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