How does the method of aggregating votes influence the outcome of elections?

This essay was written as a formative part of my undergraduate studies at the London School of Economics.

Part of the function of electoral systems is to take the individual preferences expressed by voters and aggregate them into coherent packages. When assessing and designing electoral systems, a primary concern for political scientists is how closely these packages, and their outcomes, match the individual preferences or whether a deficit arises between these two sets of preferences. 

This paper will the influence that different methods of aggregating votes can have on elections, showing that electoral systems are reductive in nature and that the very nature of electoral systems shows that you cannot create coherent social outcomes from the aggregation of individual preferences without the distortions that electoral systems cause. Ultimately, I intend to argue that the reductive nature of electoral systems is actually not a problem in itself, but the question we should be asking is what type of government we wish to see; we should be aiming to minimize the gap between individual preferences and aggregate outcomes when designing and choosing electoral systems as the key implication for the validity and stability of democratic regimes of government.

There is an inherent difficulty in taking individual preferences and mapping them to collective outcomes through electoral systems. Condorcet (1785) was one of the first political scientists to identify this difficulty, positing the Condorcet Paradox. The Paradox holds that whilst individuals are believed to be rational and that their preferences are transitive when taken in isolation, when taken as an aggregate, a group’s preferences can become intransitive1.

In certain scenarios, there is no mapping from individual preferences to a coherent social outcome. Different electoral systems – or more pragmatically, political elites that design these systems – make judgements about how to resolve this dead-lock scenario, but in doing so make inferences, where none can be made, on behalf of the electorate about their preferences.

Condorcet’s Paradox, whilst irrefutable, required quite specific conditions in order to occur. Arrow (1951) generalised the Paradox by creating a set of minimal fairness criteria against which electoral systems can be judged; universal admissibility, that all preferences are allowed; Pareto optimality, that if individuals prefer one outcome to another, then the opposite cannot be true at the aggregate level; independence from irrelevant alternatives, that individual’s preferences over irrelevant alternatives cannot affect the ranking of society’s preferences; monotonicity, that increasing the ranking of an outcome cannot disadvantage the outcome; and non-dictatorship, that no individual can dictate the group preference2.

The effective conclusion of the work was that there exists no single electoral system that doesn’t violate at least one of these principles as the political elites make judgements about which of these fairness principles are more important – more fair – than others when designing electoral systems. Electoral systems distort the preferences of individuals in order to create coherent social outcomes and to ensure a Condorcet Winner; the outcomes of electoral systems therefore are not necessarily representative of the majority of the electorate, and certain electoral systems will make the collective outcome more or less representative than others. So far it is clear that electoral systems seem to shape the outcomes they create, but exactly why this occurs is relatively unexplained by Condorcet and Arrow.

Duverger assessed the impacts of electoral systems on the outcomes of elections, splitting the effects into two areas – the mechanical effect and the psychological effect3. The mechanical effect shows how, holding electoral behaviour constant, different electoral systems produce different outcomes by focussing on the distortive effect of the formulae used to allocate seats and reductive effects of electoral systems that reduce the number of parties that will obtain seats through electoral competition and force some parties not to gain any parliamentary representation. The psychological effect exerts pressure on the electorate not to ‘waste’ their votes but instead to co-ordinate around viable candidates that are closest to them on a left-right policy space4. This behaviour has been referred to as strategic or tactical voting and aims to ensure that a voter’s least preferred candidate is not successful. The fact that this behaviour occurs shows again that electoral systems can be reductive in nature and limit the choices of voters at the ballot box.

The consequences of Duverger’s mechanical and psychological effects are profound for our concepts of democracy; it gives us two distinct “laws”. Firstly that “the majority [plurality] single- ballot system tends to party dualism” (Duverger, 1954, p.247) and secondly that “the second-ballot [majority] system and proportional representation tend to multipartyism” (Duverger, 1954, p.269). In essence, the more proportional an electoral system we choose the greater the choice voters get. If we are concerned with the ability of voters to have freedom of expression, as a core principle of democracy, it is logical to assert that proportional electoral systems are better systems to use when aggregating votes as they allow voters to choose parties closer to them on a left-right policy space. This is as opposed to the outcomes of the majoritarian plurality systems which tend to lead to two-party systems and a convergence around the Median Voter and thus a shift away from many voter’s ideal policy position.

Of course, the debate around this issue is deceptive. The increase in the number of parties – and thus the choices presented to the electorate – under proportional electoral systems is not as a result of some multiplicative factor. Parties increase in number under proportional systems because of the removal of some of the barriers put in place by plurality systems; it is a comparative gain, but it is still reductive because you cannot have an infinite range of political parties that are viable5. It should by now be clear that the electoral process restricts our breadth of choice by reducing the numbers of viable parties, but is this a problem?

When discussing electoral systems, the system itself is not, of course, the real issue at hand. Instead, it is the type of government that forms that we are concerned with. Do we want an electoral system that promotes two-party races with single-party government, or do we want a system that promotes coalitions? Do we want our parliaments to be highly accountable or highly representative? Do we want cohesive parties or individually accountable politicians? These are the real questions political scientists should be concerned with when they ask about aggregating votes.

Duverger’s laws lead us to the question of a trade off between proportional and majoritarian electoral systems. On the one hand, political elites may choose proportional systems because of the representation gains they give; because seats are allocated in direct proportion to the share of votes received, parliament’s tend to be a microcosm of society that represent broad sections of the electorate. Parliament therefore maps, as closely as possible, the preferences of the median voter6. Proportional systems also tend to be seen as better at mitigating tensions in highly divided societies – Northern Ireland being a classic example, where unionists and nationalists are forced into a power-sharing agreement that has brokered and sustained a peace-process for over a decade. Majoritarian systems however give very different outcomes; strong, single-party governments are frequent. These governments are decisive and face down crises in a far more efficient manner than coalition governments formed by proportional systems as there are fewer veto-players to contend with7. Majoritarian systems can however see large swings in government policy as small vote changes cause big changes in seat allocations; this flip-flopping on policy can mean the median voter is ill-represented. The reductive nature of the electoral systems we choose can cause the actual policy outcomes of government to be vastly different to that of the individual preferences of voters. We should therefore be concerned with the democratic deficit this creates; this deficit is the primary effect of electoral systems and should be a principal concern.

Of course, the preceding arguments have very much focussed on institutions being the things that shape our behaviour. But this institutionalist view can also be challenged by looking at the “freezing” hypothesis of Lipset & Rokkan. Their theory argues that parties are born from the organisation and association of groups within social cleavages – like the Labour Party in the UK being formed by working class, trade union members – and that these cleavages became frozen in the 1920s. These cleavages, they argue, still shape our electoral behaviour today; many people vote the way they do because of social conditioning; the fact they come from a working class or middle class family, where they live, etc8. If the cleavage model of electoral behaviour is correct, my earlier arguments are irrelevant. Electoral systems can be reductive in nature but they can’t make us vote in a different way; Duverger was essentially wrong in his thesis and there are no broader impacts on democracy arising from the choice of our electoral systems. Of course, the steady decline in partisan identification over the past few decades, and the structure of modern European society is shifting with an increase in the middle-classes and so the freezing hypothesis itself may not be relevant to today’s society. This is may have been a plausible argument for the 1960s, but for 2011, it holds less weight.

If we are truly concerned with the democratic implications of electoral systems, our principle concern should be the gap between the package of social outcomes governments create and the expressed opinions that individuals make. It is impossible to create coherent packages without electoral systems, but they have side-effects. Electoral systems are reductive, which brings us a narrower field of choice than we might otherwise have, however, they also help us to coordinate around viable candidates and parties that represent us in some fashion; if they didn’t, we simply wouldn’t vote for them. It is possible to minimize the democratic deficit between these outcomes and preferences through the choice of electoral system, but which one to choose depends on the type of government people want. If they want a government that is genuinely representative – as far as possible within the previously mentioned constraints – then they should choose a proportional electoral system. If they prefer the stability and performance gains of a plurality system, this should be their choice. A better pursuit however may be to look for the electoral “sweet spot”9 – to get the best of both worlds, accepting that there never will be the perfect outcome.

  1.  Condorcet, M. (1785). “Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix”, France: De l’Imprimerie royale. 

  2.  Arrow, K. (1951). “Social choice and individual values”, London: Chapman & Hall. 

  3.  Duverger, M. (1954), “Political parties: their organization and activity in the modern state”. Methuen: Wiley. 

  4. Capoccia, G. (2002). “The Political Consequences of Electoral Laws: The German System at Fifty” In: “West European Politics” London: Frank Cass. Vol. 25, No. 3. pp.171-202. 

  5.  Sartori, G. (1986). “The influence of electoral systems: faulty laws or faulty method?” In: “Electoral Laws and their Political Consequences”, New York: Agathon Press. p.57. 

  6. Downs, A. (1957). “An Economic Theory of Democracy”. New York: Harper & Row. 

  7. Tsebelis, G. (2002). “Veto Players: How Political Instituions Work”. New York: Princeton. 

  8. Lipset, S.M & Rokkan, S. (1967). ‘Cleavage Structures, Party Systems, and Voter Alignments: An Introduction’, In: “Party Systems and Voter Alignments: Cross- National Perspectives”. London: Collier Macmillan, pp.1-64. 

  9. Carey, J. M. & Hix, S. (2010). “The Electoral Sweet Spot: Low-Magnitude Proportional Electoral Systems”.