Published online by Cambridge University Press: 27 January 2009
The relationship between electoral systems can be examined on a number of dimensions. Seat allocation methods are conveniently divided into two groups: those based on largest remainders and those based on highest averages. The single transferable vote has its own distinct characteristics. Focusing on certain elements – the quota, thresholds, paradoxes and the conditions under which a majority of seats can be won – enables comparisons to be drawn between seat allocation methods. Certain seat allocation methods conventionally seen as variants of proportional representation (PR) cannot be regarded as such. PR methods can be rank ordered according to whether, when complete proportionality is not attainable, they display electoral bias towards larger or smaller parties. However, a definitive ordering is elusive, since some methods that are generally more favourable to larger parties can in some circumstances set lower thresholds of representation than methods generally favourable to smaller parties.
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2 The terms ‘smaller’ and ‘larger’ are entirely relative. For a more formal demonstration that larger parties benefit from a low quota, see Appendix.
3 For example, Rae, Douglas, The Political Consequences of Electoral Laws, revised edn (New Haven and London: Yale University Press, 1971), p. 34Google Scholar, says that, compared with LR-Hare, LR-Imperiali lowers the price of the first seat, thereby ‘helping weak parties’.
4 For an English translation of his article, see Lijphart, Arend and Gibberd, Robert W., ‘Thresholds and Payoffs in List Systems of Proportional Representation’, European Journal of Political Research, 5 (1977), 219–44, pp. 241–2.CrossRefGoogle Scholar
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10 So do LR-Hare and LR-Droop, but LR-Imperiali does not function effectively as its low quota of 3,704 votes would ‘allocate’ twenty-six seats initially. It too, therefore, cannot be classified as a PR method. We are excluding STV from this part of the discussion as it embodies a more sophisticated conception of ‘perfect proportionality’ by considering voters' lower preferences.
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20 Vote management at this election may have affected the outcome in eleven of the forty-one constituencies. It is discussed in Gallagher, Michael, ‘The Election Results and the New Dáil’, in Gallagher, Michael and Sinnott, Richard, eds, How Ireland Voted 1989 (Galway: Centre for the Study of Irish Elections, 1990), pp. 68–93, at pp. 81–3.Google Scholar
21 This philosophy is outlined in Huntington, ‘A New Method of Apportionment’.
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26 Both are demonstrated by Lijphart, and Gibberd, , ‘Thresholds and Payoffs’, pp. 228–9.Google Scholar
27 Balinski, and Young, , Fair Representation, p. 39.Google Scholar Another example of the Alabama paradox is given by Carstairs, , Short History of Electoral Systems, p. 25.Google Scholar In the case he illustrates, a hundred seats would be awarded on a 45–44–11 basis under both LR-Hare and Sainte-Laguë, while if the number of seats is increased to 101, Sainte-Laguë produces a 45–45–11 outcome whereas under LR-Hare the smallest party loses a seat and the outcome is 46–45–10.
28 Newland, , Comparative Electoral Systems, pp. 40–2.Google Scholar
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30 Brams, Steven J., Paradoxes in Politics (New York: Free Press, 1976), p. 157.Google Scholar
31 Balinski, Michel L. and Young, H. Peyton, ‘The Quota Method of Apportionment’, American Mathematical Monthly, 84 (1975), 450–5CrossRefGoogle Scholar; Balinski, and Young, , Fair Representation, pp. 79–81 and 129–34.Google Scholar
32 This is demonstrated by Balinski, and Young, , Fair Representation, p. 90.Google Scholar
33 For example, Van Den Bergh, , Unity in Diversity, p. 25.Google Scholar The other side of the argument is that a large party can often win a majority of seats with a minority of votes under d'Hondt, LR-Droop and STV if the other votes are scattered among a number of opponents. This may happen under Sainte-Laguë and LR-Hare, though it would require a greater degree of fragmentation of the other votes, and cannot happen under Adams.
34 Gallagher, , ‘Proportionality, Disproportionality and Electoral Systems’.Google Scholar
