[EM] more questions about PR allocation formulas

[James Gilmour]

James G-A wrote:
> 	I must have got all confused. I thought that 
> Newland-Britton was the method of doing fractional transfers 
> of surpluses rather than transferring randomly selected 
> ballots. He talks about a specific form of that, the 
> "senatorial rules," but he doesn't give it a general name. 
> Does it have one? (I'm not talking about Meek, but the one 
> which only calculates the fractional value of the votes once, 
> that is at the time that a candidate who holds them is elected.)

In the taxonomy of voting systems someone may have defined "the Newland-Britton method", but I
suspect this is really a reference to the codification of the STV-PR rules that Newland and Britton
produced when STV-PR was re-introduced for Assembly and District Council elections in Northern
Ireland in 1972 (first elections in 1973).  A booklet containing these rules was published by the
Electoral Reform Society in 1973 and the rules also appeared in legislative form in the relevant UK
NI Orders.

The Newland & Britton 1973 publication superseded "Regulations: Proportional Representation by the
Single Transferable Vote" written by A J Gray in 1936 and revised by J Fitzgerald in 1955.  The
1936/1955 rules were substantially those in the Education Authorities Election Order (Scotland) 1928
and in the University Elections (Single Transferable Vote ) Regulations 1918.  These defined the
quota as (valid votes / (seats + 1)) + 1, ignoring any remainder from the division.  When surpluses
were transferred, a number of papers equal to the number of votes in the surplus (ignoring any
fractional remainder) was transferred.  The papers actually transferred were "those last filed" in
the sub-parcels for each continuing candidate.  This gave a representative result (in statistical
terms), but a different result might be obtained if the papers were shuffled in a different order.
(This method is still used to elect the Dáil Éireann.)  The Newland & Britton rules removed this
element of chance by transferring all relevant papers at a fractional value.

The "Senatorial Rules", introduced for the election of the Irish Senate in 1921, also removed the
element of chance by transferring all relevant papers.  However, to avoid calculations involving
fractions, each valid voting paper was assigned the value one hundred.  Reduced transfer values were
calculated by dividing the surplus by the number of transferable papers, ignoring any residual
fraction.

James Gilmour