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Social Choice and Welfare

Erschienen in:

01.01.2015

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

verfasst von: Maurice Salles

Erschienen in: Social Choice and Welfare | Ausgabe 1/2015

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This is an important, thought-provoking and unexpected book. It is unexpected because with such a title one would expect a textbook in the vein of Riker and Ordeshook’s ‘An Introduction to Positive Political Theory’ (1973), or Austen-Smith and Banks’s ‘Positive Political Theory I and II’ (1999, 2005), or Schofield’s ‘Social Choice and Democracy’ (1985).¹ …

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

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

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

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.

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.

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).

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

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

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)’.

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

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).

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).

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Titel: 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
verfasst von: Maurice Salles
Publikationsdatum: 01.01.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 1/2015
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-014-0823-x

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