Choosing a voting system

Voting rules range form the very simple such as the plurality rule (commonly known as "first past the post") to a plethora of more or less complex schemes. These schemes attempt to capture notions of fairness such as proportional representation and and majority preference. Voting takes place for many purposes; even choosing a voting system. Whatever the more general position may be, if there is one, proportional representation has been Liberal Democrat policy on voting reform at all levels of government for so long it has become an entrenched view. In its defence, the policy is well worked out in the sense that there is a specific actionable proposal but the major problem has been in getting wider agreement on implementation. The Liberal Democrats went into the 2010 election with a specific position on electoral reform. The 2010 manifesto promised to:

Change politics and abolish safe seats by introducing a fair, more proportional voting system for MPs. Our preferred Single Transferable Vote [STV] system gives people the choice between candidates as well as parties. ...

Is there a liberal counter view. Yes, and it is embedded in a liberal classic. It is to be found in Karl Popper's major contribution to political philosophy "The Open Society and its Enemies". In this book Popper strenuously, but only briefly, defends the two party system and simple majority voting (plurality rule). In 1988 the Economist invited Popper to return to these themes in   The open society and its enemies revisited. In this piece he expands on his defence of the two party state and majority voting with detailed objections to proportion representation. Here I will engage with the presentation of the same arguments in an update provided by David Deutsch in his wide ranging book The Beginning of Infinity. Although, I will conclude that the criticism of proportional representation is not as conclusive as Popper and Deutsch would claim and that they underplay the weaknesses of "first past the post" or plurality voting, the critical engagement with their arguments brings out some points that strengthen the case for a proportional system.

Choices

In Chapter 13 of "The Beginning of Infinity" Deutsch devotes much space to working through examples to illustrate just how difficult it is to design a voting system that all parties agree to be fair. He then moves on to to more formal account using the setting of social choice theory.  This leads him to present and discuss the Arrow no-go theorem.This states that there is no rule that maps the preferences of the individuals in a group on to the preferences of the group as a whole that can satisfy a complete set of five intuitive, desirable and rational properties. These desirable properties (axioms) are:

1. The rule should define a group’s preferences only in terms of the preferences of that group’s members.
2. The rule must not simply designate the views of one particular person to be ‘the preferences of the group’
3. If the members of the group are unanimous about something – in the sense that they all have identical preferences about it – then the rule must deem the group to have those preferences too.
4. If a given definition of ‘the preferences of the group’, the rule deems the group to have a particular preference – say, for A over B, then it must still deem that to be the group’s preference if some members who previously disagreed with the group (i.e. they preferred B) change their minds and now prefer A too.
5. If the group has some preference, and then some members change their minds about something else, then the rule must continue to assign the group that original preference.

Remarkably, Arrow proved this set of 5 axioms is logically inconsistent. That is, no voting system can satisfy them all. This is a blow for a rational foundation to social choice theory but that has not stopped research and the development of a variety of voting rules.

In the UK the Electoral Reform Society (ERS) accepts the theorem but recognises the need to get on with voting system definition and evaluation, otherwise how would representational democracy work? An alternative, and more radical, reaction is to reject the social choice setting of the problem. This is implicit in "Open Society and its Enemies" but is made explicit by Deutsch.

The ERS introduce or exploit criteria such as locality and proportionality to rank and make trade-offs between voting systems. As could be anticipated from this approach, the ERS has come out in favour of compromise that includes an element of proportionality and and an element of locality, this is the Single Transferable Vote system, as adopted by the Liberal Democrats. In this system the more proportionality gained the less locality and vice versa, with the number of seats per constituency as the free parameter. In practice, the final position chosen will be a pragmatic trade-off with public opinion and wider political support.  

Proportional representation

After presenting Arrow's no-go theorem Deutsch attacks rather than discusses proportional representation (PR) voting systems. It is evident that PR shares weaknesses with all voting rules that are formulated in a social choice setting. Most of Deutsch's specific objections are effectively, if not absolutely conclusively, answered by the ERS in its pamphlet PR Myths. The first objection Deutsch makes is, however, not addressed in the pamphlet. This is:

... the ‘More-Preferred-Less-Seats paradox’, in which a majority of voters prefer party X to party Y, but party Y receives more seats than party X.

Deutsch neglects to mention that this also a weakness of the plurality rule. The system that avoids this particular paradox is Condorcet ranking, of which there are a number of variants, just as there are for STV. It would take us too far from the present discussion to examine Condorcet methods in detail. It has a formal weakness that the originator discovered, which is, basically, that a ranking is not guaranteed to exist. However this risk has recently been mitigated by factoring in preference structures in realistic population models. This recent work was carried out by Partha Dasgupta and Eric Maskin in a very formal version of social choice theory. However, what this objection highlights is that STV and other systems with similar ranking rules will be in conflict with an alternative view of fairness to PR, which is that preference should be given to option X over Y if  the majority prefers X to Y.

Beyond Social Choice

At this point Deutsch makes an interesting move against social choice theory itself that gains support from Popper's wider philosophy:

It [social choice theory] conceives of decision-making as a process of selecting from existing options according to a fixed formula (such as an apportionment rule or electoral system). But in fact that is what happens only at the end of decision-making – the phase that does not require creative thought.

The creative aspect is what happens before a set of choices are put before the electorate. Arguments, explanations, economic theories, values, public opinion and so on, all contribute to formulating the set of options. It is argued that the quality of the options on offer is more important than the voting rule that provides the preferences. Deutsch argues further that the weakness of the social choice setting and the paradoxes associated with it means that a more fundamental and wider criterion for voting is required. The more fundamental criterion is, according to Deutsch:

Popper’s criterion that the system facilitate the removal of bad policies and bad governments without violence.

Whether this is the only or dominant criterion, it is clearly a valuable one. Deutsch adopts Popper's arguments that a plurality voting rule matches this criterion better than any proportional rule. The ERS pamphlet PR Myths seeks to address the Popper objection directly. They frame it differently  as  "PR doesn't let you kick out an unpopular government", which moves it back into the social choice setting but it is close enough to the criterion for the purpose of the present argument. The counter evidence presented by ERS is straight forward observation. Countries that practice PR do not only get changes of government but it is not even a rare occurrence. This is followed up by the further observation that plurality rules have historically failed to remove unpopular governments and removed popular ones. Popper himself originally had the excuse that these observations were not available at the time of the first edition of the "Open Society" but not in 1988 and it is certainly not the case for  Deutsch. It is understandable that in the 1940's that the USA and UK were taken a the outstanding examples of the stable and effective liberal democracies but since then the problems with the two party system underpinned by a plurality voting rule have become evident.

Seen from the stand point of Popper's criterion both plurality and PR can provide in practice adequate mechanisms for removing policies or governments without resorting to violence but in both cases the importance of other institutions, constitutional checks and balances, and a fertile public sphere of debate and ideas is required. What this discussion is leading towards is the need to manage expectations of what can be achieved merely through adopting one voting rule rather than another. Behind Popper's criterion there is a philosophy closely related to his theory of knowledge. This requires a diversity of theories, conjectures, ideas and, in the political context, policies. This is facilitated by a system that encourages the growth of a diverse number of groupings that can formulate, criticise and propose solutions to the challenges in society. The plurality voting rule tends to lead to two major party blocks. Other sources of ideas and opinion can be safely ignore by these two major groupings. In the past, during the formative years of liberal democracy, the major groupings have been the Conservatives and the Liberals but for the last seventy years it has been the Conservatives and Labour. What also happens is the absorption by the major parties of more extreme positions, as can be seen clearly in the current situation in the UK and to some extent in the USA. In the UK the Conservatives contain a substantial and influential group of English nationalists and currently the Marxist faction leads the Labour party. So, there is some internal diversity but it is a management issue for the main parties not a constructive component of the national debate. Smaller parties are traditionally ignored except when there are small majorities or hung parliaments.

For a well functioning constitutional democracy it is this suppression of opinion and diversity that is the damning consequence of the plurality voting rule. PR is much stronger in nurturing small parties and opinion groups. What is needed is further reform of institutions that make sure that this diversity leads to more robust debate and effective policies.

Plurality voting rules should go, but this leaves Condorcet methods as an alternative to PR and there are numerous versions of PR. It is easy to see that Condorcet methods will tend to correct for any formulation of two polarising groups but whether these methods provide for and nurture diversity of opinion awaits further analysis. In a social choice setting the fairness encapsulated in the Condorcet mechanism is just as valid as the proportionality notion with which it is in conflict. Consideration should be given in a case by case basis as to which is the appropriate voting rule; whether in general elections, internal voting in Parliament and other bodies, and at different levels of government. Not only theory but the evidence from practice shows PR to have an established advantage in the creation of a diverse, multi-party public sphere, which together with the right institutions should provide a robust foundation for a liberal order.