Introduction

There are a host of voting procedures under which voters either can rank candidates in order of their preferences or allocate different numbers of votes to them, which we call preferential voting systems because they enable voters to distinguish more preferred from less preferred candidates. We shall describe four of the most common systems, discuss some properties that they satisfy, and illustrate paradoxes to which they are vulnerable. They are:

1. The Hare system of single transferable vote (STV)

2. The Borda count

3. Cumulative voting

4. Additional-member systems.

The rationale underlying all these systems is that of affording different factions or interests in the electorate the opportunity to gain representation in a legislature or council proportional to their numbers, which we call proportional representation (PR). We shall briefly analyze each of these systems here and then make some comparisons, based on different criteria, at the end of the chapter. What is worth noting here, however, is that each of these systems offers a different approach to the problem of achieving PR, especially of minorities, which is the notion of fairness we take as our starting point in the study of elections with multiple winners.

The remainder of the chapter takes an unusual turn in that it was inspired by the request of a professional association to advise it on a voting procedure to use in electing its governing board.