Categoric and Ordinal Voting: An Overview

There are many ways to aggregate individual preferences to a collective preference or outcome. The outcome is strongly dependent on the aggregation procedure (election mechanism), rather than on the individual preferences. The Dutch election procedure is based on proportional representation, one nation-wide district, categoric voting and the Plurality ranking rule, while the British procedure is based on non-proportional representation, many districts, categoric voting and the Plurality choice rule to elect one candidate for every district. For both election mechanisms we indicate a number of paradoxes. The German hybrid system is a combination of the Dutch and British system and hence inherits the paradoxes of both systems. The STV system, used in Ireland and Malta, is based on proportional representation (per district) and on ordinal voting. Although designed with the best intentions – no vote should be wasted – , it is prone to all kinds of paradoxes. May be the worst one is that more votes for a candidate may cause him to lose his seat. The AV system, used in Australia, is based on non-proportional representation (per district) and on ordinal voting. It has all the unpleasant properties of the STV system. The same holds for the French majority-plurality rule. Arrow’s impossibility theorem is presented, roughly saying that no ‘perfect’ election procedure exists. More precisely, it gives a characterization of the dictatorial rule: it is the only preference rule that is IIA and satisfies the Pareto condition. Finally we mention characterizations of the Borda rule, the Plurality ranking rule, the British FPTP system and of k-vote rules.

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