Elect and Exclude. Binomial STV Hand Count Basics

Power corrupts and absolute power corrupts absolutely, as Lord Acton said. Monopoly power, principally of the state, even in civilised countries, can grievously oppress the innocent.
No man is good enough to be another mans master, as William Morris said.
Binomial STV is able to exclude, as well as elect candidates. It promotes friends and helpers. It can also remove masters and oppressors.
A Binomial STV ballot paper looks like any preference vote, in order of choice: 1,2,3,4, etc. But the binomial count means that the last preference counts as much to exclude a candidate, as the first preference counts to elect a candidate. Similarly for the second preference compared to the second last preference. And so on.
The exclusion power of voting encourages friendlier and more courteous candidates.
Leaving the ballot more or less blank, of preferences, withdraws up to ones whole vote, from the candidates. Abstentions go towards a NOTA quota, leaving a seat unfilled. A "None Of The Above" power encourages better quality candidates.

I have already written a booklet on this subject – “The Super-Vote supercharged. Binomial STV elections Hand Count.”
I wrote that, when I realised that binomial STV could be popularised, as a hand count, in any local club elections.
Previously, I thought of Binomial STV as a grand logical structure, capable only of a computer count. I wrote a full-scale book about this – “FAB STV: Four Averages Binomial Single Transferable Vote.” FAB STV has higher orders of counts.
Binomial STV, explained in two booklets, is just first order binomial STV. (That is symbolised by STV^1. But, for purposes of holding elections, it is not necessary to know about higher orders of binomial STV, based on the binomial theorem.)
Descending from FAB STV, to a basic form of Binomial STV, gave-up a modicum of accuracy, to achieve much greater simplicity. Traditional hand counted STV has been producing reliable election results for over a century. Binomial STV could adopt that advantage. But traditional counts don’t have the advantage of binomial STV, which gives voters the power to exclude, as well as elect, candidates.
I believe (first order) Binomial STV to be the best combination of the simplest and most powerful voting method, to elect and exclude candidates.
So far, so good. My first booklet came up with a hand counted binomial STV. Then I realised I had missed a trick. There is an even simpler tradition of hand counting STV, which I hadn’t adopted for binomial STV. Rather than add this simplest method to my first booklet, I decided to write another booklet.
There are several reasons for this. I didn’t want to complicate my first booklet, which is enough to learn, at one go. Essentially, it adopts Gregory method, which is the arithmetic of how to transfer an elected candidates surplus vote, equitably, to all that candidates next preferences.
This second booklet also explains how to adopt Gregory method to binomial STV. But it does this, in the context of a simpler non-arithmetic method of transfering surplus votes to their next preferences. This non-arithmetic method takes a random sample, the size of a candidates surplus vote over their elective quota of votes. The randomness of the sample is what makes it representative of a winning candidates total vote, because it favors no one preference over another.
At Irish elections, the returning officers tumble the ballot boxes, so the ballot papers are tumbled about in the box, in no sort of order. This is to remove the bias that can occur, from any ward accumulating a clump of preferences for one candidate, that may not be representative of the whole district. Taking a sample, from any such clump, might not constitute a representative sample.
The Irish method of counting surplus votes, by taking a representative sample of a winning candidates total vote, is also practised in Cambridge, the home of MIT, the Massachusetts Institute of Technology.