234:
399:
Raiffa argues as follows. Suppose someone has the following preferences. If forced to take Gamble A they would bet on the boxer, but if given a free choice between the gambles they would prefer Gamble B. Presumably, such a person when allowed to choose Gamble A would prefer to simply bet on the boxer
384:
Gamble A, in which you bet on the outcome of a fight between the world's greatest boxer and the world's greatest wrestler in a ring fight. (Assume you are fairly ignorant about martial arts and would have great difficulty making a choice of whom to bet on.) If your chosen champion wins you win $ 500
388:
Gamble B. Draw a ball from an opaque urn known to contain 50 orange and 50 blue balls. You will receive $ 500 if you draw an orange ball and nothing for a blue ball. The balls have been thoroughly mixed and you should assume that all balls are equally likely to be drawn. The draw takes place after
416:, they should also prefer to bet on the boxer than on Gamble B. A similar argument can be used to show that when the player has no preference between the boxer and the wrestler he should also have no preference between Gamble A and Gamble B.
395:
Raiffa argues that a decision-maker should in fact assign a subjective probability of one-half to each outcome of Gamble A, provided that no information was available that makes one outcome more likely than the other.
863:
527:
Raiffa, H. and
Schlaifer, R. (1961). Applied Statistical Decision Theory. Division of Research, Harvard Business School, Boston. 1968 paperback edition, MIT Press, Press, Cambridge, MA. Wiley Classics Library edition
215:
After service in the Army Air Forces during World War II, Raiffa received a bachelor's degree in mathematics in 1946, a master's degree in statistics in 1947 and a PhD in mathematics in 1951, all from the
392:
Many people would feel more unsure about taking Gamble A in which the probabilities are unknown, rather than Gamble B, in which the probabilities are easily seen to be one half for each outcome.
848:
534:
Keeney, R. L. and Raiffa, H. (1976). Decisions with
Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York. Reprinted, Cambridge Univ. Press, New York (1993). MR0449476
419:(The axiom of substitutability says that if someone is indifferent between outcomes A and B and indifferent between outcomes A and C, they should be indifferent between B and C. The
400:
rather than toss a coin to decide the matter of whether they should bet on the boxer or the wrestler. But this randomised approach is equivalent to Gamble B. So, by the
838:
549:
Raiffa, H., Richardson, J. and
Metcalfe, D. (2003). Negotiation Analysis: The Science and Art of Collaborative Decision. Harvard Univ. Press, Cambridge, MA.
204:
638:
I think of myself as a decision analyst who believes in using subjective probabilities. I would prefer being called a "subjectivist" than a "Bayesian."
868:
430:
disagree with Raiffa's reasoning and have devised alternative interpretations of decision theory. One of the most radical departures is
818:
735:
540:
Pratt, J. W., Raiffa, H. and
Schlaifer, R. (1995). Introduction to Statistical Decision Theory. MIT Press, Cambridge, MA. MR1326829
823:
298:
270:
586:
557:
531:
Raiffa, H. (1968). Decision
Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley, Reading, MA.
843:
317:
277:
153:
853:
833:
828:
676:
552:
Raiffa, H. (2011). Memoir: Analytical Roots of a
Decision Scientist. CreateSpace Independent Publishing Platform
715:
284:
255:
251:
664:
I got an idea: call it applied systems analysis, because nobody will know what it means. We had a clean slate.
858:
787:
467:. Annals of Mathematics Studies. Vol. 2. Princeton, N. J.: Princeton University Press. pp. 51–73.
777:
543:
Hammond, J. S., Keeney, R. L. and Raiffa, H. (1998). Smart
Choices. Harvard Business School Press, Boston.
602:
Fienberg, Stephen E. (2008). "The Early
Statistical Years: 1947–1967. A Conversation with Howard Raiffa".
354:
scientist the idea of using
Bayesian methods to search for a missing US Air Force hydrogen bomb lost near
266:
385:
otherwise you get nothing. You place your choice in a sealed envelope, which is opened after the game.
423:
says that if someone prefers outcome A to B and also prefers B to C, then they should prefer A to C.)
359:
244:
173:
98:
346:
A lecture of his in the 1960s concerning the use of
Bayesian methods for betting on horses gave
431:
370:
217:
177:
69:
443:
420:
381:
Consider a situation in which you are required to gamble and are given two possible gambles.
363:
355:
813:
808:
519:
472:
291:
537:
Raiffa, H. (1982). The Art and Science of Negotiation. Harvard Univ. Press, Cambridge, MA.
8:
409:
485:
629:
611:
460:
435:
181:
86:
711:
704:
582:
553:
491:
374:
192:
108:
759:
633:
792:
754:
621:
508:
456:
405:
336:
130:
112:
93:
515:
481:
468:
427:
347:
340:
188:
185:
162:
625:
503:
802:
546:
Raiffa, H. (2002). Negotiation Analysis. Harvard Univ. Press, Cambridge, MA.
783:
651:
373:
and argues that subjective probabilities should follow the same rules (the
864:
University of Michigan College of Literature, Science, and the Arts alumni
495:
362:. Craven used the same methods again in the search for the lost submarine
200:
196:
161:; January 24, 1924 – July 8, 2016) was an American academic who was the
731:
258: in this section. Unsourced material may be challenged and removed.
795:
from the Institute of Operations Research and the Management Sciences
169:
165:
59:
233:
616:
413:
351:
401:
369:
in 1968. Raiffa has analysed situations involving the use of
849:
Members of the United States National Academy of Engineering
576:
455:
145:
139:
463:; Thrall, R. M. (1953). "The double description method".
579:
Profiles in Operations Research: Pioneers and Innovators
654:. International Institute for Applied Systems Analysis
738:
Games and Decisions: Introduction and Critical Survey
510:
Games and decisions: introduction and critical survey
154:
142:
205:
International Institute for Applied Systems Analysis
203:. He helped found and was the first director of the
136:
133:
703:
507:
479:
595:
199:, behavioral decision theory, risk analysis, and
800:
839:Fellows of the American Statistical Association
577:Arjang A. Assad; Saul I. Gass (June 30, 2011).
701:
377:) as objective, frequency-based probabilities.
195:, with works in statistical decision theory,
730:
643:
502:
758:
615:
318:Learn how and when to remove this message
601:
801:
649:
650:Raiffa, Howard (September 23, 1992).
438:completely, in favour of a theory of
740:by R. Duncan Luce and Howard Raiffa"
465:Contributions to the theory of games
256:adding citations to reliable sources
227:
333:Applied Statistical Decision Theory
13:
869:Fellows of the Econometric Society
524:Paperback reprint, Dover, New York
484:; Thrall, Robert M., eds. (1954).
14:
880:
771:
677:"Harvard remembers Howard Raiffa"
232:
129:
819:Harvard Business School faculty
760:10.1090/s0002-9904-1958-10180-9
449:
243:needs additional citations for
824:Harvard Kennedy School faculty
724:
695:
669:
570:
1:
788:Mathematics Genealogy Project
563:
210:
191:and pioneer in the field of
172:, a joint chair held by the
7:
442:, which do not satisfy the
434:, which rejects the use of
10:
885:
793:Biography of Howard Raiffa
626:10.1214/088342307000000104
506:; Raiffa, Howard (1957).
360:1966 Palomares B-52 crash
223:
168:(Emeritus) of Managerial
118:
104:
92:
82:
75:
65:
55:
43:
28:
21:
844:Bayesian econometricians
710:. Simon & Schuster.
389:the ring match is over.
184:. He was an influential
854:American game theorists
702:John P. Craven (2001).
339:introduced the idea of
99:Arthur Herbert Copeland
834:Bayesian statisticians
829:American statisticians
753:(3, Part 1): 108–111.
432:Dempster-Shafer theory
371:subjective probability
218:University of Michigan
178:Harvard Kennedy School
70:University of Michigan
747:Bull. Amer. Math. Soc
444:axioms of probability
421:axiom of transitivity
859:Negotiation scholars
252:improve this article
201:negotiation analysis
604:Statistical Science
514:. New York: Wiley.
490:. New York: Wiley.
652:"History of IIASA"
487:Decision processes
436:probability theory
182:Harvard University
87:Harvard University
375:Kolmogorov axioms
328:
327:
320:
302:
193:decision analysis
189:decision theorist
122:
121:
109:Gordon M. Kaufman
105:Doctoral students
77:Scientific career
16:American academic
876:
765:
764:
762:
744:
728:
722:
721:
709:
699:
693:
692:
690:
688:
673:
667:
666:
661:
659:
647:
641:
640:
619:
599:
593:
592:
574:
523:
513:
499:
482:Coombs, Clyde H.
480:Raiffa, Howard;
476:
440:belief functions
426:Others, such as
406:substitutability
337:Robert Schlaifer
323:
316:
312:
309:
303:
301:
260:
236:
228:
157:
152:
151:
148:
147:
144:
141:
138:
135:
113:Robert B. Wilson
94:Doctoral advisor
50:
39:January 24, 1924
38:
36:
19:
18:
884:
883:
879:
878:
877:
875:
874:
873:
799:
798:
780:page at Harvard
774:
769:
768:
742:
729:
725:
718:
700:
696:
686:
684:
675:
674:
670:
657:
655:
648:
644:
600:
596:
589:
575:
571:
566:
504:Luce, R. Duncan
461:Thompson, G. L.
452:
428:Daniel Ellsberg
358:, Spain in the
348:John Craven USN
341:conjugate prior
324:
313:
307:
304:
267:"Howard Raiffa"
261:
259:
249:
237:
226:
213:
174:Business School
163:Frank P. Ramsey
155:
132:
128:
111:
66:Alma mater
48:
34:
32:
24:
17:
12:
11:
5:
882:
872:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
797:
796:
790:
781:
773:
772:External links
770:
767:
766:
723:
716:
706:The Silent War
694:
683:. 11 July 2016
668:
642:
610:(1): 136–149.
594:
588:978-1441962812
587:
568:
567:
565:
562:
561:
560:
558:978-1461146926
550:
547:
544:
541:
538:
535:
532:
529:
525:
500:
477:
459:; Raiffa, H.;
457:Motzkin, T. S.
451:
448:
379:
378:
344:
343:distributions.
326:
325:
240:
238:
231:
225:
222:
212:
209:
120:
119:
116:
115:
106:
102:
101:
96:
90:
89:
84:
80:
79:
73:
72:
67:
63:
62:
57:
53:
52:
51:(aged 92)
45:
41:
40:
30:
26:
25:
22:
15:
9:
6:
4:
3:
2:
881:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
806:
804:
794:
791:
789:
785:
784:Howard Raiffa
782:
779:
778:Howard Raiffa
776:
775:
761:
756:
752:
748:
741:
739:
733:
727:
719:
713:
708:
707:
698:
682:
678:
672:
665:
653:
646:
639:
635:
631:
627:
623:
618:
613:
609:
605:
598:
590:
584:
580:
573:
569:
559:
555:
551:
548:
545:
542:
539:
536:
533:
530:
526:
521:
517:
512:
511:
505:
501:
497:
493:
489:
488:
483:
478:
474:
470:
466:
462:
458:
454:
453:
447:
445:
441:
437:
433:
429:
424:
422:
417:
415:
411:
407:
403:
397:
393:
390:
386:
382:
376:
372:
368:
367:
361:
357:
353:
349:
345:
342:
338:
334:
330:
329:
322:
319:
311:
308:November 2017
300:
297:
293:
290:
286:
283:
279:
276:
272:
269: –
268:
264:
263:Find sources:
257:
253:
247:
246:
241:This section
239:
235:
230:
229:
221:
219:
208:
206:
202:
198:
194:
190:
187:
183:
179:
175:
171:
167:
164:
160:
159:
150:
126:
125:Howard Raiffa
117:
114:
110:
107:
103:
100:
97:
95:
91:
88:
85:
81:
78:
74:
71:
68:
64:
61:
58:
54:
46:
42:
31:
27:
23:Howard Raiffa
20:
750:
746:
737:
726:
705:
697:
685:. Retrieved
680:
671:
663:
656:. Retrieved
645:
637:
607:
603:
597:
581:. Springer.
578:
572:
509:
486:
464:
450:Bibliography
439:
425:
418:
410:transitivity
398:
394:
391:
387:
383:
380:
365:
332:
314:
305:
295:
288:
281:
274:
262:
250:Please help
245:verification
242:
214:
124:
123:
83:Institutions
76:
49:(2016-07-08)
47:July 8, 2016
814:2016 deaths
809:1924 births
732:Gale, David
681:harvard.edu
197:game theory
56:Nationality
803:Categories
717:0684872137
658:4 December
564:References
278:newspapers
211:Early life
35:1924-01-24
736:"Review:
617:0808.0781
414:utilities
356:Palomares
331:His book
170:Economics
166:Professor
734:(1958).
634:62668400
366:Scorpion
186:Bayesian
60:American
786:at the
687:12 July
520:0087572
473:0060202
352:US Navy
292:scholar
714:
632:
585:
556:
528:(2000)
518:
496:639321
494:
471:
402:axioms
294:
287:
280:
273:
265:
224:Career
743:(PDF)
630:S2CID
612:arXiv
335:with
299:JSTOR
285:books
712:ISBN
689:2016
660:2010
583:ISBN
554:ISBN
492:OCLC
412:for
408:and
364:USS
350:, a
271:news
176:and
44:Died
29:Born
755:doi
622:doi
404:of
254:by
180:at
158:-fə
156:RAY
805::
751:64
749:.
745:.
679:.
662:.
636:.
628:.
620:.
608:23
606:.
516:MR
469:MR
446:.
220:.
207:.
140:eɪ
763:.
757::
720:.
691:.
624::
614::
591:.
522:.
498:.
475:.
321:)
315:(
310:)
306:(
296:·
289:·
282:·
275:·
248:.
149:/
146:ə
143:f
137:r
134:ˈ
131:/
127:(
37:)
33:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
