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Voting Theory for Democracy

Colignatus, Thomas

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

ISBN 978-90-804774-9-0. The book website is:
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