¹ Merrill, Samuel, ‘A Comparison of Efficiency of Multicandidate Electoral Systems’, American Journal of Political Science, XXVIII (1984), 23–48CrossRefGoogle Scholar; Doron, Gideon and Kronick, Richard, ‘Single Transferable Vote: an Example of a Perverse Social Choice Function’. American Journal of Political Science, XXI (1977), 303–11.CrossRefGoogle Scholar Monotonicity is the property that additional support cannot possibly adversely affect a candidate's prospects. Under multi-stage systems, additional support can in some circumstances damage a candidate's prospects of election, by changing the order in which the other candidates are eliminated.

² Brams, Steven J. and Fishburn, Peter C., Approval Voting (Boston: Birkhauser, 1983), pp. 7–8, 143–4.Google Scholar

³ Nurmi, Hannu, ‘Voting Procedures: a Summary Analysis’, British Journal of Political Science, XIII (1983), 181–208.CrossRefGoogle Scholar Cf. Sugden, Robert, ‘Free Association and the Theory of Proportional Representation’, American Political Science Review, LXXVIII (1984), 31–43.CrossRefGoogle Scholar

⁴ Black, Duncan, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958), p. 81.Google Scholar

⁵ Meek, B. L., ‘Une Nouvelle Approche di Scrutin Transferable’, Mathematiques et Sciences Humaines, XXV (1969), 13–23Google Scholar and XXIX (1971), 33–9; Woodall, D. R., ‘Computer Counting in STV Elections’. Representation, XXIII (1982–1983), 4–6.CrossRefGoogle Scholar

⁶ See, for example, Lakeman, Enid, How Democracies Vote, 4th edn (London: Faber and Faber, 1974), pp. 229–73Google Scholar; Finer, S. E., ‘Adversary Politics and Electoral Reform’, in Finer, S. E., ed., Adversary Politics and Electoral Reform (London: Anthony Wigram, 1975), pp. 3–32Google Scholar; Bogdanor, Vernon, The People and the Party System (Cambridge: Cambridge University Press, 1981), pp. 255–9.Google Scholar

⁷ The quota is the minimum number of votes needed to secure election. It is calculated as the smallest integer greater than vv/(s + 1), where vv is the total number of valid votes, and s is the number of seats in the constituency.

⁸ For concise accounts of the counting of votes under Irish STV, see Chubb, Basil, The Government and Politics of Ireland, 2nd edn (London: Longman, 1982), pp. 350–3Google Scholar; Hand, Geoffrey, ‘Ireland’, in Hand, Geoffrey, Georgel, Jacques and Sasse, Christoph, eds, European Electoral Systems Handbook (London: Butterworths, 1979), pp. 121–39.Google Scholar

⁹ Lakeman, , How Democracies Vote, pp. 139–40.Google Scholar A more recent study also calls attention to the existence of the problem, and provides a useful history of ‘the random element’ in STV, but does not attempt to calculate its importance. See Coakley, John and O'Neill, Gerald, ‘Chance in Preferential Voting Systems: an Unacceptable Element in Irish Electoral Law?’, Economic and Social Review, XVI (1984), 1–18.Google Scholar

¹⁰ For a comment on this practice see Van den Bergh, G., Unity in Diversity (London: B. T. Batsford, 1956), pp. 65–7.Google Scholar

¹¹ For example, Gallagher, Michael, ‘Party Solidarity, Exclusivity and Inter-party Relationships at Irish Elections 1922–1977: the Evidence of Transfers’, Economic and Social Review, X (1978–1979), 1–22.Google Scholar

¹² Coakley, and O'Neill, , ‘Chance in Preferential Voting Systems’, p. 11.Google Scholar

¹³ For details of counting procedures under STV in Australia, see Wright, J. F. H., Mirror of the Nation's Mind: Australia's Electoral Experiments (Sydney: Hale and Iremonger, 1982), pp. 115–16, 130, 133Google Scholar; Wright, Jack, ‘Change in Australia's Federal Electoral Laws in 1983’. Representation, XXIV (1983–1984), 1–4.CrossRefGoogle Scholar

¹⁴ In some cases, the distribution of A's surplus carries a member of B over the quota. This candidate's surplus is in turn distributed (the transferred votes being taken entirely from the package he received from A), and some or all of the votes from this distribution pass to C and D. This situation, although in some ways different from the straightforward one outlined in Table 1, can be dealt with by an adaptation of the model outlined here.

¹⁵ This could underestimate the effect of sampling, as it must be borne in mind that a seat other than the last could be affected by sampling, and that therefore more than one seat per constituency could be involved. For example, if two candidates of the same party are chasing the same seat the stage at which one of them has a few votes less than the other and is consequently eliminated is crucial, even though it may not be the final stage of the count.

¹⁶ It should be reiterated that the figures represent upper limits for probabilities rather than actual probabilities. The two will coincide only when the assumptions made in the model hold true in their entirety.

¹⁷ Cf. Fanning, Ronan, Independent Ireland (Dublin: Helicon, 1983), p. 194.Google Scholar

¹⁸ The figure of 149 constituencies refers to the election of 806 councillors to the twenty-seven county councils and the four main city councils.

¹⁹ Wright, , Mirror of the Nation's Mind, p. 144Google Scholar; Van den Bergh, , Unity in Diversity, pp. 13–14, 59–60Google Scholar. Wright even disputes the view that the Gregory method necessarily makes the counting process lengthier and more complicated, although this seems inevitable.