"What P.R. Is
The P.R. League believes that Proportional Representation with the single transferable vote, otherwise known as the Hare system, is the most suitable method for the election of representative bodies. This method is already in use for important elections in many parts of the world notably in the parliamentary and municipal elections of the Irish Free State. It is used in Cleveland, Winnipeg, Calgary and a number of other U.S. cities.
P.R., as it is usually called, gives every group of like-minded voters the share of the members elected that it has of of the votes cast.
It does this
1. by giving every voters a single vote in a district electing several members, so that each member is elected by a separate group of the districts' voters, and
2. by giving the voter a chance to express alternative choices, so that his vote will not be wasted on a candidate who does not need it or cannot use it.
No primaries are needed. Nominations made freely by petition.
The voter casts his ballot by putting the figure 1 opposite his first choice, the figure 2 opposite his second, the figure 3 opposite his third, and so on for so many choices as he cares to express.
[When votes are counted, quota (the minimum required to win) is calculated. Some achieve quota on the first count. Their surplus is moved to the next back-up reference.]
When all the votes are grouped behind candidates who actually need their support, the smallest group of votes is broken up. Rather than be wasted, the votes go to where they can support others who have a chance of election.
Other groups then are broken up for the same reason. Each group stays together as long as there is a possibility of gaining from smaller groups. But when it is the smallest group left, each member of the group goes to help the candidate marked as the next preference among those still running, the ones who could use more votes.
This process of gradual elimination continues until, in cases where there five seats to be filled, there are only six groups left, when the smallest of the six concedes the election to the other five.In this way the greatest possible number of voters have a real share in the elected representation.Exactly what voters would do in person in a case where their first choice is not able to be elected, P.R. count does with their ballots. The figures on the ballots are sufficient directions for the necessary transfers."
(Proportional Representation Review, April 1924, p. 91)
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[The writer provided the metaphor of voters physically grouping themselves about their candidate. Forming groups then finding that too many (more than quota) are grouped about some candidates, the surplus people going to other candidates that are most liked. Some of this was morphed into the straight vote count process in my version above.
Oddly enough some of this physical candidate/room set-up is used today in the U.S. for Iowa primaries, where people physically place themselves in the different camps. However these "rooms" are not used to elect multiple winners, hence no proportionality or surplus is therein. In Iowa, they are used to perform run-off elections to choose the Iowa choice of Democratic presidential candidate. (Helier Cheung, "Iowa caucuses Nine unusual things about them", BBC News, Feb. 1, 2020)
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