Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops
David Blackwell, 1967

Chapter 1 · Observation, Beliefs, and Decision

David Blackwell

1919 – 2010

Photograph: David Blackwell, Seattle, 1967. Photo by Konrad Jacobs, copyright MFO, via Wikimedia Commons, CC BY-SA 2.0 DE (https://creativecommons.org/licenses/by-sa/2.0/de/). Indicate any crop or colour treatment. Shown toned. File and licence

The problem on the desk

When is one experiment more informative than another for making decisions? Blackwell compared experiments by what a decision-maker could achieve with their observations, linking statistical information to attainable risk rather than to a particular estimator.1

A life in moments

  1. 1919

    Centralia

    Born on 24 April.2

  2. 1935

    University of Illinois · Urbana–Champaign

    Entered university at sixteen.2

  3. 1941

    University of Illinois · Urbana–Champaign

    Completed his doctorate under Joseph Doob.3

  4. 1944

    Howard University · Washington, D.C.

    Joined the mathematics faculty.4

  5. 1954

    University of California, Berkeley · Berkeley

    Joined Berkeley; his permanent statistics professorship followed in 1955.5

  6. 1965

    National Academy of Sciences

    Was elected to the Academy.2

  7. 2010

    Died on 8 July.2

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

When you reach the point where you’re not learning anything, then it’s probably time to change something.

A Conversation with David Blackwell, 19867

A story

An attempted counterexample led to a collaboration

After hearing Girshick lecture on Wald’s equation, Blackwell thought he had a counterexample and sent it to him. Girshick invited him to lunch. Blackwell recalled this as the beginning of their collaboration.6

Retrospective first-person account; the proposed counterexample was not valid.

Around Blackwell

  • co-author Kenneth J. Arrow Arrow, Blackwell and Girshick published on Bayes and minimax sequential decisions in 1949.8
  • co-author Meyer Girshick Co-authored Theory of Games and Statistical Decisions in 1954.9

Advisor in the record Joseph Leo Doob Students in the record Richard Bucy, Morton Davis, Roger Wets Mathematics Genealogy Project record

The genealogy lists only what the database records; a missing name is not a missing teacher.

The card in the book

Born in Centralia, Illinois; doctorate at the University of Illinois in 1941 under Joseph Doob. He taught at Howard University, worked with the RAND Corporation on duels and games of timing, and joined the University of California, Berkeley, in 1954 as a visiting professor, becoming Professor of Statistics in 1955. His work spans the Rao–Blackwell theorem, renewal theory, the comparison of statistical experiments, approachability in repeated games with vector payoffs, dynamic programming, and the determinacy of infinite games.

Main works “Comparison of experiments” (Proc. Second Berkeley Symposium, 1951); “Equivalent comparisons of experiments” (Ann. Math. Statist. 24, 1953); “An analog of the minimax theorem for vector payoffs” (Pacific J. Math. 6, 1956); Theory of Games and Statistical Decisions, with M. A. Girshick (1954).

To read further

Sources (9)
  1. David Blackwell, 1919–2010: An explorer in mathematics and statistics, Peter J. Bickel, 2020; Research discussion of comparison of experiments
  2. David Blackwell, 1919–2010: An explorer in mathematics and statistics, Peter J. Bickel, 2020; Opening paragraph
  3. David Blackwell, 1919–2010: An explorer in mathematics and statistics, Peter J. Bickel, 2020; Doctoral years and thesis-adviser discussion
  4. David Harold Blackwell (1919–2010), Howard University Department of Mathematics, 2019; Opening paragraph
  5. Curriculum Vitae, David Blackwell; Celebratio Mathematica, 1993; Positions held: 1954–1955 and 1955–1973
  6. A Conversation with David Blackwell, Morris H. DeGroot; interviewee David Blackwell, 1986; Celebratio reprint, opening discussion of Girshick
  7. A Conversation with David Blackwell, Morris H. DeGroot; interviewee David Blackwell, 1986; Celebratio reprint p. 9 (PDF p. 10), discussion of teaching from his own books
  8. A Conversation with David Blackwell, Morris H. DeGroot; interviewee David Blackwell, 1986; References [e2]
  9. A Conversation with David Blackwell, Morris H. DeGroot; interviewee David Blackwell, 1986; References [e3]

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.