## The mathematics of Victorian representation: part 2

In an earlier blog on Victorian double-member elections, we looked at the differences between the total vote received by candidates and the levels of support for each party. Put simply, owing to splitting (cross-party voting) and other ‘non-party’ forms of behaviour, Victorian election results reveal little about party performance in multi-member contests. Most reference works providing a breakdown of each party’s share of the vote in nineteeth-century general elections, in this respect at least, are rather misleading.

Original pollbooks, of course, offer a complete breakdown of the poll, but unfortunately they do not exist for every contest, although new ones continue to be unearthed, not least due to the interest they hold for genealogists. Even without pollbooks, however, it is still possible to work out the different types of votes that were cast, from a surprisingly limited amount of information. This is especially true of the so-called ‘triangular’ contests, where two candidates from one party faced a solitary opponent from another. With so much data about turnout, plumping (single votes) and splitting (shared votes) now accessible from digitized local newspapers, many of the gaps in our knowledge of Victorian polling can begin to be filled.

Below is a typical set of data from a Victorian ‘triangular’ poll, in which three candidates A, B and C competed for two seats in a double-member constituency. Note that there was no difference between casting a vote for AB or BA. In both cases the outcome was the same – a vote received by each of the candidates A and B. The winning candidates here were A and C, whose totals are given as TA and TC in order to avoid confusion. The result for C, who topped the poll, was made up as follows:

• Single votes for C = 559
• Votes for A and C = 193
• Votes for B and C = 89

In these polls, the total number of people who voted (turnout) is not the same as the total number of votes received by all the candidates. This is because some people cast two votes and some cast one. So the total number of votes (TV) received by all three candidates is: 813 + 575 + 841 = 2,229. But the number of people who actually voted (TN) is: A+B+C+AB+AC+BC = 204 + 70 + 559 + 416 + 193 + 89 = 1,531

The difference between these two figures is the number of people who cast double votes. This is because when adding the results together, the shared votes are counted twice. So from just the results and turnout figures alone, it is possible to tell how many people chose to use single votes (A+B+C) and how many cast double votes (AB+AC+BC). The sums here are: 2,229 – 1,531 = 698 double votes. Therefore 1,531 – 698 double votes = 833 single votes. Alternatively, to find the number of single votes more quickly, multiply the turnout (TN) by two and subtract the total number of votes (TV). Based on the above, it is possible to reconstruct a poll from limited data.

One of the most common scenarios involves knowing the final results and finding reports of the turnout (TN) and of the number of single votes received by either all three or sometimes just two of the candidates, for instance A and B. The remaining single vote C is obviously the total number of single votes (as calculated above) minus A and B, but the distribution of the double votes is less obvious. To work out the three types of double votes (AB, AC and BC) that were cast, subtract the single votes (A, B, C) from each candidate’s result (TA, TB, TC) and calculate AB as follows: Once AB is known, AC is easy to calculate (AC=TA-AB-A) and then BC can also be found (BC=TC-AC-C).

Another frequent discovery in original documents is information about how many votes just one of the candidates shared with another, especially when standing for the same party, as well as the number of single votes that candidate received. Finding data about A and AB, for instance, allows AC to be calculated from the total result for A (TA). Knowing the turnout (TN) then enables the remaining double vote (BC) to be worked out:

BC = (TA+TB+TC) – TN (turnout) – (AB+AC)

Using these and similar methods, it is possible to reconstruct many of the missing polling figures for Victorian multi-member elections. As our project progresses, the snippets of information needed to fill in these gaps are gradually coming to light. These poll breakdowns reveal for the first time the true (rather than estimated) level of party-based support experienced in Victorian elections as well as the incidence of cross-party voting behaviour. This will be particularly revealing for county polls, the largest type of election, where so little electoral analysis has been done.