Theory of voting

Abstract

As with every important book, more questions are posed than answered. In particular, in an appendix a sketch is given of a theory involving group stability in voting where the equilibrium is immune to defections by groups. Farquharson uses only the ordinal properties of individual preferences. It would be fascinating to see how much more can be obtained starting with such Spartan fare. Farquharson has opened up much new terrain for exploration. Can we characterize classes of voting systems according to the amount of sophisticated voting to be encountered, i.e., by the amount to which people do not vote directly in accord with their preferences? What are the limiting characteristics of large voting games of this variety when the number of individuals and/or the number of issues become large? Can we extend his analysis to include games with unknown preferences, where, for example, a government is drawing up a constitution that will specify the voting process, but it has only probability estimates on the preference scales of the citizens? This is a very non-esoteric book. Together with its logical elegance and use of game theory it conveys a deep concern with and understanding of voting procedures as they are. The examples are a delight.