Voting systems core principles

One of the purposes of this site is to prompt debate about the core voting method attributes that contribute to the ‘representativeness’ of an electoral system, or of an election outcome.

The political scientist Hanna Pitkin, in the classic work on this subject The Concept of Representation (1972), saw the idea of political representation as encompassing four objectives:

• establishing systems of authorisation or public decisions, and also of accountability
• offering some symbolic meaning to those being represented, generating legitimacy for the political system
• ensuring that representatives in some way mirror the characteristics of the people represented
• determining what it is that representatives actually do for the benefit of those represented – that is, the actual political outputs of representative democracies

Voting systems can help – or hinder – in the achievement of all four of Pitkin’s aspects of representation, depending on the specific design of the voting and vote counting methods.

Ultimately, some attempt must be made to determine the attributes, or measures, against which different voting methods are to be assessed and chosen.

Such attributes will be of a fundamental nature – similar to axioms in mathematics – so it is hard to know how to derive them. Perhaps such axiomatic principles must simply be asserted, and then tested. The following list of attributes is, therefore, an assertion of a possible fundamental set of desirable voting system attributes:

• directness – does the system allow voters to specifically vote for individual candidates as their representative?
• participation – how many of the voters are allowed to, are enabled to, and in the end actually do participate in elections?
• choice – how wide is the range of candidate and political choice available to voters; is choice limited, constrained or manipulated by the voting system or any aspect of how the election is conducted?
• equality of influence – is the power to influence the election’s outcomes equal for all electors, or are some electors more influential than others?
• extent of representation – what proportion of the electorate ends up having a representative in the elected assembly whom they personally supported?

Overall, these five attributes aim to provide a set of tools for designing – and measuring the performance of – the voting systems used in the election of representatives.

The five attributes are distinct, in that it it difficult to see that any one of them can be conceptually subsumed within another. (As a separate issue, the achievement of some attributes through various voting methods does impact the achievement of others, both positively and negatively, but that is unrelated to the logical separation of the concepts.)

The five attributes appear to be a complete set, in that no obvious attributes of equivalent type appear to be missing. Standard evaluations of voting systems appear to be applications or one or more of these five attributes.

On that last point, two specific issues should be addressed immediately relating to well-known psephological concepts: localness, and party-proportionality.

One possible candidate for a 6th attribute is the electoral system design feature that might be termed localness.  Most electoral systems are based on the notion that members of parliament represent local geographical areas.

The extent to which this is a suitable design for an assembly may depend on the constitutional role of the assembly in question. For example, in a federal system local, or state, governments may have reasons directly related to their policy responsibilities to maintain local aspects of their electoral system. On the other hand, at the level of national parliaments, scale as well as the national and international scope of the policy decisions in question may make the local connection much less relevant.

In any case, what is argued here is that localness, correctly understood, is not a distinct design goal but is in fact just one aspect of the goal of choice. Voters might well be provided with the option of selecting a representative who offers ‘local representation’ as one among many factors in attracting support. But whether they are constrained from choosing from outside such options is, ultimately, an issue of the extent of choice granted to the voter.

Another possible candidate for an additional core attribute is party-proportionality, or the measure of the ratio of votes cast for parties to seats allocated to them. Since the 1960s an enormous amount of attention has been given to the issue of party-proportionality in the political science community. The interest is most prominent in Europe, no doubt because the continent is the home of the party-based seat-allocation proportional representation systems.

But party-proportionality is only a derivative result, not directly linked to the voter-representative relationship.

Party-proportionality is also a measure of the success of parties, not the success of voters, in achieving ‘fair’ outcomes. The fundamental point of difference of the seat allocation systems from the direct voting systems it that they treat political parties as the subject of the system – as the ‘customer’ – rather than the electorate itself.

What is argued here is that party-proportionality, correctly understood, is in fact a specific application of the principle of equality of voter influence. The extent to which voters choosing political parties gain differing levels of representation, which is what party-proportionality measures, is actually one way of measuring inequality of voter influence. (There are also other measures of voter influence). For these reasons, party-proportionality of election outcomes should not be elevated to the status of a core design principle.

Finally, there are a number of practical factors arising from different voting methods: complexity, convenience, ease of administration, and vulnerability to manipulation.

These issues are real, but they are not core attributes of the same type as the five attributes listed above. These matters tend to amount to practical problems, which are best addressed through practical solutions.

For that reason these matters are best separated from the ‘core’ attributes of voting methods.

Which voting system best addresses the core attributes

A surprisingly simple argument follows about which of the variety of voting methods in existence is best at satisfying the identified five core attributes of representation.

Adhering to the principle of direct election rules out the use of any of the party list seat allocation systems favoured in Europe and other parts of the world.

Choice comes in a spectrum of degrees. The number and diversity of candidates on offer is obviously a basic driver of how much choice is on offer.

But the selection of the voting system also controls how much choice is offered in several ways. Basic voting systems which offer voters just one step in exercising their choice, by supporting one single candidate and doing nothing further, deny voters the capacity to have ‘fallback’ positions, which means that their first and only choice may be constrained by tactical considerations. Allowing a series of fallback choices to be expressed is, of course, exactly what preferential voting systems make possible.

The goal of voter equality would seem to require that it should take exactly the same number of voters to elect every candidate to Parliament. This in turn suggests the need for a uniform quota for election.

From these conclusions we can see the following specific voting devices will form part of an optimal voting system:

• direct marking against the names of individual candidates on the ballot paper
• no use of ‘party lists’ in any form
• the setting of a common quota of votes for awarding every seat to a winning candidate
• multiple preferences in a sequence are recorded
• all preferences are optional choices
• no use of rules invalidating the ballots of voters because of their choices

Electoral scientists will recognise in these conclusions the outlines of the single transferable vote method (STV), specifically the variant using ‘optional preferencing’.

STV was invented in the mid 19^th century and subsequently developed in significant ways by Australians. STV’s mechanism is at the heart of the package of voting techniques widely used in Australia and known as the Hare-Clark system.

There is solid statistical evidence that choosing STV over single-member division voting systems yields strong results in terms of the principle of actual representation.

To understand the features that would make up an optimal way of voting to achieve all the above goals, it may help to use a visual metaphor of the voting process.

Suppose that all the voters are gathered in a field. Candidates are nominated, and each one takes up a visible position; perhaps they are arranged in clusters to represent alliance as parties. The voters then move around the field, each choosing to stand around the candidate whom they support to be their representative in parliament.

Voters may change their minds and shift around within a pre-agreed timeframe in which to settle. As each candidate attracts a quota of votes, that support is locked in, but voters surplus to the quota are released to continue in search of other options.

The election has achieved its end, and voter movements cease, when as many of the voters as possible are gathered in equal numbers in support of the chosen candidates.

In this illustration, the principle of direct election is maintained by ensuring that the only form of support that matters is that of an individual elector choosing to stand by the position of an individual candidate. No practice is permitted which would allow proxy voting through intermediaries, or the collection and direction of individual votes by intermediaries, or involving voting for clusters (that is, parties) rather than for individual candidates.

Next, two simple rules serve jointly to give effect to each of the principle of equality of influence and that of actual representation. One rule is that the election of every successful candidate must be based on attracting the same number of voters – a quota – showing their support. The second rule is that if more voters than the required common quota support one candidate, some of them may be released to give support for other candidates.

The first rule gives us the basic result of voter equality, while the second rule prevents that equality from being immediately undermined by diminishing the relative value of voters who support a candidate in over-quota numbers, compared to others who more closely match the target quota. And both rules work together to ensure a high rate of actual representation.

The principle of choice is upheld by ensuring that all voters can see all the options available, and their responses are limited only by the effort they wish to put in to explore those options. In addition, choice is not undermined by any practice that creates rewards or penalties for choosing one candidate over another. Free choice also extends to the right to shift support during the sorting process without any discriminatory pressures being imposed.

Finally, the option of stepping out of the process altogether (ie: by their ballot becoming exhausted) is available, so long as it is an entirely voluntary option.

The principle of participation is protected when all voters are freely able to join in the voting exercise. There are no ‘barriers to entry’ to the field. No procedure is used which threatens to discourage or to exclude any voter from the voting process on the basis of the candidate choices they prefer.

No other method of direct election gives voters equality of influence, high levels of actual representation and high levels of choice to the extent that STV does.

STV has no adverse impacts on participation rates (although variants which invalidate ballots through compulsory preferencing requirements do have a negative impact), and indeed the high levels of choice and control have a measureable effect of increasing participation rates.

STV sometimes suffers from unpredictable results arising from the use of sequential elimination (ie: the exclusion of the lowest-ranked candidate in the successive rounds of counting). This is a traditional, but not a necessary, approach to sorting the votes towards a set of winners.

Sequential elimination causes several problems, not least of which is that by creating a ‘single chain’ of preference transfer tallying, it takes on the appearance of being random in nature, and in turn brings into question for some observers the legitimacy of the specific outcome of a count as against other possible outcomes that might have occurred.

The defects caused by sequential elimination can be cured by the use of the Condorcet principle, a voting principle aimed at identifying winners who would prevail over any candidate to whom they are compared, rather than winner who defeats only the candidate against whom they are finally matched after just one particular sequence of candidate eliminations.

The equivalent for STV is to determine the set of multiple winners which is collectively preferred by the voters to all other alternative sets of winners. The calculation demands on doing this with STV are significant, and while Nicholas Tideman (1995) and Marcus Schulze (2008-11) have outlined possible Condorcet-STV voting systems, no convenient method of implementing them in practice has yet been developed.

Non-core attributes of voting systems

Earlier we noted the existence of complexity, practicality and convenience issues in voting systems – factors of a less ‘mechanical’ kind (ie: not related to the level of representation generated by the vote counting method itself) by which voting methods and electoral systems can be evaluated. Before concluding, let’s tackle these a little more in relation to STV.

These issues generally fall into the following categories:

• the information convenience of electors (ie: the burden of information needed to utilise any given voting method or electoral practice)
• the convenience and cost-effectiveness of voting methods for the administrators of the system
• the vulnerabilities (if any) of a given voting system to being manipulated, or gamed, by candidates or political parties (or even by the electors)

What is argued here is that these kinds of problems are ones best addressed by pragmatic operational solutions. They ought not be elevated into matters on which the primary selection of voting methods should turn.

In particular, we should avoid the conclusion that voting systems which present lots of choice will always be too complex for voters to understand. Human beings cope every day with surprising skill at understanding rule systems relating to sporting codes and gambling opportunities that are far more complex that any voting method.

The problems of complexity are usually only of any significance when inherently simple voting systems are unhappily coupled with devices such as compulsory preferencing, or the need to understand the impact of distortions such as group voting tickets.

Gaming vulnerabilities can sometimes be addressed by pragmatic solutions, but it is true that some failings of this kind do go to the merits of voting systems themselves (for example, block voting and Borda counting are two voting systems that are highly subject to gaming.)

Simple STV is a very difficult voting system to game by either the candidates or by the voters, and indeed voters have no real incentive even to seek to do so.

Voting systems that subject either the nominees or the electors to perverse incentives or disincentives (such as by forcing parties to strategize about which or how many candidate to nominate, or forcing voters to mark insincere or tactical preferences) all reduce the degree and quality of voter choice, and usually also create inequalities of voter influence.

The creation of single-member electoral divisions is in fact an example of a manipulation of the electorate through the control of choice. Malapportionment of such divisions has been another historical practice that worsened the inequality of voter influence.

Moreover as single-member divisions create concentration distortion effects, they unavoidable create voter inequality, often to a striking degree. The practice of gerrymandering – the specific manipulation of electoral boundaries – has been used to make such impacts even more exaggerated.

Also possible are contrivances in the design of ballot papers. For example, the recently abandoned system of ‘group voting tickets’ used in elections for the Australian Senate was an instance not of gaming caused by STV itself but of gaming through the ballot paper design. (This system, abandoned in 2016, is still in force in respect of future elections of some Australian state assemblies.)

In the end, gaming opportunities are created by system designers, and are usually very easy to remove. All that is required is the application of principle by those who lay down the specific system rules.

Malcolm Baalman
(revised) May 2016