33. Introduction
Kenneth Arrow (1950, 1951, 1963) presented an Impossibility Theorem in which he showed that decisions about ‘the general welfare’ are impossible in certain cases or have to be left to a dictator. Arrow presented some five axioms that each seemed reasonable when considered by itself, and he argued as well that these axioms are morally desirable and fitting to the concept of ‘general welfare’. He also formulated the problem in general terms so that it concerns choices on goods or people. Subsequently, he derived a contradiction. This result caused quite some consternation, but eventually the mathematical rigour caused acceptance, and since then the Theorem forms the core of many books, such as Sen (1970) and Mueller(1989). The Theorem was also one of the reasons to award Arrow the Nobel Prize in economics.
A voting example is given by the US Presidential election of 2000. Apart from the problems around the ballot process itself, there was a more basic problem: with main contenders Bush, Gore and Nader, Bush got elected, but in another system, such as a run-off between the two ‘major’ contenders, the Nader vote apparently would have switched largely to Gore, making him the US President. So the choice depends as much upon the system chosen as on the preferences. Can we find a generally good system ? Arrow’s Theorem suggests ‘No’.
Arrow’s Theorem has had a huge influence on scientific and political thought. Part of this influence is subtle, where skepsis arises about the concept of ‘democracy’. That shiny goal loses its appeal when we don’t know how representatives should be elected and when morally desirable rules would be impossible. Opting for the natural forces in the social process may be more pragmatic. The influence of the Theorem can sometimes be more explicit. Next to the model of the utility maximising individual, there is the model for society as a whole and then the maximisation of a Social Welfare Function (SWF). But when a morally acceptable SWF is impossible, what would be the use of research into such an inherently flawed concept ? Many nations co-ordinate their economic policy, and have created institutions for this, like the Council of Economic Advisors (US), the Commissariat du Plan (France), the Sachverständigenrat (Germany), and the Central Planning Bureau (Holland). Such an institution, given its role in the co-ordination of economic policy, could be expected to do reseach on the national SWF. However, those institutions tend to abstain from that kind of research, pointing to Arrow’s Theorem as one of the arguments, if not the major argument.
Over the years an ‘accepted view’ has grown in economics concerning the meaning of Arrow’s Theorem. This accepted view however has also implied a kind of moral stagnation.
There are two main reasons to reconsider the accepted wisdom on the meaning of the Theorem and to rekindle the debate on it. The first reason is destructive, since it rejects Arrow’s position; the second reason is constructive, since it provides an alternative.
These reasons are: (1) There is a distinction between the mathematical framework on one hand and its interpretation on the other hand. The Theorem holds, and the impossibility holds for Arrow’s axioms, but the questions of reasonableness and moral desirability are of a different kind. (2) The area of application of Arrow’s axioms seems rather static, while reality is dynamic. By considering the role of time, there is more scope for morality, and then one can identify a voting procedure that many would find attractive.
The two following chapters develop these arguments subsequently. Readers interested in more details are referred to Colignatus (2001), “Voting Theory for Democracy”. That book develops the theory of direct single seat elections from the bottom up while it also provides programs (in Mathematica) to eliminate the tedious work of the calculations of the various voting procedures.