Skip to main content
Log in

Democracy, the theory of voting, and mathematics: a review of Andrank Tangian’s ‘Mathematical theory of democracy’

Springer, Heidelberg, 2014, ISBN 978-3-642-38723-4, xx, 615 pp

  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Notes

  1. See also Schofield’s more recent ‘The Spatial Model of Politics’ (2007).

  2. A first version was published in Italian in 1993 and a French second edition with a rather extended postscript in 2012.

  3. Jonathan Israel’s books are highly recommended, particularly ‘Democratic Enlightenment’ (2011) and ‘Revolutionary Ideas’ (2014).

  4. The author mentions utilities associated to candidates and speaks of ‘degrees of preference’. Having worked on fuzziness and vagueness of preferences, I disagree with this terminology. Furthermore, while he introduces cardinal utilities by taking the (absolute value) of difference of utilities, he does not hesitate to add these differences.

  5. The French 1793 constitution is viewed by Israel (2014) as the ‘World’s first democratic constitution’, even if the word ‘democracy’ is, according to Tangian, never used. Furthermore, the draft constitution presented to the Convention on 15 February 1793 is based on Condorcet’s ideas.

  6. In French, an earl is a ‘comte’, not a ‘compte’ which is a count or account. Furthermore, Alexis de Tocqueville was not a comte, but a ‘vicomte’ (viscount).

  7. Individuals are characterized by their weights, which can be the same for all, but not necessarily.

  8. The lack of a real discussion of the meaning of weights, their origin, and the significance and possibility of the additions is rather disappointing.

  9. There is some ambiguity in the treatment of independence of irrelevant alternatives. It is sometimes the Arrovian variety, but sometimes the Nash–choice-theoretic–version as in page 101 where the author mentions regarding Borda’s rule the ‘dependence of the election outcome on adding new candidates (contrary to the desirable independence of irrelevant alternatives)’.

  10. On Arrovian independence and democracy, see also Mackie (2003).

  11. Gödel’s theorems are too often invoked for absurd analogies–rarely explained and justified–in a social context as by famous French ‘intellectuals’, mainly Régis Debray and Michel Serres (see Sokal and Bricmont 1997, 1998; Bouveresse 1999; Franzén 2005).

  12. There is a funny anecdote regarding John von Neumann saying to Oskar Morgenstern about books on mathematical economics: ‘You know, Oskar, if these books are unearthed sometime a few hundred years hence, people will not believe that they were written in our time. Rather they will think that they are about contemporary with Newton, so primitive is their mathematics’ (Morgenstern 1976).

  13. Related to deliberation and direct democracy is the interesting view due to Marc Fleurbaey (2006) asserting that, as a principle of democracy, ‘a decision must be taken by the concerned individuals and the power to decide must be distributed in proportion of the interests in question.’ Of course, as for Tangian’s weights regarding questions, one must tackle the difficult problem of providing/calculating the proportions.

References

  • Austen-Smith D, Banks JS (1999) Positive political theory I. The University of Michigan Press, Ann Arbor

    Google Scholar 

  • Austen-Smith D, Banks JS (2005) Positive political theory II. The University of Michigan Press, Ann Arbor

    Google Scholar 

  • Bouveresse J (1999) Prodiges et vertiges de l’analogie. Raisons d’Agir, Paris

    Google Scholar 

  • Colyvan M (2012) An introduction to the philosophy of mathematics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Fleurbaey M (2006) Capitalisme ou démocratie ? L’alternative du XXI\(^e\) siècle. Grasset, Paris

    Google Scholar 

  • Franzén T (2005) Gödel’s theorem-An incomplete guide to its use and abuse. AK Peters, Wellesley

    Book  Google Scholar 

  • Israel J (2011) Democratic enlightenment. Oxford University Press, Oxford

    Google Scholar 

  • Israel J (2014) Revolutionary ideas. Princton University Press, Princeton

    Google Scholar 

  • Mackie G (2003) Democracy defended. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Manin B (1995) Principes du gouvernement représentatif. Flammarion, Paris

    Google Scholar 

  • Manin B (1997) Principles of representative government. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • McLean I, Urken AB (1995) Classics of social choice. The University of Michigan Press, Ann Arbor

    Google Scholar 

  • Morgenstern O (1976) The collaboration between Oskar Morgenstern and John von Neumann on the theory of games. J Econ Lit 14:805–816

    Google Scholar 

  • Riker WH, Ordeshook PC (1973) An introduction to positive political theory. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Rothschild E (2001) Economic sentiments-Adam Smith, Condorcet, and the enlightenment. Harvard University Press, Cambridge (Mass.)

    Google Scholar 

  • Russell B (1946) History of western philosophy. George Allen & Unwin, London

    Google Scholar 

  • Ryan A (2012) On politics. Allen Lane, London

    Google Scholar 

  • Saari DG (2008) Disposing dictators, demystifying voting paradoxes-social choice analysis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Schofield N (1985) Social choice and democracy. Springer, Heidelberg

    Book  Google Scholar 

  • Schofield N (2007) The spatial model of politics. Routledge, Abingdon

    Google Scholar 

  • Sokal A, Bricmont J (1997) Impostures intellectuelles. Odile Jacob, Paris

    Google Scholar 

  • Sokal A, Bricmont J (1998) Fashionable nonsense: postmodern intellectuals’s abuse of science. Picador, New York

    Google Scholar 

Download references

Acknowledgments

I am very grateful to Steven Brams, Bernie Grofman, Iain McLean who commented on Tangian’s book in a special session during the meeting of the Public Choice Society in Charleston on March 7th, 2014.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maurice Salles.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salles, M. Democracy, the theory of voting, and mathematics: a review of Andrank Tangian’s ‘Mathematical theory of democracy’. Soc Choice Welf 44, 209–216 (2015). https://doi.org/10.1007/s00355-014-0823-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-014-0823-x

Navigation