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Published online by Cambridge University Press: 27 January 2009
The ‘paradox’ of swing resides in the expectation that ‘if national influences were completely paramount,. swings would not involve identical fractions of the total vote or electorate in each constituency, but a fraction proportional to the prior strength of the party that was losing ground’. The mass of the evidence is however that swings are virtually equal across constituencies. The intention here is to demonstrate that the ‘prior proportional’ expectation is a mistaken one since it leads to a logical contradiction, and therefore that the phenomenon of equal swing is not paradoxical.
1 Butler, David and Stokes, Donald, Political Change in Britain (London: Macmillan, 1969), pp. 303–4.Google Scholar
2 Strangely, as a result of our analysis, we might well become able to attribute a rationale. As we shall show, the only circumstance in which ‘proportional swing’ gives us an acceptable pattern of voting change is where each constituency is a precise microcosm of the total electorate. An inference from a whole to a part is only valid where the part has the same characteristics as the whole. We have no reason to expect such a relationship between individual constituencies and electorates; the ‘proportional swing’ expectation may be the result of a fallacy of composition.
3 Butler, and Stokes, , Political Change in Britain, p. 303, fn. 2.Google Scholar
4 Berrington, H., ‘The General Election of 1964’, Journal of the Royal Statistical Society, Series A, 128 (1965), 17–51, p. 19.CrossRefGoogle Scholar
5 Throughout the argument a two-party system and a constant turnout and electorate is assumed. Swing is therefore defined to equal where net change since previous vote is the sum of the gross changes between the two parties halved. The transition probability in the ‘proportional swing’ hypothesis is the swing normalized for the size of the total population at risk:
6 Miller, W. L., ‘The Analysis of Electoral Change’, Journal of the Royal Statistical Society, Series A, 135 (1972), 122–42.CrossRefGoogle Scholar
7 This is simply to say that where the voter has more than one criterion, in a state of the universe where he has contradictory evaluations between criteria, he has a rule of the form ‘criteria shall have an order of preference O’.
8 This assumption is of course not trivial in a general philosophical sense. But since for our purposes we consider that the significant factor in the state of the universe is the relative party posture, to the extent that the events intervening between the two states considered to be equivaent have not altered the voters’ relative perceptions of the two parties, the assumption will be acceptable. And the events to be considered equivalent in this analysis may also be considered to be very narrowly separated in time, obviating most of the possible objection here.
