AXIOM 1.5B (STRICT OBJECTIVE SUBSTITUTION). If e >s f h and 0 < a 5_ 1, then ae + (1 — a)g >s of + (1 —...
null	null	null	null	1.3 Axioms (cid:9) 11 To fully appreciate the importance of the substitution axioms, we may find it helpful to consider the difficulties that arise in decision theory when we try to drop them. For a simple example, suppose an individual would prefer x over y, but he would also prefer .5[y]+ .5[z] over .5[x] + .5...
null	null	null	null	But this lottery .5[x] + .5[z] is worse than w. So we get the contradictory conclu- sion that he should have taken w in the first place. Thus, if we are to talk about "rational" decision-making without sub- stitution axioms, then we must specify whether rational decision-makers are able to commit themselves to foll...
null	null	null	null	12 (cid:9) 1 Decision-Theoretic Foundations AXIOM 1.7 (INTEREST). For every state t in S2, there exist prizes y and z in X such that [y] >m [z]. Axiom 1.8 is optional in our analysis, in the sense that we can state a version of our main result with or without this axiom. It asserts that the decision-maker ...
null	null	null	null	That is, E p(u( f )1 S) =- (cid:9) p(tIS) (cid:9) u(x,t)f(x1t). THEOREM 1.1. Axioms I.1AB, 1.2, 1.3, 1.4, 1.5AB, 1.6AB, and 1.7 are jointly satisfied if and only if there exists a utility function u:X X SI —) R and a conditional-probability function A(1-1) such that
null	null	null	null	1.4 • Expected-Utility Maximization Theorem (cid:9) 13 (1.3) (cid:9) (1.4) (cid:9) max u(x,t) = 1 and min u(x,t) = 0, bit E sEX (cid:9) xEX p(R1T) = p(Rjs)p(siT), VR, VS, and VT such that RCSCTCfland SOO; (1.5) (cid:9) f (cid:9) g if and only if E p(u( f )IS) (cid:9) E p(u(g)IS), Vf,g E L, VS...
null	null	null	null	Notice that, with X and Cl finite, there are only finitely many utility and probability numbers to assess. Thus, the decision-maker's preferences over all of the infinitely many lotteries in L can be com- pletely characterized by finitely many numbers. To apply this result in practice, we need a procedure for a...
null	null	null	null	14 (cid:9) 1 • Decision-Theoretic Foundations and worst prizes can be found in every state because the preference relation (....{,}) forms a transitive ordering over the finite set X. For any event S in E•„ let bs denote the lottery such that bs(.1t) = a,(.1t) if t E S, b5(.1t) = a„(•1t) if t 0 S. T...
null	null	null	null	Then let p(tls) equal the number that he specifies, such a, that b{,} (cid:9) p(tIS)a, + (1 — p(t1S))ao. In the proof of Theorem 1.1, we show that defining u and p in this way does satisfy the conditions of the theorem. Thus, finitely many questions suffice to assess the probabilities and utilities that comp...
null	null	null	null	1.4 .Expected-Utility Maximization Theorem (cid:9) 15 u(x,t)b{, } + (1 - u(x,t))ao. Then subjective substitution implies that, for every event S, s u(x,t)b{,} + (1 - u(x,t))ao. Axioms 1.5A and 1.5B together imply that f (cid:9) g if and only if ( 1 (cid:9) i ) f + (1 1 (cid:9) 1,—(1-1 ) ao (cid:9) 1...
null	null	null	null	16 (cid:9) 1 • Decision-Theoretic Foundations (Ep(u(f )1 S)/1,111)a, + (1 — (Ep(u(f )1S)/IniDao (Ei (it(g)1S)/ini)a l + (1 — (Ep(u(g)IS)/ini))ao• But by monotonicity, this final relation holds if and only if E p(u(f)1S) (cid:9) E p(u(g)IS), because interest and strict subjective substitution guarantee t...
null	null	null	null	Now, suppose that R CSC T. Using b, — s a, again, we get b„ (cid:9) p(RIS)b, + (1 — p(RIS))ao. Furthermore, because b„, bs, and a, all give the same worst prize outside 5, relevance also implies b„ --r\s p(Ris)b, + (1 — p(RIS))ao. (Here T\S = {ti t E T, t 0 S}.) So, by subjective and objective subst...
null	null	null	null	1.4 • Expected-Utility Maximization Theorem (cid:9) 17 p(RIT)a, + (1 — p(RiT))ao. Also, a, >7- a0, so monotonicity But b, (cid:9) implies that p(R1T) = p(Ris)p(sIT). Thus, Bayes's formula (1.4) follows from the axioms. If y is the best prize and z is the worst prize in state t, then [y] {t} a, and [z] ...
null	null	null	null	By (1.5), E p(u(f)IS) E p(u(g)IT). But Bayes's formula (1.4) implies that Ep(u(f)1S U T) = p(tis U T)f(x1t)u(x,t) r = E E p(ths)p(sis U T)f(x1t)u(x,t) /ES vEX + (cid:9) E POI nP(TIs U T)f(xlt)u(x,t) 1E7' vEX = p(SIS U T)E p(u( f )1 S) + pals U T)E p(u( f )1S) and Ep(u(g)1S U T) = p(SIS...
null	null	null	null	18 (cid:9) 1 Decision-Theoretic Foundations 1.5 Equivalent Representations When we drop the range condition (1.3), there can be more than one pair of utility and conditional-probability functions that represent the same decision-maker's preferences, in the sense of condition (1.5). Such equivalent representatio...
null	null	null	null	Suppose first that A and 13(•) exist as described in the theorem. Then, for any lottery f, E q(v( f )1 S) (cid:9) f(xlt)q(tIS)v(x,t) IES xEX = (cid:9) E focloop(o)u(x,t) + B(0) IES xEX = AEIf(Xlop(tis)u(x,t) + (cid:9) B(t) (cid:9) foclo tES xEX (cid:9) tES (cid:9) xEX = AE p (u(f)IS) + (cid:9) ...
null	null	null	null	1.5 • Equivalent Representations (cid:9) 19 Conversely, suppose now that v and q represent the same preference ordering as u and p. Pick any prize x and state t, and let X = E q(v(cx t)I S) — E q(v(ao)IS) ' E q(v (a 1) I S) — E q(v(ao)I S) Then, by the linearity of the expected -value operator, Eq(...
null	null	null	null	zEX Thus, going back to the definition of X, we get p(tis)u(x,t) .--- q(t I S)(v(x a) — min v(z,t)) zEX E q(v(a 1)1 S) — E q(v(a0)I S) Now let A = E q(v (a 01 S) — E q(v (601 S) , and let B(t)' = q(tI S) min v(z,t). zEX
null	null	null	null	20 (cid:9) 1 • Decision-Theoretic Foundations Then Ap(tIS)u(x,t) + B(t) = q(tIS)v(x,t). Notice that A is independent of x and t and that B(t) is independent of x. In addition, A > 0, because a, >s a, implies Eq(v(a,)IS) > E ,(v (a 0)1S). n It is easy to see from Theorem 1.2 that more than one probabil...
null	null	null	null	Proof. Let A = ,(v(a S) — from the proof of Theorem 1.2, q(v(ao) I S), and let C = minzExv(z). Then, Ap(t1S)u(x) + q(tIS)C = q(tIS)v(x), Vx E X, Vt E S. Summing this equation over all t in S, we get Au(x) + C = v(x). Then, substituting this equation back, and letting x be the best prize so u(x) ...
null	null	null	null	1.6 • Bayesian Conditional-Probability Systems (cid:9) 21 1.6 Bayesian Conditional-Probability Systems We define a Bayesian conditional-probability system (or simply a conditional- probability system) on the finite set f2 to be any conditional-probability function p on SI that satisfies condition (1.4) (Bayes...
null	null	null	null	This fact is asserted by the following theorem. For the proof, see Myerson (1986b). THEOREM 1 . 4 . The probability function p is a Bayesian conditional-prob- ability system in if and only if there exists a sequence of probability distributions {fik },7_, in A°(S2) such that, for every nonempty subset S of Cl ...
null	null	null	null	22 (cid:9) 1 Decision-Theoretic Foundations 1.7 Limitations of the Bayesian Model We have seen how expected-utility maximization can be derived from axioms that seem intuitively plausible as a characterization of rational preferences. Because of this result, mathematical social scientists have felt confident th...
null	null	null	null	When a person has had sufficient time to learn about a situation and think clearly about it, we can expect that he will make relatively few mistakes. Thus, we can expect expected-utility maximization to be predictively accurate in many situations. However, experimental research on decision-making has revealed som...
null	null	null	null	1.7 • Limitations of the Bayesian Model (cid:9) 23 here three of the best-known examples in which people often seem to violate expected-utility maximization: one in which utility functions seem inapplicable, one in which subjective probability seems inapplica- ble, and one in which any economic model seems inappli...
null	null	null	null	Other paradoxes have been generated that challenge the role of subjective probability in decision theory, starting with a classic paper by Ellsberg (1961). For a simple example of this kind, due to Raiffa (1968), let X = {—$100,$100}, let SZ = {A,N}, and let bA($1001A) = 1 = bA(—$1001N), b,(—$1001A) = 1 = bN($10...
null	null	null	null	24 (cid:9) 1 • Decision-Theoretic Foundations the state in which the National League will win the next All-Star game. (One of these two leagues must win the All-Star game, because the rules of baseball do not permit ties.) Many people who feel that they know almost nothing about American baseball express the pr...
null	null	null	null	You did not buy tickets in advance, but you put $40 in your pocket when you left home. You suddenly realize that the $40 has fallen out of your pocket and is lost. You must decide whether to buy a pair of tickets for $40 with your charge card (which you still have) or simply go home. As Kahneman and Tversky (1982...
null	null	null	null	1.7 • Limitations of the Bayesian Model (cid:9) 25 wealth and theatrical consumption are all that should matter to the decision-maker in these situations. Any analytical model must derive its power from simplifying assump- tions that enable us to see different situations as analytically equivalent, but such simp...
null	null	null	null	For example, let us reconsider the problem of betting on the All-Star game. To get a decision-maker to express his preference ordering (.--11) over fb,, 6,, .5[$100] + .5[—$100]}, we must ask him, for each pair in this set, which bet would he choose if this pair of bet-options were offered to him uninformatively, ...
null	null	null	null	26 (cid:9) 1 Decision-Theoretic Foundations an opportunity to bet on one side of the All-Star game should (by Bayes's formula) make someone who knows little about baseball decrease his subjective probability of the event that this side will win, so he may well prefer to bet on a fair coin toss. We can try to offe...
null	null	null	null	Consider a decision-maker who has a state-dependent utility function u:X x SZ --> R and can choose any x in X. That is, let us reinterpret X as the set of decision-options available to the decision-maker. If his subjective probability of each state t in Si were p(t) (that is, p(t) = 0111), Vt E 14), then the d...
null	null	null	null	1.8 Domination (cid:9) 27 (1.7) (cid:9) E p(t)u(y,t) (cid:9) E p(t)u(x,t), vx E X. (En (cid:9) tEO Convexity is an important property of many sets that arise in math- ematical economics. A set of vectors is convex iff, for any two vectors p and q and any number X between 0 and 1, if p is in the set and ...
null	null	null	null	With only two states, p(01 ) = 1 — p(02). The decision a is optimal for the decision-maker iff the following two inequalities are both satisfied: 8p(01 ) + 1(1 — p(01 )) (cid:9) 5p(0,) + 3(1 — p(01 )) 8p(01 ) + 1(1 — p(01 )) > 4p(01 ) + 7(1 — p(01 )). Table 1.1 Expected utility payoffs for states 0, and 02 ...
null	null	null	null	28 (cid:9) 1 Decision-Theoretic Foundations The first of these inequalities asserts that the expected utility payoff from a must be at least as much as from p, and the second asserts that the expected utility payoff from a must be at least as much as from y. By straightforward algebra, these inequalities imply t...
null	null	null	null	Option 13 is a kind of intermediate decision, in that it is neither best nor worst in either column of the payoff table. However, such intermediate decision-options are not nec- essarily dominated. For example, if the utility payoffs from decision 13 were changed to 6 in both states, then 13 would be the optimal d...
null	null	null	null	1.8 Domination (cid:9) 29 Tails. We may denote this strategy by .5[a] + .5[y], because it gives a probability of .5 to a and -y each. If the true state were 01, then this randomized strategy would give the decision-maker an expected utility payoff of .5 x 8 + .5 x 4 = 6, which is better than the payoff of 5 that ...
null	null	null	null	We have now used the term "strongly dominated" in two different senses. The following theorem asserts that they are equivalent. THEOREM 1.6. Given u:X x f/ —> R, where X and ft are nonempty finite sets, and given any y in X, there exists a randomized strategy o- in A(X) such that y is strongly dominated by c...

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CORPUS ANALYSIS REPORT

Document Statistics:

Total PDF documents: 31
Total pages: 11890
Pages with errors: 0
Empty pages: 1082
Pages per document:
- Average: 383.5
- Minimum: 2
- Maximum: 871

Content Statistics (words per page):

Minimum: 1
Maximum: 2,524
Average: 397.1
Median: 417.0

Words per Page Distribution:

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  41.4 |█████                                             | 145
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Outliers > 808.0 words: 107 pages

Pages per Document Distribution:
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  88.9 |███████                                           | 1
 175.8 |███████████████████████████████████               | 5
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Metadata Statistics:

Documents with metadata: 31
Unique CreationDate values: 28
Unique GTS_PDFXVersion values: 1
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Unique Producer values: 24
Unique Creator values: 16
Unique Author values: 14
Unique Title values: 16
Unique EBX_PUBLISHER values: 5
Unique Keywords values: 6
Unique Session Id values: 2
Unique Subject values: 3
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Document Details:

American Herbal Academy - The Native American Herbalism Encyclopedia - A Complete Medical Herbs Handbook_ Discover How to Find and Grow Forgotten Herbs a (2020, Herbalism Academy) - libgen.li.pdf Pages: 167 Author: Academy, American Herbal Creator: calibre 3.48.0 [https://calibre-ebook.com]
Claude V. Palisca - Humanism in Italian Renaissance Musical Thought (1986, Yale University Press) - libgen.li.pdf Pages: 240 Creator: PFU ScanSnap Manager 4.1.12
David Griffiths - Introduction to elementary particles (1987, John Wiley & Sons Inc) - libgen.li.pdf Pages: 403 Author: David Griffiths Creator: PdfCompressor 3.1.34
David Hoffmann - Medical Herbalism_ The Science and Practice of Herbal Medicine (2003, Inner Traditions _ Bear & Co) - libgen.li.pdf Pages: 675
Dr Simon J. D. Prince - Computer Vision_ Models, Learning, and Inference (2012, Cambridge University Press) - libgen.li.pdf Pages: 582 Author: Prince, Simon J. D. Creator: LaTeX with hyperref package
Ellen Meiksins Wood - Liberty and Property_ A Social History of Western Political Thought from Renaissance to Enlightenment (2012, Verso Books) - libgen.li.pdf Pages: 336 Author: Ellen Meiksins Wood
Jacob Burckhardt - The Civilization of the Renaissance in Italy - libgen.li.pdf Pages: 281 Creator: PScript5.dll Version 5.2.2
John Rewald - The History of Impressionism (1961, Museum of Modern Art) - libgen.li.pdf Pages: 673 Author: Rewald, John, 1912-1994 Creator: Digitized by the Internet Archive
John Von Neumann, Oskar Morgenstern - Theory of Games and Economic Behavior (1966, Princeton University Press) - libgen.li.pdf Pages: 674
Michael Moore - Medicinal Plants of the Mountain West (2003, Museum of New Mexico Pr) - libgen.li.pdf Pages: 368 Creator: PFU ScanSnap Manager 4.2.14
Otto Georg Von Simson - The Gothic Cathedral_ Origins of Gothic Architecture and the Medieval Concept of Order (1956, Harper & Row) - libgen.li.pdf Pages: 177 Creator: Adobe Acrobat 9.4
Paul Oskar Kristeller, Thomas A. Brady, Heiko Augustinus Oberman - Itinerarium Italicum_ The Profile of the Italian Renaissance in the Mirror of Its European Transformations (Studies in Medieval (1975, Brill Academic Publishers) - libgen.li.pdf Pages: 580
Risto Saarinen - Weakness of Will in Renaissance and Reformation Thought (2011, Oxford University Press, USA) - libgen.li.pdf Pages: 257 Author: Saarinen, Risto.
Roger B. Myerson - Game Theory_ Analysis of Conflict (1997, Harvard University Press) - libgen.li.pdf Pages: 587 Creator: ImageToPDF
Samuel K. Cohn Jr. - Cultures of Plague_ Medical thought at the end of the Renaissance (2010) - libgen.li.pdf Pages: 357
Stull, Roland B. - An Introduction to Boundary Layer Meteorology __ __ Front_matter (1988) [10.1007_978-94-009-3027-8_FM] - libgen.li.pdf Pages: 11
[American Journal of Physics 1997-may vol. 65 iss. 5] Weinberg, Steven - Post-Use Review. The Quantum Theory of Fields. Vol. I_ Foundations (1997) [10.1119_1.18603] - libgen.li.pdf Pages: 2
[Book 1 in the Surface Series] Alainna MacPherson - Beneath the Surface (2020) - libgen.li.pdf Pages: 306 Author: Alainna MacPherson Creator: calibre (4.12.0) [https://calibre-ebook.com]
[Harvard Historical Studies (Book 98)] John Buckler - The Theban Hegemony, 371-362 BC (Harvard Historical Studies) (1980, Harvard University Press) - libgen.li.pdf Pages: 177 Author: Scan2Net Creator: BE4-SGS-V2
[Harvard Historical Studies, 88] Angeliki E. Laiou - Constantinople and the Latins_ The Foreign Policy of Andronicus II, 1282-1328 (Harvard Historical Studies) (1972, Harvard University Press) - libgen.li.pdf Pages: 399 Creator: Adobe Acrobat 8.0
[Harvard Historical Studies] Aurora Gómez-Galvarriato_ Aurora Gómez-Galvarriato - Industry and Revolution _ Social and Economic Change in the Orizaba Valley, Mexico (2013, Harvard University Press) - libgen.li.pdf Pages: 362 Author: someAuthor
[Harvard Historical Studies] David Paull Nickles - Under the Wire_ How the Telegraph Changed Diplomacy (Harvard Historical Studies) (2003, Harvard University Press) - libgen.li.pdf Pages: 272 Author: David Paull Nickles
[Harvard Historical Studies] Sarah Kinkel - Disciplining the Empire_ Politics, Governance, and the Rise of the British Navy (2018, Harvard University Press) - libgen.li.pdf Pages: 317 Author: Sarah Kinkel Creator: Adobe InDesign CC 2015 (Macintosh)
[Harvard Historical Studies_ 18] Albert Howe Lybyer - The Government of the Ottoman Empire in the Time of Suleiman the Magnificent (1913, Harvard University Press) [10.4159_harvard.9780674337053] - libgen.li.pdf Pages: 360
[Harvard Historical Studies_ 9] Arthur Lyon Cross - The Anglican Episcopate and the American Colonies (1902, Harvard University Press) [10.4159_harvard.9780674368910] - libgen.li.pdf Pages: 380
[Harvard Historical Studies_ Ser.] Meredith Martin - Dairy Queens_ The Politics of Pastoral Architecture from Catherine de' Medici to Marie-Antoinette (2011, Harvard University Press) - libgen.li.pdf Pages: 337 Author: someAuthor
[Harvard historical studies 118] Robert McCune Kingdon - Adultery and Divorce in Calvin's Geneva 118 (1994, Harvard University Press) - libgen.li.pdf Pages: 226 Author: Kingdon, Robert M. (Robert McCune), 1927- Creator: Internet Archive PDF 1.4.13; including mupdf and pymupdf/skimage
[Harvard historical studies 183] Manjapra, Kris - Age of Entanglement_ German and Indian Intellectuals Across Empire (2014, Harvard University Press) - libgen.li.pdf Pages: 455 Author: Manjapra, Kris;
[International Geophysics] John M. Wallace, John Michael Wallace, Peter V. Hobbs - Atmospheric Science. An Introductory Survey (2006, Academic Press) - libgen.li.pdf Pages: 505 Author: INTEGRA Creator: Adobe Acrobat 8.1 Combine Files
[Quantum Field Theory and the Standard Model] Schwartz, M.D. - Quantum Field Theory and the Standard Model (2013, Cambridge University Press) - libgen.li.pdf Pages: 871 Creator: Canon iR-ADV C5045 PDF
[The International Geophysics 88 89] James R. Holton - An Introduction to Dynamic Meteorology (2004, Academic Press) - libgen.li.pdf Pages: 553

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