Voting Theory for Democracy

4th Edition, May 2014, ISBN 978-90-804774-9-0 (323 pages)

EUR 29.95


 Ordering     Related software

Printable PDF (2 MB)

You can also download from Zenodo 291985

The summary papers "The solution to Arrow's difficulty in social welfare" (1997) and "Without time, no morality" (2002) also got updated versions in "DRGTPE" (2005) - best see the PDF there. 

Sheets (in Word for Windows, zipped)

Mathematica and books at Wolfram

Cover text


VOTING THEORY FOR DEMOCRACY provides the concepts and tools for democratic decision making. Voting is used not only in politics and government, but also in business - and not only in the shareholders' meetings but also in teams. Voting however can suffer from paradoxes. In some systems, it is possible that candidate A wins from B, B from C, and C from A again. This book explains and solves those paradoxes, and thereby it gives a clarity that was lacking up to now. The author proposes the new scheme of 'Pareto Majority' which combines the good properties of the older schemes proposed by Pareto, Borda and Condorcet, while it adds the notion of a (Brouwer) 'fixed point'. Many people will likely prefer this new scheme over Plurality voting which is currently the common practice.

The literature on voting theory has suffered from some serious miscommunications in the last 50 years. Nobel Prize winning economists Kenneth Arrow and Amartya Sen created correct mathematical theorems, but gave incorrect verbal explanations. The author emphasises that there is a distinction between 'voting' and deciding. A voting field only becomes a decision by explicitly dealing with the paradoxes. Arrow and Sen did not solve the paradoxes and used them instead to conclude that it was 'impossible' to find a 'good' system. This however is a wrong approach. Once we understand the paradoxes, we can find the system that we want to use.

This book develops the theory of games (with Rasch - Elo rating) to show that decisions can change, even dramatically, when candidates or items are added to the list or deleted from it. The use of the fixed point criterion however limits the impact of such changes, and if these occur, they are quite reasonable. Groups are advised, therefor, to spend time on establishing what budget they will vote on.

You can benefit from this book also when you do not have the software. However, with the software, you will have an interactive environment in which you and your group can use the various voting schemes, or test them to decide which scheme better fits your purposes. The software is included in The Economics Pack - by the same author - which is an application of Mathematica, a system for doing mathematics with the computer. The Pack has users in many countries in the world. The Pack is available for Windows XP, Macintosh and Unix platforms and requires Mathematica 8.0.1 or later. It can be freely downloaded, but you need a licence to run it. 

80% of this book is at an undergraduate level and 20% requires an advanced level.

Developed, supported and published by: 
Thomas Cool Consultancy & Econometrics


Back to the home page.

Warning: This book proves radical new ideas and must be read with care. If you spend more than a cursory glance on the PDF then it is advisable to get the hardcopy and continue reading from paper. I tend to focus my research on misconceptions that lead society away from common sense, and then I select pivots that cause crucially different points of view depending on how the argument is resolved. Such a pivot only works well if the argumentation gets proper attention.


On Voting Theory for Democracy and The Economics Pack:
Listed in the Journal of Economic Literature, September 2001, Vol 39, no 3, JEL 2001-0960
Ron Shone, The Economic Journal, July 1998:
"For anyone wishing to become very familiar with Mathematica, this is a useful package to have (...)"

Papers w.r.t. voting are here.



A. The book and/or software
Type Price Description
The book VTFD
EUR 29.95
One copy of "Voting Theory for Democracy" (VTFD)     Order
See The Economics Pack (TEP)
B. Site licences
For site licences, contact the author.

PM. Legacy versions

1st Edition, January/February 2001, ISBN 90-804774-3-5 (Legacy PDF, 4 MB, no longer in print)

3rd Edition, March 2011, ISBN 978-90-804774-8-3 (Legacy PDF, 2 MB, no longer in print)

Erratum on VTFD 1st-3rd editions, November 2011.  Short Response for Voting Matters, Published in issue 30, 2013.