Allan Gibbard

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Soon after his doctoral degree, Gibbard provided a first proof of a conjecture that strategic voting was an intrinsic feature of non-dictatorial voting systems with at least three choices, a conjecture of Michael Dummett and Robin Farquharson. This work would eventually become known as "Gibbard's theorem", published in 1973. [2] Mark Satterthwaite later worked on a similar theorem which he published in 1975. [8] [9] Satterthwaite and Jean Marie Brin published a paper in 1978 describing Gibbard's and Satterthwaite's mathematical proofs as the "Gibbard–Satterthwaite theorem" and described its relationship to Arrow's impossibility theorem. [10]

Gibbard's theorem

In the fields of mechanism design and social choice theory, "Gibbard's theorem" is a result proven by Gibbard in 1973. [2] It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

  1. The process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome;
  2. The process limits the possible outcomes to two options only;
  3. The process is open to strategic voting: once an agent has identified their preferences, it is possible that they have no action at their disposal that best defends these preferences irrespective of the other agents' actions.

A corollary of this theorem is Gibbard–Satterthwaite theorem about voting rules. The main difference between the two is that Gibbard–Satterthwaite theorem is limited to ranked (ordinal) voting rules: a voter's action consists in giving a preference ranking over the available options. Gibbard's theorem is more general and considers processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates (cardinal voting). Gibbard's theorem can be proven using Arrow's impossibility theorem.

Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [11] and Hylland's theorem, which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance. The Gibbard's theorem assumes the collective decision results in exactly one winner and does not apply to multi-winner voting.

Gibbard–Satterthwaite theorem

In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by Gibbard in 1973 [12] and economist Mark Satterthwaite in 1975. [13] It deals with deterministic ordinal electoral systems that choose a single winner. It states that for every voting rule, one of the following three things must hold:

  1. The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
  2. The rule limits the possible outcomes to two alternatives only; or
  3. The rule is susceptible to tactical voting: in certain conditions, a voter's sincere ballot may not best defend their opinion.

While the scope of this theorem is limited to ordinal voting, Gibbard's theorem is more general, in that it deals with processes of collective decision that may not be ordinal: for example, voting systems where voters assign grades to candidates. Gibbard's 1978 theorem and Hylland's theorem are even more general and extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the voters' actions but may also involve a part of chance.

Ethical theory

Gibbard is best known in philosophy for his contributions to ethical theory. He is the author of three books in this area. Wise Choices, Apt Feelings: A Theory of Normative Judgment (1990) develops a general theory of moral judgment and judgments of rationality. Gibbard argues that when we endorse someone's action, belief, or feeling as "rational" or warranted we are expressing acceptance of a system of norms that permits it. More narrowly, morality is about norms relating to the aptness of moral feelings (such as guilt and resentment). [14]

Gibbard's second book, Thinking How to Live (2003), offers an argument for reconfiguring the distinctions between normative and descriptive discourse, with implications as to the "long-standing debate" over "objectivity" in ethics and "factuality" in ethics. [15]

Gibbard's third book, Reconciling Our Aims: In Search of Bases for Ethics (2008), from the Tanner Lectures, argues in favour of a broadly utilitarian approach to ethics. [16]

Gibbard's fourth and most recent book is titled Meaning and Normativity (2012). [17]

A recent review, including extensive citing of Gibbard's work above, is in the Stanford Encyclopedia of Philosophy (2015). [18]

Interviews with Gibbard

See also

Related Research Articles

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The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and states that for every voting rule of this form, at least one of the following three things must hold:

  1. The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
  2. The rule limits the possible outcomes to two alternatives only; or
  3. The rule is susceptible to tactical voting: in some situations, a voter's sincere ballot may not best defend their opinion.
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In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:

  1. The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
  2. The process limits the possible outcomes to two options only.
  3. The process is not straightforward; the optimal ballot for a voter depends on their beliefs about other voters' ballots.

References

Footnotes

  1. ↑ "Allan Gibbard Vita" (PDF). Retrieved 4 June 2023.
  2. 1 2 3 Gibbard, Allan (1973). "Manipulation of voting schemes: A general result" (PDF). Econometrica. 41 (4): 587–601. doi:10.2307/1914083. JSTOR   1914083.
  3. ↑ Rudolf Farra and Maurice Salles (October 2006). "An Interview with Michael Dummett: From analytical philosophy to voting analysis and beyond" (PDF). Social Choice and Welfare. 27 (2): 347–364. doi:10.1007/s00355-006-0128-9. S2CID   46164353.
  4. ↑ The International Who's Who 2011 (74th ed.). Routledge. 2010. p.  726. ISBN   978-1-85743-546-7. ISSN   0074-9613. OCLC   502032895.
  5. ↑ "72 New Members Chosen by Academy".
  6. ↑ "Brian Skyrms, UC Irvine — Institute for Social Sciences".
  7. ↑ "2005-2006 Lecture Series | Tanner Lectures".
  8. ↑ Satterthwaite, Mark A. (1975). "Strategy-proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions". Journal of Economic Theory . 10 (2): 187–217. CiteSeerX   10.1.1.471.9842 . doi:10.1016/0022-0531(75)90050-2.
  9. ↑ Dummett, Michael (1984). Voting Procedures. New York: Oxford University Press. ISBN   978-0-19-876188-4.
  10. ↑ Blin, Jean Marie; Satterthwaite, Mark A. (1978-10-31). "Individual decisions and group decisions. The fundamental differences" . Journal of Public Economics. 10 (2): 247–267. doi:10.1016/0047-2727(78)90037-3. ISSN   0047-2727.
  11. ↑ Gibbard, Allan (1978). "Straightforwardness of Game Forms with Lotteries as Outcomes" (PDF). Econometrica. 46 (3): 595–614. doi:10.2307/1914235. JSTOR   1914235.[ permanent dead link ]
  12. ↑ Gibbard, Allan (1973). "Manipulation of voting schemes: A general result". Econometrica. 41 (4): 587–601. doi:10.2307/1914083. JSTOR   1914083.
  13. ↑ Satterthwaite, Mark Allen (April 1975). "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions". Journal of Economic Theory. 10 (2): 187–217. CiteSeerX   10.1.1.471.9842 . doi:10.1016/0022-0531(75)90050-2.
  14. ↑ Allan Gibbard (1990). Wise Choices, Apt Feelings. Description (from back cover), Contents, Description (from back cover) and Preface. Harvard University Press. On the book, comments of Simon Blackburn & John McDowell.
  15. ↑ Allan Gibbard (2003). Thinking How to Live. Description, Contents, & Preface. Harvard University Press. Reviewed in Matthew Chrisman in (2005), "Allan Gibbard. 'Thinking How to Live'", Ethics, 115(2), pp. 406–412.
  16. ↑ Allen Gibbard (2008). Reconciling Our Aims: In Search of Bases for Ethics. Description & Content. Oxford.
  17. ↑ Allan Gibbard (2012). Meaning and Normativity. Description & Contents. Oxford University Press. Review at Christopher S. Hill (2013), "Allan Gibbard Meaning and Normativity," Notre Dame Philosophical Reviews, July 20.
  18. ↑ Mark van Roojen (2015). "Moral Cognitivism vs. Non-Cognitivism", The Stanford Encyclopedia of Philosophy (Fall 2015 Edition), beginning at § 2.3 Quasi-realism, 2.4 Expressivism, & 2.5 Norm-expressivism and Plan-expressivism. Accessed 3/9/2016.

General references

Allan Gibbard
Born
Allan Fletcher Gibbard

(1942-04-07) April 7, 1942 (age 82)
NationalityAmerican
Academic background
Alma mater
Thesis Utilitarianisms and Coordination (1971)
Doctoral advisor John Rawls
Influences
Academic offices
Preceded by Tanner Lecturer on Human Values
at the University of California, Berkeley
2006		Succeeded by
Professional and academic associations
Preceded by President of the  American Philosophical
Association, Central Division
2001–2002		Succeeded by
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