Equality, Proportionality and Statistics: Political Representation from the English to the French and American Revolutions

Abstract

Debates on the proportionality of political representation surfaced repeatedly, and in similar forms, from the English to the American and French Revolutions. They contributed to shaping those revolutions’ outcomes and, through them, to the emergence of modern democracy – especially so as they were linked up with voting rights: demands to make seats in assemblies more numerically proportionate to electorates – in other words, to weigh all votes equally – implied the equal weight of individual votes and thus also entailed calls for more equal standards regarding the right to vote. This did not yet signify voting rights for all: only specific categories of individuals – as a rule, male and propertied – were considered, even by the most ‘enlightened’ writers, to be politically entitled. Nevertheless, it was only one step from here to envisage voting rights for all individuals – or at least, for the time being, for all male individuals – as can also be seen in all three revolutions. If claims for more proportional and equal representation showed their full impact only on the American and French Revolutions, finally, this was due to the intervening emergence of statistics (or ‘political arithmetic’) as a tool of reflection and debate that gave numbers and calculations increasing persuasive power.

Introduction

Debates on the proportionality of political representation surfaced repeatedly, and in similar forms, in the 150 years from the English to the American and French Revolutions. They contributed to shaping those revolutions’ outcomes and, through them, also to the emergence of modern democracy – the more so as they were closely linked to the issue of voting rights. Detailed retracing of those debates will show consistent patterns and reveal their specific contribution to those revolutions and to the (pre)history of modern democracy.¹

As democracy is under pressure today, it is important to reconsider the historical conditions of its genesis. The idea that representative democracy is a necessary long-term outcome of history is not only challenged by populist parties; it has also been discredited, on a conceptual level, by postmodernist theory. This article shares this sceptical attitude towards the notion, prevalent among earlier generations, of an all-but natural, gradual gravitation towards democratic government during the seventeenth and eighteenth centuries. Recent studies on European states and regions have shown that neither Estate assemblies nor popular rebellions were usually poised for broader forms of political participation before the late eighteenth century. Until then, in fact, participation often became yet more restricted and oligarchical across Europe, including Britain.

This article will contribute to understanding the elements that did finally make modern representative democracy plausible and possible by focusing on one such element: the evolution of demands to make seats in assemblies more numerically proportionate to electorates, or, in other words, to weigh all votes cast more equally. As such demands implied the equal weight of individual voices and votes – self-evident to us but sharply contradicting traditional hierarchies and collective identities, so firmly entrenched at the time – they also entailed new demands for equal standards regarding the right to vote. Equal standards did not, though, mean voting rights for all: only specific categories of individuals – male and propertied or otherwise economically viable – were considered, even by the most ‘enlightened’ writers, to be entitled to equal political rights. Yet, it was just one more step from here to envisage voting rights for all individuals or at least, for the time being, for all male individuals. This can be seen in all three revolutions, too, although such rights were fully implemented only in the twentieth century.

Claims for more proportional and, as a corollary, more equal representation came to the fore in the English no less than in the American and French Revolutions but they had a major and lasting impact only on the latter two. An important clue to this divergence, it will be argued, lies in the timing of the emergence of statistics, or ‘political arithmetic’ as it was then called. The growing persuasive power of numbers and calculations, from the second half of the seventeenth century onwards, proved decisive to underpin the related notions of proportionality and standardised individual voting rights in the later eighteenth century. The same numerical rationality, as we will see, too, would ultimately make those notions gravitate towards universal voting rights.

The article will point to some pivotal moments and elements of the discussions around these issues. It will not, and cannot, offer a complete and coherent account of the subject over the 150 years that its (early) history covers. Such an account will require more in-depth research and a book-length presentation. Still, the present article seeks to show the acuity and continuity of debates on the proportionality of representation across those 150 years and their relevance for democracy's (pre)history.

Setting the frame: civil war and Commonwealth

In England, the creation of ever more parliamentary seats for boroughs, particularly over the sixteenth century, had led to a massive preponderance of borough over county seats and, thus, to a highly disproportionate representation of the electorate as a whole.² It had also led to a steady increase in ‘rotten boroughs’ with few voters, so that among the boroughs, too, representation was becoming ever more uneven. As a result of constituencies’ extremely divergent size and composition, the soon-to-be-revolutionary ‘Long’ Parliament of 1640 was further away from evenly representing the country than any of its predecessors. Still, setting aside some temporary changes in the 1650s, only very few alterations were to be made over the next two centuries. As a consequence of uneven population growth, moreover, parliamentary representation would become ever more distorted. Most notoriously, but not exceptionally, before the reform of 1832 the industrialising cities of Birmingham and Manchester had no seats in Parliament at all.

This state of affairs had been a matter of criticism already in the sixteenth century – but this was more partisan than principled, reflecting corporate or personal indignation over the fact that one's own home had no seat in Parliament. Nor were complaints accompanied by remarks on the fact that, quite apart from their divergent sizes, voting rights, too, differed massively between boroughs. (In the counties, the electorate was at least nominally on the same footing across the country as all owners of freehold land worth at least forty shillings a year were entitled to vote.) In a number of disputed cases in the first decades of the seventeenth century, particularly in the 1620s, Parliament resolved in favour of a larger franchise. But this did not flow from overarching principles, either: the Commons tended to favour broader voting rights mainly so as to diminish court influence on particularly small elite electorates.³ Generally speaking, the absence of any actual competition among candidates meant that voting rights were a symbolic much rather than a real asset. Mostly, local and regional elites agreed before an ‘election’ on the two candidates to be chosen, while contested – and, in this sense, proper – elections with more than two candidates were rare. As a result, neither the number of voters nor, as a corollary, the entitlement to vote was much of an issue. This began to change in 1640: with the broader political struggle, elections became more competitive on the level of candidates and, thus, also of voters.⁴

Popular participation in politics generally widened in the 1640s in the face of massive political and religious contestation, civil war and revolution. Beginning in 1640 with the election, after eleven years without Parliament, of the Short and, after its speedy dissolution, the Long Parliament, the public's minds and souls became objects of campaigning – and so did its financial and physical resources, as war broke out in mid-1642. Print poured out in hitherto unknown quantities, appealing to the people at large and spelling out their enhanced political role. This translated into active participation by urban populations who started to sign, and to bring forward, political petitions in their thousands.⁵ Such mobilisation was most intense in London – but it would also permeate the New Model Army whose officers and soldiers saw themselves as a political force and religious vanguard in their own right, especially after the decisive defeat of royal forces at Naseby in 1645. It was in those two particular social orbits, too, and around that same time, that intellectual radicals, later labelled ‘Levellers’, emerged to propagate a consistently individualised and bottom-up vision of society – and, indeed, a degree of egalitarian popular sovereignty unprecedented in either historical practice or theory.⁶

With the mobilisation of a broader public and an incipient rhetoric of empowerment of ‘the nation’ and ‘the people’, the question of who had the right to vote took on more relevance, too. Yet, a generic concept of the franchise, beyond the multiplicity of local franchises, was still not immediately evident and was not spelled out even by those who appealed to ‘the people’ or ‘the nation’ as the ultimate source of political power. This was certainly due, to some extent, to the absence of general elections after 1640 (hence, the ‘Long’ Parliament). But there was also a conspicuous absence of calls for a broader ‘franchise’ by either side, be it only to court popular support – an absence relatively more conspicuous in the case of Parliament which, in its struggle for legitimacy with the king, claimed to be the true representative of the people. After the (first) end of civil war in 1646, though, a notion of ‘the’ national franchise emerged due to two interlinking discourses: an insistence on equal, proportionate representation among all constituencies, spelled out by the Levellers; and the New Model Army soldiers’ demand for their own individual share in future politics. Both of these claims merged in the autumn of 1647, catalysed by half a year of conflict with a parliament that refused any kind of redress.

In October 1646, Leveller figurehead John Lilburne, imprisoned at the hands of Parliament, denounced the ‘insufferable injury, and wrong, that is done unto thousands of the freemen of England’ by the highly uneven representation of regions and localities: Cornwall had ‘almost 50 Parliament-men; and Yorkeshire twice as big, and three times as populous, and rich, not half so many’ – not to mention ‘my poor Country the Bishoprick of Durham’ with no seats in the Commons at all.⁷ Lilburne therefore thought it ‘a great deale of more Justice and Equity … to proportion out to every County, [i.e.] to chuse a proportionable number, sutable to the Rates, that each County by their Bookes of Rates are assessed, to pay towards the defraying of the Publique charge of the Kingdome’.⁸ Counties should be weighted according to their tax yields for parliamentary seats, and the same distributive principle was to apply within them.⁹ Such a general redistribution of seats could also end the other injustice: uneven voting rights. For whilst ‘divers … men of great estates in money and stock’ had no voice, some boroughs featured ‘scarse any but Ale-housekeepers, and ignorant sots, who want principles to chuse any man, but only those, that … some … great man … recommends; or else who bribes them for their votes’.¹⁰ Lilburne here advances standard arguments against giving the vote to the poor – as being ignorant, unprincipled and prey to bribery. Thus, his first call for fairer representation is, rather surprisingly, not at all a plea for equal voting rights but one for more proportionality and equality among those men who were economically viable and independent.¹¹

Half a year later, the army took up the issue in the midst of its confrontation, political as well as religious, with Parliament's Presbyterian majority. In mid-June 1647, with the antagonism approaching its climax – and two weeks after Lilburne had repeated his views¹² – very similar statements appeared in the first overtly political ‘Representation of the Army’:

… that some Provision may be now made for such Distribution of Elections for future Parliaments, as may stand with some Rule of Equality or Proportion, as near as may be, to render the Parliament a more equal Representative of the whole, as for Instance, that all Counties or Divisions and Parts of the Kingdom … may have a Number of Parliament-Men … proportionably to the respective Rates they bear in the Common Charges … of the kingdom, … or some other such like Rule.¹³

While the gist of the demand is clearly the same as Lilburne's, other potential criteria than mere tax returns are envisaged now to provide proportionality among constituencies. The same demand was included in the ‘Heads of the Proposals’, a more fully fledged constitutional scheme published at the beginning of August, after the army had secured control over Parliament. Again, it stressed that seats could be reapportioned on the basis of taxation – or ‘according to some other rule of equality or proportion’.¹⁴ The most obvious alternative was the number of people (or voters) in the constituencies, but this was not as yet spelled out: this only happened in the famous Agreement of the People, a more radical constitutional scheme drawn up in October 1647, to be discussed presently. The radicalising potential of such an alternative, however, was already present, in the summer, in the soldiers’ demands for a continuing and equal share in national politics. These demands were a reaction, at least in part, to parliamentary threats of disbandment – and thus degradation to soldiers’ former, mostly lowly and politically impotent status – and to the peremptory manner in which Parliament was handling the soldiers’ grievances. The latter, moreover, began to equate their own case with the nation's: the ‘Representation of the Army’ urged the defence of ‘our owne and the peoples just rights, and liberties’, with the aim that ‘we, and all the free-born people of this Nation’ could live quietly.¹⁵ A few months later, in mid-October 1647, ‘The Case of the Army Truly Stated’ would develop these juxtapositions further, bracketing ‘the Army [and] the poore oppressed people of the nation’, the ‘rights and freedomes of our selves and the people’ and, in short, ‘our own & the peoples case’.¹⁶ Consistent with such bold and potentially radical rhetoric, the ‘Case of the Army’ for the first time also explicitly asked for broad, and potentially even full, (male) voting rights.¹⁷

Both strands of demands – for a more equal representation and for the soldiers’ and, at least by extension, other men's voting rights – were to merge fully in the propositions made at the Putney debates in late October 1647. It was only here that the (national) ‘franchise’ became a topic proper, although even now the term was not employed.¹⁸ The Agreement of the People, drawn up on the eve of the debate and serving as its starting point,¹⁹ was silent on voting rights – but it did state for the first time explicitly, and prominently, that constituencies ‘ought to be more indifferently proportioned according to the number of the inhabitants’.²⁰ Although all participants in the debate, including also the army leadership under Cromwell, essentially agreed on this, the clause led to the explosive opening question by General Henry Ireton: did it signify only ‘that every man that is an inhabitant is to be equally considered’ when creating proportionality among constituencies – something he might concur with – or was it also supposed to mean that every man was ‘to have an equal voice in the election of the representers’?²¹ In which case, he stated, ‘I have something to say against it’.²² The challenge was borne squarely by Maximilian Petty: ‘We judge that all inhabitants that have not lost their birthright should have an equal voice in elections.’²³ The question of the franchise in the debate thus arose from the Agreement's apportionment clause; and it was immediately divisive, with Ireton, Cromwell and other officers defending existing franchise regulations, and some officers, soldiers and civilians arguing for a sweeping franchise extension – possibly to include all adult males.

Ironically, the franchise debate at Putney is still almost as controversial now as it was then. Ever since its protocols surfaced in the late nineteenth century, it has elicited countless interpretations and counter-interpretations – but the specific content of the plea for franchise extensions has remained, and probably always will remain, something of an unassailable black box. The search for a coherent stance, especially on the side of the Levellers and/or the army ‘radicals’, is understandable in view of the later historical relevance of the franchise and also in view of the fascinating exchanges that the issue occasioned at Putney. The search might, however, be somewhat anachronistic: in contrast to the proportionality issue, the franchise question was so novel and so abruptly introduced, and it evolved so haphazardly during the debate – which is partly why it is so fascinating – that we cannot assume that individual speakers had arrived with a consistent view on it, let alone sharing a view between them. In any case, though, it seems by now generally acknowledged that the intricacies of the nuances in terminology and statement, conscious or fortuitous, are impossible to disentangle completely. The impression that clear pronouncements for a full male franchise were made during the debate is strong – but again, it might well be biased by the anachronistic assumptions of us modern readers, as first argued by Crawford B. Macpherson.²⁴ When it came to settling for a compromise after the debate, moreover, the soldiers were ready to exclude servants and receivers of alms, as long only as they themselves were given the vote regardless of their previous social status.²⁵

Another, overlapping debate concerns the extent and timing of the influence of Leveller leaders and ideas on the army, the Agreement and the debates at Putney.²⁶ Those London political radicals most prominent in the context of the last two also seem to have created vital links, by the autumn of 1647, between the army and Leveller writings and ideas.²⁷ But while Leveller notions concerning individual rights, basic equality and popular sovereignty certainly exerted a strong influence, directly and indirectly, on New Model Army political radicalism, it is hard to establish an immediate contribution of their core figures – John Lilburne, William Walwyn and Richard Overton – to the Agreement, to the Putney debates and, indeed, to the discussion of the franchise.²⁸ In any case, crucial for our context is the point – not made in this way before – that against a background of evolving political radicalism, most consistently represented by the Levellers, it was only the convergence of a specific Leveller insistence on the proportionality of parliamentary representation, on the one hand, and of the soldiers’ demand for their own voting rights, on the other, that first put ‘the franchise’ (and its enlargement) on the agenda. In this perspective, the franchise debate did not hinge on any specific Leveller notion – which doesn't seem to have existed – of who ought to be enfranchised. It did, however, hinge on their insistence on equal representation in Parliament irrespective of a person's social status or place of residence (if not of his economic viability). To this end, the uneven distribution of seats among counties and boroughs ought to give way to their strictly proportional distribution across the country. It has been said that the Levellers precociously conceived of a generalised ‘liberty’ pertaining to all individuals, in place of the various traditional collective liberties.²⁹ In the same vein, it can be said that they framed an overarching national space of equal representation, fundamental for discussing the franchise – but not equivalent to its extension.

In fact, as we have already seen, while Lilburne wanted to end the inequality of representation, he consistently wanted to do so on the basis of tax yields – in 1646, again in 1647, and yet again in 1648, after population figures had already been mooted as the potentially better yardstick.³⁰ (It is also true, of course, that tax yields were much more easily available than population data.) Lilburne also wanted to synchronise voting rights across the nation: but rather than pleading for a full franchise, he had explicitly added a rationale for excluding the lowlier sort from the vote – a rationale mirrored by the contours of his more concrete franchise proposals.³¹ It is obvious that a fiscally based proportionality of representation, on the one hand, and an individual economic (or fiscal) threshold for the right to vote, on the other, obeyed the same logic: those, and only those, who contribute materially to society and are not dependent on others should have an equal say in politics. Conversely, it also seems obvious that proportionality based on sheer numbers of people entailed a somewhat different logic – namely, to give the vote to all those very people, or at least to all adult men among them. For if each and every person was to count as ‘1’ in apportioning parliamentary seats, it could seem just as logical that (at least) every man should also have the vote. Precisely this is the ‘radical’ reading of the Putney debates.

It was the first logic that was pursued into the Commonwealth period – at least in part, as the franchise extension envisaged by Lilburne, while endorsed by the army leaders, never materialised.³² The plea for a more equally proportioned parliament, on the other hand, was not only given renewed rhetorical emphasis in 1649:³³ rather, after the ‘Rump’ Parliament had sat out any effective changes,³⁴ the ‘Instrument of Government’ of December 1653, establishing the Commonwealth of England, Scotland and Ireland together with the Protectorate, fixed ‘proportions’ among constituencies – according to their tax yields.³⁵ As a result, the elections of 1654 and 1656 were of a more proportionate nature than any others before the nineteenth century.

The apportionment reform died together with the Protector.³⁶ Yet, the dozen years in which it had been intensely discussed, and at least partly put into practice, had created templates to be evoked over and over again for many decades to come. As with other features of the republican experiment, they would also spur on more systematic reflection – reflection on how to make representation more proportional and equitable, and possibly also more egalitarian.

Arithmetical calculations and radical projections

Various proposals were made, between the mid-1640s and mid-1650s, to attribute seats to existing constituencies according to their population or their tax yields. In the ensuing decades, suggestions were made to make parliamentary representation yet more proportional by devising an entirely new electoral geography from the ground up, starting from the parishes.³⁷

The most celebrated piece of seventeenth-century republican writing, James Harrington's Commonwealth of Oceana (1656), had its ideal republic organise ‘the people, according [to] the places of their habitation, unto parishes, hundreds and tribes’ for administrative and military purposes as well as for elections.³⁸ If ‘tribes’ are equated with counties, this hierarchy of units mirrored the situation in England. In Oceana, however, they were perfectly arithmetically proportioned – and not riddled by boroughs: 10,000 parishes made up 1,000 hundreds and 50 tribes. Propertied men from the age of thirty were to take part in annual elections at parish level.³⁹ Deputies elected here would then meet on the hundred level to elect a deputy for the tribe; finally, the tribe deputies chose seven deputies for a lower house, and two for a Senate.

Harrington's scheme was followed up and further developed by the polymath William Petty, co-inventor – together with his friend John Graunt – of statistics or what he termed ‘political arithmetic’. Petty was intimate with some of the most pre-eminent protagonists of the incipient scientific revolution, in England as well as in the Netherlands and in Paris (where he assisted Hobbes), but he was also embroiled in the very midst of Commonwealth debates and realities of parliamentary elections.⁴⁰ Petty and Harrington rubbed shoulders in the latter's Rota club, one of the first coffee-house clubs in London, during the months before the Restoration.⁴¹ The short-lived but celebrated club also had among its regulars Samuel Pepys, the political writer Henry Neville and former Leveller John Wildman. Fellow member John Aubrey noted that Petty ‘was a Rota man, and troubled Mr. James Harrington with his Arithmeticall proportions, reducing Politie to Numbers’.⁴² More likely, it was Aubrey himself who was thus troubled – judging by his Oceana, Harrington was hardly less obsessed with numbers in politics.

For Petty, one of the ‘impediments of Englands greatness’ was

the inequality of Shires, Diocesses, Parishes … and other Precincts, as also the Representation of the People in Parliament; all which do hinder the Operations of Authority in the same manner, as a Wheel irregularly made, and excentrically hung; neither moves so easily, nor performs its Work so truely, as if the same were duely framed and poised.⁴³

Petty's urge for proportional rationality was congenial with his approach to reform in many other political contexts, such as taxation and population policies. With the help of numerical data and arithmetical logic, England's – and indeed, a UK's – ‘impediments’ could all be solved at one stroke: ‘May not the three Kingdoms be United into one, and equally represented in Parliament? … Might not the Parishes, and other Precincts be better equalized. … Might not the Taxes be equally applotted?’⁴⁴ To such an end, Petty suggested remoulding the 9,600 parishes of England, being of very different sizes, into 12,000 same-sized electoral ‘precincts’ or ‘districts’. On this basis stood a pyramidal system similar to Harrington's – but with a radically egalitarian male franchise.⁴⁵

In another piece of writing, Petty went yet further.⁴⁶ He lowered the age threshold to eighteen and advanced a radically decimal logic – a logic or ‘system’ that simply ‘is the best; because with such computation do we deal with numbers in arithmetic … and because no one else clearly found a more suitable number system’.⁴⁷ Thus, 10,000 basic units or ‘centumvirales’, i.e. 100 men, formed 1,000 ‘chiliarchies’, 100 ‘comitatus’ and finally 10 provinces. An assumed total of one million adult men chimed with actual estimates for England – as well as with the figure in Oceana.⁴⁸ The latter's arithmetical rationality was driven to a perfectly decimalised end – and the analogy of, on the one hand, proportionality based on population and, on the other, a full franchise was fully spelled out: an analogy already present, if as yet obliquely, at Putney.

It was only after Petty's death and the publication of his eponymous Political Arithmetick in 1690 that his ideas became widely known and taken up, including more specific calculations on the proportionality of elections. Population and especially taxation data were contrasted with representation, such as by John Houghton who, in 1693, compared the number of MPs per county (including boroughs) with tax burden, acreage and number of houses – to conclude, not surprisingly, that they all matched quite badly.⁴⁹ Five years later, a similar table appeared, again comparing the number of MPs per county (with their boroughs) with both the land tax yields of 1693 and the subsidies of 1697 – with the result that the disproportion was even bigger if measured by the second than by the first: ‘6 Northern and 5 Western Counties’ paid less than half of Middlesex and Essex, but occupied 216 seats in the place of a bare 16.⁵⁰ The under-representation of London and its environs preoccupied other authors of the time, too.⁵¹

If Houghton and others advanced hard data only on taxation,⁵² it might have had less to do with an inclination towards taxation-based proportionality and more with the fact that such data were easier to obtain than regional population data.⁵³ This suggestion is further corroborated by the way in which Gregory King, the most important ‘political arithmetician’ after William Petty, adapted Harrington's pyramidal apportionment scheme to the administrative and fiscal realities of England.⁵⁴ Breaking down a rough total of £10 million in annual direct taxes, King attributed first-tier deputies to the parishes at the ratio of 1:£200.⁵⁵ These parish deputies were then to meet at the hundred level to elect a tenth of their number as the next tier of deputies – who then met at county level where, again, they would choose a tenth of them, so as to arrive at a total of 500 members of Parliament. The model did not require a complete remake of the administrative landscape, as Harrington's and especially Petty's schemes did, but it still apportioned each parliamentary seat to (roughly) an equal amount of taxes paid.⁵⁶

As no new data became available, those of the late seventeenth century, especially those of King and of his colleague Charles Davenant (through whose publications many of King's figures and calculations first became accessible), were taken up time and again throughout the eighteenth century – together with much the same kind of political arguments against the distorted representation in Parliament.⁵⁷ After a national census bill had been thwarted by the House of Lords in 1753, only the census of 1801 began to supply reliable data for apportionment based on population⁵⁸ – as first attempted by the 1832 Reform Act, and even then only to a very rudimentary extent.

Proportionality and the franchise in the Enlightenment

Neither the radicalism of Harrington and Petty, nor the support by arithmetical precision and concrete data aimed at by him and his followers, characterised the ensuing political discourse in Britain or abroad. Characteristic, rather, was the more distanced and conservative stance of John Locke – who nevertheless helped to pass some of the seventeenth-century notions on proportionality on to eighteenth-century political thought. His Second Treatise of Government, written around 1680, noted the desirability of re-establishing the distorted balance between representation and constituency size (suggesting that an original balance was offset by later demographic and economic changes).⁵⁹ Locke further argued that, as Parliament could neither reform itself nor be reformed by the people who had ceded their power to it, that distorted balance had to be fixed by the executive, i.e. the king.⁶⁰ And in accordance with the general trend of the century – if not with Harrington and Petty – Locke saw the balance or ‘true proportion’ warranted by ‘the assistance, which it [a constituency] affords to the publick’, that is, its tax yields.⁶¹

The two clauses in the Second Treatise concerned with this theme have frequently been read as an explicit stance in favour of a property-based franchise. Yet, Locke's lack of clarity on the issue has caused much headache and discussion – not unlike Putney and the Levellers.⁶² But against the background of the preceding half-century's debates on proportionality, the relatively greater weight he lends to this issue – and the absence of any explicit mention of ‘the franchise’ – appears much less puzzling: against that background, it can be argued that what was relevant for Locke, too, and for his ‘fair and equal Representative’,⁶³ was equality both among constituencies and among the voters in different constituencies: a standardised franchise, in other words, much more than any clearly specified (let alone broadened) electorate.

This can be further confirmed by placing Locke's stance in the context of the Exclusion Crisis and the early Whig electoral reform proposals that it engendered.⁶⁴ A bill brought forward by the first Earl of Shaftesbury, whose associate Locke had been since the mid-1660s, stipulated a radically standardised borough franchise:⁶⁵ every householder from the age of twenty-one who had ‘payed and born his Scot and Lot towards the maintenance and defraying the Poor, and other publick Charges and Payments’ was to have the vote.⁶⁶ This would have broadened the franchise in most boroughs while narrowing it down in some others (as further emphasised by an insistence on excluding all others)⁶⁷ – but, crucially, it would have equalised it among them.

Curiously, in a memorandum presumably also authored by Shaftesbury, two contrasting alternatives were put forward.⁶⁸ The first advocated a sharp restriction of voting rights: ‘The power of Election [ought] to be fixed in the Optimacy only,’ as most men were too easily ‘misguided … by their ignorance’ and ‘under the temptation of being Corrupted and Seduced by the inveiglements of a little Mony, or a Pot of Ale’.⁶⁹ The second alternative, however, suggested that the only way ‘to bring an old irregular Structure into a convenient Uniformity’ was ‘by razing it to the Ground, and erecting a new Pile by some better contrived design’.⁷⁰ Such a design, apart from featuring a Harrington-style electoral pyramid, would rest on the premise that ‘every individual Person in the Nation, has a Natural Right to Vote’ and envisage the franchise for all male householders.⁷¹ This would achieve ‘a perfect Representative of the whole Body of the People, and also of every numerical person in the Kingdom’.⁷²

To the extent that we can make sense of these contrasting schemes, it is again by acknowledging that the Whigs’ goal was to rationalise representation by creating equality among voters – however these were to be defined. This meant, on the one hand, proportionality among constituencies, measured by the taxes they paid. On the other hand, it meant an equal – that is, a standardised – franchise, which they strove to obtain by legislation. In the 1690s, in fact, another electoral bill – drawn up, among others, by Locke – again envisaged a standardised borough franchise to be awarded to every man paying local taxes (scot and lot).⁷³ Rather than being radically egalitarian, again, the aim was to ‘bring an old irregular Structure into a convenient Uniformity’, to quote Shaftesbury. This uniformity was to be predicated on the payment of taxes – for more proportional constituencies as well as for the entitlement of individual voters. This was a standard that was not only relatively easy to measure but also one that local and central elites might agree upon.⁷⁴ If the move failed again, it was not because it was too egalitarian – but because the rationalising, standardising logic of proportionality and individual (or voter) equality contradicted the traditional logic of hierarchical and corporate rights.

The first logic was, broadly speaking, that of the European Enlightenment – and the equalising, while not egalitarian, stance of Locke and the Whigs was precisely that of all but a few Enlightenment thinkers.⁷⁵ They wanted representation to be more equal – but not shared by all. They wanted to see it untied from traditional categories of birthright and group membership – but they wanted it to be tied to economic independence, moral and intellectual capacity, personal achievement and individual contribution to the public weal (all of which were seen as closely linked). Enlightened thinkers, in other words, envisaged a new kind of social and political stratification: not inherited and collective but utilitarian and individual. It contrasted sharply with the traditional early modern logic of birth, and corporate, status and rights, while corresponding to the functional, materialist rationality of the Enlightenment. (By the same token – by obeying an essentially materialistic logic – such stratification was measurable and quantifiable, through property registers, tax lists or otherwise.) This vision of stratification undercut traditional birth and corporate hierarchies by putting the right to vote within each and every (male) individual's reach – based on his economic success. Here, then, was Locke's ‘true proportion’ and ‘true reason’;⁷⁶ here was his – and later the Americans’ – ‘no taxation without representation’;⁷⁷ here were French revolutionary Sieyès's ‘true shareholders’ of society.⁷⁸

This, too, was the gist of the entry on ‘representation’ in Diderot's Encyclopédie, authored by the German expatriate philosopher baron d'Holbach whose Paris salon was frequented by the crème of French and British philosophers.⁷⁹ For Holbach and the Encyclopédie, it was clear that ‘the people’ were to be represented proportionately – but proportionately according not just to their numbers but also to their usefulness.⁸⁰ Only the educated and wealthy, in fact – those who had a true understanding of, and true stake in, society and politics – ought to represent the people: ‘It is in proportion of his possessions that the voice of the citizen should have weight in national assemblies.’⁸¹ Indeed only they were to be represented, as ‘it is property that makes the citizen … [He] acquires the right to be represented as a proprietor, in function of his possessions.’⁸²

This logic was translated, from the 1770s onwards, into attempts by French ministers to set up Provincial Assemblies to oversee taxation and streamline local administration. The original plan put forward, in particular, by physiocratic writers, saw these as consisting of regional landowners, noble and non-noble alike, representing taxpayers at large and looking beyond particularist spheres of interest. When Finance Minister Necker initiated two such Assemblées provinciales in the late 1770s, however, they were organised along the lines of the traditional three Estates and fully dominated by noble elites.⁸³ In early 1787, Finance Minister Calonne tried to take up the original idea of gathering landowners, regardless of rank, but this foundered on the resistance of the Assembly of Notables.⁸⁴ His successor Loménie de Brienne, finally, put almost twenty Assemblies – organised along the conventional lines – in place by the end of 1787.⁸⁵ Yet, just like Necker's prototypes, they featured a ‘doubled Third’ – they contained, that is, the same number of representatives from the Third as from the first two (clerical and noble) Estates together, thus prefiguring the form which the Estates General of 1789 would take. More than that, their members voted individually – ‘by head’ – rather than collectively by Estates,⁸⁶ thus anticipating the logic of the revolutionary Third Estate during the first two months of the Revolution. In this restricted way at least, the pre-revolutionary Provincial Assemblies translated a notion of individual, but functionally qualified, proportionality and equality into practice. Together with the lower-level, elected Municipal Assemblies that were set up during autumn 1787 they helped, on the eve of the Revolution, to spread an individual, property- or taxation-based logic of proportionality and representation among a large public.⁸⁷

From Estates to Assembly: proportionality and equality in the French Revolution

The call for a revocation of the Estates General or some other form of ‘national representation’⁸⁸ to solve the financial and political impasse of the monarchy was growing ever louder throughout 1787 – and at the end of the year, the king promised the convocation of an Estates General. After 175 years of slumber, however, they could not, in most people's eyes, simply be revived in their ancient form, as the government envisaged it: to accord the church and the nobility each the same weight as the entire rest of society – represented in the ‘Third Estate’ (Tiers État) – appeared just as anachronistic as insulting. At the same time, the new Provincial Assemblies pointed towards a fairer form of representation.⁸⁹ In the Alpine province of Dauphiné, in July 1788 – a few weeks after the ‘Day of the Tiles’, when citizens of the province's capital, Grenoble, had hurled roof tiles on the soldiers deployed in the streets – members of the three Estates assembled to reconvene their long-deceased Provincial Estates: but not, as in the past, with an equal number of representatives from each Estate but, following the Provincial Assemblies, with a ‘doubled Third’ and the vote ‘by head’.⁹⁰ They proclaimed this to be the proper set-up for the upcoming Estates General, too. However, the central authorities insisted that these be modelled on their last convocation in 1614 – triggering a pamphlet war throughout autumn 1788 that pitted traditionalists against self-styled ‘patriots’ clamouring for a larger share of seats for the Third Estate.⁹¹

In this debate, arguments for more proportional forms of representation could be readily based on statistical, and in particular demographic, reasoning which had started to attract much general attention over the past decades.⁹² In France, it was popularised in particular by the hefty debate over an alleged long-term depopulation of the kingdom – prompting Rousseau to ask, provocatively, for population counts to evaluate governments; and the government, in turn, to carry out yearly demographic surveys.⁹³ Such statistical reasoning and practice not only underscored the relevance of proportionality but also a notion of basic individual equality – implicit in the simple proposition to count each and every person as an identical ‘1’ regardless of social rank (as well as, potentially, of sex and age). A decade before the Revolution, demographer Jean-Baptiste Moheau had stated that his discipline, by revealing the general laws of life, showed men ‘naked’ in their ‘natural equality’, without the trappings of society. There was no difference between kings and the least of their subjects: they all shared the same needs and pleasures; they all shared ‘the same beginning, the same end, one cradle, and one grave’.⁹⁴

In autumn 1788, arguments starting from the numerical proportionality of equal citizens were forcefully brought forward by the eminent lawyer Guy-Jean-Baptiste Target. In his view, delegates ought to be sent ‘from all parts of the kingdom according to wise rules and just proportions’.⁹⁵ Such proportions were absent in the past, as Target proved with a survey of membership figures since the fourteenth century: contrary to what traditionalists maintained, the historical record was a ‘masterpiece of irregularity and chance’ and could not serve as a rule.⁹⁶ Target did not advise a radical break. Nevertheless, as ‘there are a million individuals in the two first orders, but … twenty million in the Third Estate’, the latter constituted ‘almost the entire nation’ and should therefore clearly outweigh clergy and nobility in the Estates General.⁹⁷ Much the same point was made by Protestant pastor (and future eminent revolutionary) Jean-Paul Rabaut Saint-Étienne: ‘What is the Third Estate? It is the nation minus the clergy and the nobility,’ made up of some ‘twenty-four million Frenchmen’.⁹⁸ Thus, the muddled pedigree of tradition was now trumped by quantitative arguments – by the sheer ‘dictates of reason and justice’.⁹⁹

As already indicated by these examples, though, the concrete numbers employed varied, due to a lack of census data no less than to the bewildering array of territories recently added or (semi-)incorporated into the kingdom.¹⁰⁰ Emmanuel-Joseph Sieyès, taking up the argument in January 1789 in his What Is the Third Estate?, admitted that he knew no better what the ‘true proportion’ among the orders was – ‘but, like everybody else, I will permit myself to make my calculations’.¹⁰¹ The result was a maximum of 200,000 members of the first two orders, contrasting with no less than ‘twenty-five to twenty-six million souls’ belonging to the rest, i.e. the Third Estate.¹⁰² Considering this numerical evidence, it would be plain ‘absurdity’ to insist on the first two Estates’ conventional two-thirds majority: it would be just the same as to ‘maintain that 2 plus 2 equals 5’.¹⁰³

Although Sieyès used an argument previously deployed by others,¹⁰⁴ he gave it renewed rhetorical vigour and made it immensely popular on the eve of the elections to the Estates General. In the meantime, at the end of 1788, the king had given in to Finance Minister Necker to ‘double the Third’; but as he shrank away from conceding the vote by head, too, the first two Estates would de facto retain their two-to-one majority.¹⁰⁵ As a result, this half-hearted concession only fuelled the debate that gripped the public, much rather than appeasing it. When the crucial issue of the vote by head was taken up after the Estates General had opened on 5 May, the stubborn and arrogant refusal of the first two Estates to even consider and discuss it gave the Third Estate a common cause – and made it ‘become revolutionary’.¹⁰⁶ On 17 June, the Third Estate finally proclaimed itself the ‘National Assembly’, soon to be joined by most clergy as well as many nobles – on the rationale of its sheer numerical proportionality: ‘This Assembly is … made up of the deputies … of at least ninety-six per cent of the nation.’¹⁰⁷

But the picture is not yet complete. Omnipresent from the start was also the functional, utilitarian notion of proportionality – the notion that representation should also, if not chiefly, be proportional to individual and collective usefulness, measured by property and/or taxation. In a widely read ‘Letter to the King’ from the autumn of 1788, the precocious and much admired Estates of Dauphiné had argued that the Third Estate could not be denied the same number of deputies as the first two Estates together – considering not only that it ‘comprises the majority of your subjects; [but also that] it pays most of the taxes; it possesses most of the property’.¹⁰⁸ Similarly, many local petitions stressed the Third Estate's taxpaying performance to emphasise its rights.¹⁰⁹ The geographical proportionality of future representation, too, was discussed along these lines. Target already recommended direct tax returns as the suitable criterion and advanced calculations – reminiscent of Gregory King – that broke up a national total of taxes into the numbers of deputies that each electoral district would send.¹¹⁰ As a consequence of this general stance, the first national elections, in 1791, on the basis of the revolutionary constitution barely amended the mix of population and taxation criteria which had served to specify the weight of electoral districts back in 1789.¹¹¹

And the same logic, once again, applied to voting rights. In December 1788, an anonymous author had already made the point that the ‘model’ Estates of Dauphiné were in fact predicated on a highly restrictive franchise that flew in the face of its high-minded assertions:

You have laid great emphasis on the numerical strength of the Third Estate and the mass of its wealth; you have insisted that, to render it justice, it must have a representation in the Estates General commensurate with its importance. Yet, by the article of your constitution which defines the qualifications for suffrage and eligibility, you … exclude precisely that numerous class of citizens whose rights have served as a pretext for your demands. … Thus your constitution, if taken as the model for that of the Estates General of France, will disqualify forty-nine fiftieths [98 per cent] of the … nation.¹¹²

This criticism was as perceptive as it was rare. The notion that political entitlement depended primarily on utility, as measurable by property or taxes, simply prevailed on all levels. Sieyès, too, advanced the twofold argument of taxes and population to commend the Third Estate.¹¹³ Then, in July 1789, he hammered out the distinction, reflecting the general discourse, between ‘active’ and ‘passive’ citizens: only the first, paying a certain amount of taxes, were ‘the true shareholders of the big social enterprise’ – only they ought to have the vote.¹¹⁴ The exclusion of a substantial minority (around a third) of adult men from the vote became enshrined in the 1791 revolutionary constitution. So did various tax-related thresholds for eligibility within a two-tiered electoral pyramid – also initiated, among others, by Sieyès (and possibly inspired by Harrington).¹¹⁵ Both active and passive electoral rights in France would remain restricted in the constitutions of more than half a century to come. Only the Jacobin constitution of 1793 stipulated a universal male franchise, as well as fully spelling out demographic proportionality for electoral districts – but it remained a mere paper tiger.¹¹⁶ The logic of weighing electoral districts and granting voting rights according to economic performance was yet to prevail.

Apportioning seats in the United States’ Congress

With the United States’ census of 1790 – following up on the Constitution, drawn up three years earlier – our story turns full circle. Not only was this the first national census successfully undertaken in the wider European world: it was set up to ensure the demographic proportionality of federal elections.

Americans used demographic data already as an argument for the viability of colonial resistance – not entirely unlike the advocates of the Third Estate in France on the eve of the Revolution. Already at mid-century, Benjamin Franklin had claimed that, thanks to ideal conditions, the American population was the fastest-growing in the world – doubling about every twenty years.¹¹⁷ Franklin did not provide much evidence; but ten years later, Connecticut clergyman Ezra Stiles dug up New England parish records to substantiate such claims, adding a fair dose of divine providence.¹¹⁸

The Stamp Act of 1765 called forth further calculations by Stiles who concluded from London's expectations of fiscal profits that ‘the subjects in North America are reckoned by the Lords at about two million and a Quarter of souls’.¹¹⁹ Among those ‘souls’, slaves counted, too, according to Stiles.¹²⁰ The figure – a third of current estimates for England's population – could be adduced in favour of colonial confidence and resistance, but also, on the other side of the Atlantic, to highlight Britain's paramount interest in keeping its grip on the colonies.¹²¹

A few years later, British moral philosopher Richard Price, a friend of Franklin's – who helped to turn his interests towards demographics, and his sympathies towards the colonies – feared that Americans, ‘formerly an increasing number of friends’, were ‘now likely to be converted … into an increasing number of enemies’.¹²² The word ‘number’ was key, as the statement was made in a paper on demographics. Soon afterwards, in an influential analysis of finance and population data from all over Europe, Price reflected more systematically on the rapid growth of the colonial population.¹²³ His figures and calculations inspired Thomas Paine who, in his 1776 pamphlet Common Sense that gave a decisive final boost to American morale, declared both the swelling size and the mixed origin of colonials to be incontrovertible tokens for the viability of independence.¹²⁴

The relevance of population data for political representation, on the other hand, surfaced in 1774 when the first Continental Congress met in Philadelphia. For days, it debated how many delegates should represent each of the thirteen colonies: ought they to be apportioned according to a colony's population – or to its population and wealth combined? Demographic figures were passed around and discussed; but in the end it was decided that, for the moment, all colonies would have the same weight. Still, the discussion spread outside Congress, prompting commentaries from various quarters. Ezra Stiles, for one, considered most numbers overestimated: the figure he now advanced, if slightly above the one he had referred to a decade earlier, was some 20 per cent below that of the Continental Congress, tallied from the colonies’ specifications.¹²⁵ This discrepancy was most likely owed to their leaders’ wish to increase their relative shares of representation.¹²⁶

Already half a year later, when the Second Continental Congress met in spring 1775, another question of proportionality emerged: how much should each colony contribute to the defensive effort against Britain? The decision to apportion it according to population foreboded the later apportionment regulation of the Constitution; but for the time being, it remained dependent on the data provided by the colonies, unreliable and biased as they were – this time of course in the opposite direction, all trying to keep their contribution as small as possible.¹²⁷

Shortly afterwards, however, the Articles of Confederation – discussed in Congress as soon as Independence had been declared but ratified by all colonies only by 1781 – stipulated that the common treasury, put up for defence and welfare, ‘shall be supplied by the several states, in proportion to the value of all land within each state, granted to or surveyed for any Person’.¹²⁸ Thus, (landed) wealth was now chosen as the measuring stick for apportioning federal taxes. Apart from remaining unimplemented for practical reasons, this had not been everyone's preferred solution. In fact, in direct continuation of the provision of 1775, an alternative draft for the Articles read: ‘… shall be supplied by the several colonies in proportion to the number of inhabitants of every age, sex, and quality, except Indians not paying taxes’.¹²⁹ It would be this formula that would be taken over, in 1787, into the Constitution – which did not interfere with voting rights, arranged autonomously by each state¹³⁰ – but with three very substantial additions. First, seats in the House of Representatives were to be proportional to the number of inhabitants per state, too; second, a national census must be taken once every ten years to determine this number; third, ignominiously, slaves were not to be weighted fully but by a ratio – later referred to as the ‘federal ratio’ – of three-fifths.¹³¹

The weight accorded to slaves had been debated already in 1783 in reaction to an amendment proposal for the Articles of Confederation, aiming at the apportionment of taxes, that in turn revived the alternative draft just quoted.¹³² Although the ensuing debate remained theoretical for the time being,¹³³ it was in this context that the ugly three-fifths compromise was hammered out. Virginia, spearheading the slave-holder states, wanted to count slaves only half so as to lower the prospective tax burden, while some New England states insisted on three-quarters; James Madison suggested the compromise of three-fifths. It was resorted to, four years later, at the Philadelphia Convention – and now linked with another compromise, namely, to use population also as the yardstick for apportioning seats in the House of Representatives. In this way, other potential indices – such as land values, unsuccessfully stipulated by the Articles of Confederation – were replaced with a single and essentially clear-cut unit. At the same time, as states were rewarded with seats and burdened with taxes in exactly the same measure, the double apportionment tool promised to avoid quarrels. Here was, in short, ‘one of the classic checks and balances of the Constitution’.¹³⁴ As an integral part of it, the disgraceful three-fifths compromise worked for the Southern states, adding to their representation to the exact same degree as it did to their share of taxation.¹³⁵

The cost of the double compromise, of course, was the absurd and macabre qualification of slaves as unevenly mixed entities of humans and property. The absurdly arbitrary figure highlighted the logical incongruity of the entire construction – as spelled out already by Madison who referred uneasily to the ‘compromising expedient … which regards them [the slaves] as inhabitants, but as debased by servitude below the equal level of free inhabitants … [namely] as divested of two-fifths of the man’. In fact, Madison went further, asserting that ‘if the laws were to restore the rights which have been taken away, the negroes could no longer be refused an equal share of representation with the other inhabitants’.¹³⁶ That it would take another eighty years before slaves were formally freed, and at least nominally enfranchised, was partly the perverse effect of that same macabre compromise: it gave Southern states at least a third more seats in Congress than would have been the appropriate share of their free, white population.

Similar arguments, it may be noted, were exchanged in the French Caribbean colony of Saint-Domingue. In 1791, the mostly African-born slave majority, working on the sugar plantations, rose up in rebellion that ushered in the independent state of Haiti. Two years earlier, the white planters had claimed representation in the National Assembly – not just for their own number of some 30,000, which would barely give them one seat, but also for the almost twentyfold number of their slaves. The demand was duly spurned by Mirabeau: ‘Do the colonies claim to class their negroes … in the category of men or in that of beasts of burden? … If [they] want the negroes … to be men, they ought to free [them]; all ought to have the right to vote and to be elected.’ He concluded sardonically that when fixing the numbers of deputies back in France, ‘we have not taken into consideration the number of our horses or our mules’.¹³⁷

Beginning in 1790, the decennial US census would enshrine racial distinctions – not only by way of the three-fifths compromise but also through the continuous imprint that its categories and tabulations left on the imagination of the new nation.¹³⁸ At the same time, though, it nurtured and enhanced a general statistical mindset – already prominent among revolutionary elites – by taking the notion of quantifying and calculating all things social and political to all corners of the federation. While Madison's urge to include not only demographic but also economic data was rejected for the time being,¹³⁹ the data of the first census, completed after eighteen months,¹⁴⁰ were used in myriad ways to present, analyse and debate the state of the nation. Notwithstanding many obstacles, delays and altercations,¹⁴¹ the overall efficiency of census-based apportionment strengthened a general ‘trust in numbers’¹⁴² – in turn underpinning the viability and legitimacy of the new political system and its number-based compromises, core among them the famous ‘Connecticut compromise’ that balanced equal representation of the states, regardless of size, in the Senate and representation in numerical proportion to population in the House.¹⁴³ Madison's claim must have involved a fair degree of wishful thinking on his part – but would ultimately prove self-fulfilling: ‘It is agreed on all sides, that numbers are the best scale of wealth and taxation, as they are the only proper scale of representation.’¹⁴⁴

Conclusion

In a fine study, French historian Olivier Christin has traced the ways in which practices of decision-making by majorities in central political assemblies – together with a notion of the formal equality of individual votes – emerged in various contexts since the High Middle Ages.¹⁴⁵ He suggested, too, that gradually and cumulatively, such modes of voting within political assemblies would have fed into conceptions and practices of voting rights outside them. While Christin's nuanced panorama is fascinating and inspiring, however, he does not provide any specific suggestions as to how, when and why such a putative last step may have taken place.

It is true, to be sure, that there is a fundamental analogy between majority voting within assemblies and voting equality at large. Both rest on a quantitative, arithmetical logic. Both refer to some basic unit (such as the individual person), all manifestations of which are treated as equivalent so that they can be summed up into totals. A majority in an assembly can emerge only if all members are treated as equivalent: only then can their votes be counted as equal ‘1's and aggregated, thus yielding a majority and a minority. Like voting in assemblies, electoral proportionality, too, has to refer to a basic unit, to a general indicator that cuts across any distinctions that might otherwise exist among those who vote – that is, a quantitative indicator. Unlike in the case of majority voting in an assembly, it is true, the basic unit here need not be the individual person (or voter): it can also be predicated on some other kind of generalisable, quantifiable feature such as property, income or taxation – as was mostly advocated by those talking about proportionality in the seventeenth and eighteenth centuries. But here, too – to create electoral proportionality – the most stable and plausible unit across time and space, the least ambiguous indicator, the smallest common denominator is ultimately the individual person.

In spite of this fundamental analogy, the findings of this article (if admittedly still of a cursory nature) do not suggest that there was a direct transition from concepts and practices of voting within assemblies to practices outside them. Majority voting in England's parliament did not engender any readiness on its behalf to allow for more equal representation among constituencies, nor a more equal, let alone egalitarian franchise: and this, in spite of the striking fact that the breakthrough of majority voting in Parliament, as recently documented by William J. Bulman,¹⁴⁶ occurred at the same moment in time – the early 1640s – and due to the same divisive political and constitutional issues as caused the rise in importance of majority voting for parliamentary members in electoral constituencies. In England as elsewhere, equality among individual voters at large does not seem to have sprung from a simple transfer onto a wider electorate of individualised, quantified majority decision-making at the centre. For a similar logic to gain ground within polities at large, it seems, a different kind of catalyst was more relevant: namely, the demand to make representation more proportionate, among constituencies no less than among those who were entitled to vote.

The very concept of representation, in fact – whenever it becomes a matter of contestation, reflection and debate – seems to gravitate towards some mode of proportionality. But just as the notion of simple numerical majorities among assembly members, conceived of as equals, required a leap of confidence in pre-modern societies – profoundly characterised as they were by concepts of corporate rather than individual rights and identities, and by many status hierarchies among them, reflecting supposedly innate differential ‘qualities’¹⁴⁷ – so the idea of aggregating individuals or, for that matter, their sheer economic or taxpaying capacities clashed with the same all-pervasive belief in inherent, ‘qualitative’ differences, as embodied in traditional corporate identities and status distinctions. At the same time, a strong adherence to consensual decisions as the only way to reach good or even ‘true’ decisions¹⁴⁸ clashed with contested, adversarial decision-making by majority vote, within no less than outside assemblies.

As a result, debates around proportionality emerged properly only in moments of fundamental political upheaval that challenged dominant discourses, conventions and hierarchies. This is what happened in the English revolution of the 1640s, when a major fissure at the top – reflected, too, in the surge of majority voting in Parliament – spread through the entire polity. As we saw, the demand for more proportionality among constituencies now emerged alongside a demand for giving all votes an equal weight (though not for giving the vote to all). The Levellers were the first, at mid-decade, to plead for parliamentary representation to be more proportionate to the relative weight of constituencies. They also demanded a more equal, that is, standardised franchise throughout the country. They did not, though, at least not explicitly, demand an egalitarian franchise, i.e. voting rights for all. This last step – taking the underlying quantitative logic to its end point – was tentatively made at the 1647 Putney debates, as the Levellers’ demand for proportionality among constituencies and (entitled) voters merged with the claim of the parliamentary ‘New Model’ army's soldiers, seconded by some officers, for their political rights – bringing forth what sounds, at least, very much like a call for voting rights for all (men). It is revealing that this call, while so crucial and evident to us, arose only haphazardly as a spin-off of the debate on electoral proportionality. Accordingly, too, it was not followed up nearly as seriously, for the time being, by any of the protagonists involved.

But while the claim for broader voting rights made at Putney was not yet clearly formulated – and could not be, considering its utter novelty – it was brought forward more explicitly over the next decades. The least ambiguous pronouncement of all was made by William Petty. Not coincidentally, he was also the first to spell out the potential of statistics, or ‘political arithmetic’, as he christened it. Not coincidentally, either, his plea for a fully egalitarian (male) franchise was embedded in – and logically entirely conditioned by – the most stringent arithmetical proposal to date for establishing full electoral proportionality. But as on most other accounts, Petty's arguments in this field remained as yet largely ignored. For electoral proportionality to become a real issue, the underlying numerical logic of statistics or ‘political arithmetic’ needed to be more broadly endorsed. This happened in the last third of the eighteenth century, when a trust and belief in quantitative reasoning came strongly to the fore across Europe.¹⁴⁹

As a consequence, it was only in the political ruptures of the American and French Revolutions that the arithmetical logic of proportionality and equality took on its full political vigour. It was against the background of a now widely shared belief in quantification and statistics that demographics could now be adduced as a core political argument: by Americans, to stress the viability and legitimacy of their resistance and independence; by the French, to argue for a larger political share of the ‘Third Estate’ – and finally to declare, in June 1789, that it represented the nation as a whole all by itself. In both cases, arguments of numerical proportion went hand in hand, too, with establishing a wider franchise (in the United States within the individual states, as the Constitution did not meddle in this area). At the same time, following the strong emphasis on utilitarian merit and economic performance that had been dominant throughout the Enlightenment – and that lent itself just as easily and plausibly to quantification – the idea of material, or fiscal, rather than mere demographic proportionality still remained strong on both sides of the Atlantic. As a result, only the economically successful, or at least fully economically independent, men were generally seen as entitled to a full, active stake in politics.

And yet, there was no denying the contradiction and, ultimately, the logical incompatibility between political claims and stakes based on demographic proportionality – fully elaborated in apportioning seats in Congress by means of the national US census – and the political exclusion of major parts of the population. Already in the autumn of 1788, a critic of the Estates of Dauphiné pointed to their inconsistent, if not hypocritical, stance as they claimed more representation for the ‘Third Estate’, congruous with its numerical importance, while at the same time firmly restricting their own constituents’ franchise. Earlier that same year, James Madison had admitted that the three-fifths compromise was a bad ‘expedient’ – and insinuated that slaves, counted as they were as ‘inhabitants’ in apportioning Congress seats, could only with a massive leap of (bad) faith be denied the franchise, let alone human rights. Nevertheless, for the time being, a full (male) franchise remained exceptional, such as in Vermont, joining the United States in 1791, or in the unimplemented Jacobin constitution of 1793. Yet, over the next century, the ultimate consequence of giving the vote to all men was drawn both in the United States and in France – if only in leaps and bounds and, for ex-slaves and their descendants, as yet largely on paper.

Women, too, remained excluded throughout the nineteenth century or even, such as in France, well beyond – arguably the most striking gap between the rhetoric of ‘all inhabitants’, employed both at Putney and in Philadelphia, or of Shaftesbury's ‘every individual numerical Person’ to be weighed in order to apportion representation, and actual political representation. But excluding women was simply so self-evident for most (if not all) early modern contemporaries, apparently grounded not only in society but indeed in ‘nature’, that it barely seemed to merit comment. As this sustained exclusion of women as well as of other major groups of people shows, the ultimate upshot of the arithmetical logic – namely, to include all individuals – has always been, and might always remain, strongly modified by many other political, social and cultural factors. Yet, as this article tried to argue, that logic did play an important role for the gradual broadening of democratic participation, kicking in during phases of political upheaval and, as the persuasive power of numbers steadily grew, becoming ever more difficult to reject.