Power Indices and the Design of Electoral/Constitutional Systems

Abstract

The literature on power indices is very large, but it has had little impact on public debate regarding various aspects of constitutional reform and the design of electoral and voting systems. The need for such an impact is very substantial, as illustrated by three recent examples drawn from New Zealand and the UK. But researchers who use power indices seem to prefer to be scholars (working in ‘ivory towers’) rather than technocrats or emancipators who might engineer or stimulate informed change: their research has very little wider impact.

An earlier version of this chapter has been published in Power Measures. Volume I (Homo Oeconomicus 17), edited by Manfred J. Holler and Guillermo Owen (2000).

Postscript 2011

The 2010 general election in the United Kingdom resulted in no party having a majority in the House of Commons, so for the first time (other than during the two twentieth century world wars) the country had a coalition government. During the campaign preceding that election, the opinion polls suggested that no party would win an overall majority and commentators argued that, because of the biases currently inherent to the UK electoral system (Johnston et al. 2001), the allocation of seats across the three main parties could vary considerably with small differences in their share of the votes (see also the simulations in Rallings and Thrasher 2007). The issue of which parties might be able to form a viable coalition was much discussed but there was, however, no formal modeling of each party’s relative power in that evolving situation.

One of the coalition government’s first major pieces of legislation proposed that the voting system for the House of Commons be changed from first-past-the-post to the alternative vote, with the decision to be made by the electorate in a binding referendum (Johnston and Pattie 2011). There was much discussion that this would almost certainly mean the end of one-party government and its replacement by coalitions and a great deal of the debate regarding this focused on the power it would give to relatively small parties, probably of the centre (as with the Free Democrats for long periods in post-1945 Germany)—but there was no formal modeling. Furthermore, there was little recognition that the House of Commons now includes MPs from eight parties with more than one member (apart from the Conservatives, Labour and Liberal Democrats these are: Plaid Cymru—the Party of Wales; the Scottish National Party; and, from Northern Ireland, the Democratic Unionist Party, the Social and Democratic Labour Party, and Sinn Féin) plus three other individuals (representatives of the Green Party, the Alliance Party of Northern Ireland, and an independent—also from Northern Ireland). Those smaller parties might exercise considerable power, both individually and severally (although the five Sinn Féin MPs do not take their seats and vote), and modeling could have illustrated a range of such scenarios—including those in which parties such as Plaid Cymru, the Scottish National Party and the Green Party might have increased their representation in a Parliament elected by AV (though see Sanders et al. 2011). The potential for modeling that could illuminate the likely situations in what was an ill-informed and bad-tempered referendum campaign in 2011 was not realised, however. The referendum failed, with the switch to AV being rejected by a ratio of 68:32.

The UK Parliament is now discussing whether to replace the appointed House of Lords by an elected second chamber (with probably 20 % of the members still appointed, by a non-partisan commission). The current House of Lords comprises four main groupings—those who take the three main party whips (Conservative, Labour, Liberal Democrat) plus the cross-benchers (who have no party affiliations); there is a small number of ‘others’, including 26 bishops of the Church of England. None of the parties has a majority although the current coalition of the Conservative and Liberal Democrat parties has a majority among those who take a party whip; whether it can get its business through the House thus depends on the votes of the cross-benchers (many of whom attend the House only infrequently: Johnston and Pattie 2011). The current proposal is for the elected members of a revised House to be chosen by the quasi-proportional STV method from multi-member constituencies; the equivalent to the non-partisan cross-benchers would be appointed but, unlike their predecessors, expected to be full-time members. It is thus very unlikely that any one party—or even a coalition of two—would have a majority in such a House, and the cross-benchers (and/or other small groups outwith the main parties) could be crucial to the fate of any legislation,¹⁸ depending on how they split and assuming that members of each party group all vote the same way. This offers a major opportunity for modelling the power not only of the party groups but also, more interestingly, of the non-party cross-benchers, individually and in combinations.

The New Zealand case is a further example of the absence of any formal modelling of the allocation of power in legislatures where no party has a majority of the seats. Following the decision to change the electoral system to MMP in 1993 the country has experienced a range of single-party and multi-party governments, and it is that experience—without any detailed analysis using power indices—that informed the electorate when it was asked in a 2011 referendum to decide whether to retain MMP or switch to another system. The referendum result was not binding on the government. If the decision was for change, then Parliament would decide whether to hold a further referendum in 2014 when the electorate would choose between MMP and the most popular of the four other systems voted on in the second part of the 2011 referendum. (Even if the electors opted to retain MMP in 2011 the referendum ballot included a second question asking which of four other systems they would prefer if MMP was to be replaced.) If the electorate voted to keep MMP then there would be an independent review of that system in 2012 to determine if any elements of it should be changed; in the event, the country voted by 58:42 to retain MMP, with fptp the most popular among the four options offered in the second part of the referendum.¹⁹ Much was done to educate the electorate regarding the various electoral systems on the referendum menu, but little on the possible consequences in terms of the allocation of power.²⁰

Finally, one example where academics have been involved as technocrats, using their research expertise in the measurement of power, concerns the allocation of seats in the European Parliament. A group of mathematicians recommended that each member state be allocated a baseline of five seats and that the remaining seats be allocated proportional to the states’ populations so that: (1) no state has more seats than a larger state; and (2) the ratio of population to seats increases with state population—a principle known as ‘degressive proportionality’ (Grimmett 2011). This is a rare example of theoretical knowledge in this field being put to practical effect (see also Rose and Bernhagen 2010; Rose et al. 2012). Some academics have designed electoral systems that they consider superior to those either currently being deployed or considered (e.g. Brams 2008; Balinski and Laraki 2011—see also Szpiro 2010); they have had some success, notably in the design of systems for local governments (e.g. Balinski and Ramirez Gonzales 1999; Schuster et al. 2003; Pukelsheim 2006, 2009) but as yet not for elections to national legislatures.