The mathematics of Victorian representation: part 1

In this new series of posts, we look at the Victorian multi-member constituencies that predated the UK’s current electoral system and highlight the mathematical challenges they pose for historians.

The first-past-the-post system of electing MPs has long been viewed as a defining feature of the British representative system. Rather like the way ‘Australian’ has come to denote a specific type of ballot, ‘Westminster’ has become almost synonymous with one member constituencies and winner-takes-all polls. It therefore often comes as a surprise to many to learn that there was a long-established system of multi-member seats in operation throughout the 19th century. In England, especially, multi-member constituencies dominated. Between 1832 and 1868, for instance, 204 of England’s 258 county and borough constituencies elected two (or more) MPs at every general election. In total, 96% of the English electorate were entitled to vote in multi-member constituencies following the passage of the 1832 Reform Act.

OxfordPollcard1868 crop

Oxford polling card for electing 2 MPs

This multi-member system had all sorts of implications for Victorian voting behaviour. For a start it meant that for most electors their only experience of a modern first-past-the-post poll was at a by-election, when a solitary seat was up for grabs. The different behaviour of voters in by-elections (compared with general elections) during the 19th century has already been mentioned in a previous blog.

In general elections, meanwhile, electors in two-member constituencies could cast votes for two candidates from the same party (straights), share their votes between candidates from different parties (splitting), or cast just one of their votes (plumping). If 3 candidates (A, B and C) stood, each elector had 6 available voting options:

Plumps (single votes) Straights and splits (double votes)*

* Note that there was no difference between voting AB or BA, AC or CA, etc.

If 4 candidates stood, the options increased to 10:

Plumps (single votes) Straights and splits (double votes)

One major upshot of these multiple voting options was that the total vote received by each candidate did not necessarily correlate with the amount of party-based support exhibited during the poll. The final results reveal nothing about how each candidate’s tally was made up. Using the results of Victorian elections to gauge party performance, as many 20th century guides have done, can therefore be very misleading.

Suppose there was a contest between two Tories (T1 & T2) and a Liberal (L) and the final result was reported was follows:

T1: 50 votes, T2: 50 votes, L: 35 votes

These results could have been made up as follows:

Plumpers or single votes (where voters cast just one of their two votes)

T1: 0, T2: 0, L: 35

Shared votes (where voters cast both their two votes)

T1 & T2: 50, T1 & L: 0, T2 & L: 0

In this scenario, there are 85 voters, of whom 35 (41%) vote for the solitary Liberal, and 50 (59%) vote for both Tories. The link between the final results and party performance is amazingly clear in this case.

Unfortunately, it is rarely this simple. Supposing the same totals were made up as follows:

Plumpers / single votes: T1: 25, T2: 10, L: 0

Shared votes: T1 & T2: 15, T1 & L: 10, T2 & L: 25

There are still 85 voters, but the party behaviour making up the final results is very different. The combined Tory vote, T1 & T2, was only selected by 15 out of 85 voters, a mere 18% of the electorate. No one plumped for the single Liberal, but split votes across the parties / non-party votes (T1 & L + T2 & L), were adopted by 35 out of 85 voters (41% of the electorate).

Non-partisan plumping (supporting just one candidate when there is also another from the same party) was also taken up by 35 voters (41% of the electorate). Combined together, 82% of the voters in this poll therefore behaved in what might be described as a non-partisan way, either by splitting their votes between the parties or by casting non-partisan plumps.

And yet the reported results would still be 35 votes for the Liberal, and 50 votes for each of the Tories, implying high levels of Tory partisanship.

It is this potential mismatch between the tallies received by candidates and the level of party-based support that makes Victorian multi-member elections so compelling and complex. Using original data, showing splits and plumps, is crucial to understanding the subtle dynamics of voting that occurred across Britain prior to the adoption of single member seats. Surviving poll books are an essential resource here, but it is also possible to calculate poll breakdowns when a small number of the variables are known. This will be the subject of a follow-up post.

Drafts of our 1832-68 constituency articles, dealing with this very different method of electing MPs to Westminster, can be viewed on our preview site. For details of how to obtain access click here.

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10 Responses to The mathematics of Victorian representation: part 1

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  10. wjsboston says:

    I came across your article seeking to fill out a Mastodon account in case Twitter disappears. I mailed the article to myself because I don’t have the time right now to digest it. I’ve been around Boston politics since ‘68 and was counsel to the Boston Election Department for 7-8 years, and persisted over a dozen recounts. I’ve been fascinated both by the processes and the ways to work them or get around them. Thank you

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