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Published online by Cambridge University Press: 27 January 2009
The arrival of the Alliance on the British political scene has complicated the party system to an extent unknown for over half a century. Elections can no longer be counted upon to produce straightforward and immediate shifts in partisan control of the government. The next election could very well produce a hung Parliament.
1 The figures in this paragraph are based on Table 1 in Crewe, Ivor, ‘Can Labour Rise Again?’, Social Studies Review, I (1985), 13–19.Google Scholar
2 ‘Owen veto is price of power sharing’, The Guardian, 7 05 1985, p. 1.Google Scholar
3 The Guardian, 7 05 1985, p. 1.Google Scholar
4 Hamburger, Henry, Games as Models of Social Phenomena (San Francisco: W. H. Freeman, 1979), pp. 36–42.Google Scholar
5 Conceivably the Conservatives might feel that PR is worse than even a Labour government and would be willing to let Labour come to power if the only means of remaining in office were conceding PR to the Alliance. Such a preference, however, would be based on a belief that Labour could be trusted not to offer PR. As we shall see later, this is a high-risk gamble under the circumstances.
6 Using a matrix for the first game will facilitate comparisons with the subsequent three games. See Hamburger, , Games as Models of Social Phenomena, pp. 16, 26–30Google Scholar and Zagare, Frank, Game Theory: Concepts and Applications (Beverly Hills, Calif.: Sage Publications, 1984), pp. 16–17.CrossRefGoogle Scholar
7 While play is sequential, game theory assumes that players decide upon their strategy before play begins so that they have a well-thought out plan of action and do not just respond on the spur of the moment in the heat of the actual negotiation process.
8 Such a result is possible because the game is variable-sum, rather than zero-sum. That is, Labour's preferences are not the exact reverse order of the Conservatives'.
9 Hamburger, , Games as Models of Social Phenomena, pp. 45–7Google Scholar, discusses three other decision-making procedures. Maximum-average and minimax-regret would, for this particular game, produce the same choice of strategy. While the maximax principle results in different behaviour, it seems too naive to be a realistic guide to action. Unfortunately, as we shall shortly see, maximin strategies do not necessarily lead to equilibrium solutions in non-zero sum games.
10 A mixed strategy is precluded because for each player the largest payoffs are on a row or a column, not on a diagonal. In any event, whether mixed strategies are relevant to single-play games or are useful only for repeated play is a matter of some controversy. See Zagare, , Game Theory, pp. 34–6.Google Scholar
11 The SDP is not without a few fundamentalists of its own. Like their Liberal counterparts, they would seem to prefer a Conservative minority government to a Labour one. See Sandelson's, Neville letter in The Guardian, 16 05 1985, p. 12.Google Scholar
12 A three-player game requires a three-dimensional matrix. The grids appearing in Figure 3 should be visualized as descending slices from a cube-like solid geometric form.
13 Zagare, , Game Theory, pp. 64–70.Google Scholar
14 I have assumed that Mrs Thatcher is certain to remain leader of the Conservatives at least until the next general election. Since, unlike Mr Heath, she has not lost an election, she seems invulnerable to a coup even if she has become an electoral liability. For her to resign simply because of electoral adversity would be totally out of character. But if she fails to ‘win’ the next election – if the Conservatives are put out of office – then the stilettos are likely to be wielded. However, if Labour came to power as a minority government and another election seemed imminent – the 1974 situation – she could probably hold on, since a change of leader on the eve of an electoral campaign might be regarded as damaging to the Conservatives' prospects.
15 On removal of dominated strategies from a player's choices see Hamburger, , Games as Models of Social Phenomena, pp. 58–60.Google Scholar
16 The advantage of tacit deception is that ‘other players cannot detect the deception unless they know the user's true preference order’. A player acting in accord with an announced false preference ordering forecloses such knowledge. Thus tacit deception differs from ‘making a false announcement but acting consistently with… true preferences. Since other players can easily detect an action that contradicts the deceiver's preference order, this strategy is called revealed deception.’ Zagare, , Game Theory, p. 69.Google Scholar
17 The Labour moderates do not know, of course, that the Conservatives are practising tacit deception. Their argument to their fundamentalist colleagues is simply that when the Conservatives are playing their CON/ALL strategy, as is perceived to be the case, the moderate preference orderings for Labour offers a better outcome than do fundamentalist ones.
18 In addition to my comments ‘The Alliance Campaign, Watersheds, and Landslides: Was 1983 a Fault Line in British Politics?’ p. 93Google Scholar in Ranney, Austin, ed., Britain at the Polls, 1983: A Study of the General Election (Durham, NC: Duke University Press, 1985)Google Scholar, see also Pinto-Duschinsky, Michael, ‘The Conservative Campaign’Google Scholar, in Ranney, , Britain at the Polls, 1983, pp. 53–4, 57–9.Google Scholar