The whole-vote "Exact method" of transferring surplus votes
Two variants:
-- the British-Irish-Canadian version where "exact method" used for all surplus transfers;
--- the U.S. version where "exact method" used for surplus votes belonging to candidates elected in first count; a random method used for surplus votes of candidates elected after the first count.
There are two types of surplus vote transfers
-- those that take place just after the first count when candidates have only first-preference votes (due to the way the votes are counted, it is not possible to simply stop the candidate receiving votes when he or she attains quota so a surplus may occur.)
-- those that occur after a candidate has received transfers. in these cases, either the surplus is transferred randomly, or only the last parcel is considered (exact method), or all the votes are transferred but at fractional value (under a Gregory method).
under the U.S. system, cities used the "exact method" for the first case and then resorted to a random method for the later transfers. (example -- model PR election rules produced by PR League, reprinted in Hoag and Hallett (1926), p. 347)
British-Irish-Canadian systems used the "exact method" for both cases (but with two different categories of relevant papers - sometimes considering all the candidate's votes, and sometimes considering only "last parcel," to determine the transfers.
The election of the lower houses in the Australian Capital Territory and Tasmania used the Gregory method. The exact-ness of this method is foiled to a degree for the later transfers, by the systems using only the last parcel of voters that the candidate received to determine the transfer.
The "Exact Method" transfers votes in true proportion to the next usable marked preference marked on the relevant ballot papers but does not consider any lower preferences. (because already in the second count (usually), surplus votes are transferred, and many of those are subsequently transferred based on third or lower preferences which had not been considered when making the surplus vote transfer, Random-ness does enter into the outcome. However as most of the cand. in the winning positions in the first count are elected at the end despite transfers, and random draw may produce same composition of transfer as a mathematical method (Gregory Method), the "exact method" may work good enough. More on this below.)
The largest fractions is used to allocate the odd number of votes at the end, to give accurate results.
The "exact method" is described fully in John D. Hunt's 1923 publication A Key to P.R.
The relevant ballot papers depends on circumstance and the variant system of "exact method" in use, whether it is all the votes held by the elected candidate or only the last parcel. Next usable preference marked on all votes held by successful candidate are considered for those elected in the first Count, otherwise only "last parcel" votes are the only ones considered.
(Because the exact method does not consider secondary preferences when making transfers, it does have a potential element of chance in its mechanics.
However as all or most of the candidates in the winning position in the first count are elected in the end, transfers overall have only small effect, the surplus transfers in particular have less, and the effect of chance in transfers of surplus votes even less than that, so the effect of chance under the "exact method" seems in many cases to be only theoretical.)
The historical use of "exact method"
The "exact method" might have been used in Tasmania's first STV elections for members of its state assembly in the 1890s (or a whole-vote form of Gregory might have been used).
Boulder, Colorado (1917) and West Hartford, Connecticut used the U.S. version of the "exact method". (Hoag and Hallet, PR (1926) p. 392)
The Exact Method was used in Sligo's STV 1919 election, the first borough STV election in U.K.
It was also maybe used to fill university seats in the U.K. HofC starting in 1918.
By 1918 the Exact Method was likely being used in several cities in BC.
It was definitely used in 1920 in Winnipeg to elect both MLAs and city councillors;
in Malta in national elections, starting in 1921;
and in Ireland and Northern Ireland, starting in 1922.
(The "exact method" was not, it seems, used anywhere in Australia after 1907, and it seems it was last used in North America when the City of Winnipeg last used STV in the late 1960s. (Cambridge, Mass. uses a random method to transfer surplus votes in its city elections.)
It is not known when someone first described the "exact method" in writing...
(Hoag and Hallett, PR (1926) describes the "exact method" and its application in two different systems -- the "American exact method" STV system and the "British-Irish-Canadian method." STV system. (p. 395).
(see Montopedia blog "Methods of Transferring Surplus votes" for more info.)
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The "exact method" uses simple formula - b/c X s = B (rounded down) and where that does not fill the seats, largest remainder is used. (A version of the largest remainder is used today in Denmark to calculate party seat counts and is reputed to be very proportional.)
In Australia and the Ireland Senate, the Gregory fractional method is/was used, not the exact method.
Complicating a discussion of the whole-vote "exact method," the Hare-Clark version of Gregory Method STV used in Tasmania recorded the transfers as whole votes, not recording the votes as fractions but as the sum total of the fractions added together, with any fractional remainder recorded as "lost." This made the vote count easier to read without distorting results very much. (Some of the "lost" votes were resurrected later as the vote count progressed.)
A modern presentation of the "exact method" can be found online at
(Sources used:
Hoag and Hallett, PR (1926), p. 345-346, 389-394,
Farrell and McAllister, The Australian Electoral Systems, p. 60)
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