[EM] What IRV optimizes

[John B. Hodges]

In passing, in his post of 6 August, Forest Simmons wrote:
>In other words, there doesn't seem to be any variational (i.e.
>optimization) principle to support IRV.

IRV is the one-seat case of the Single Transferable Vote. The point 
of STV is to maximize "ballot effectiveness", i.e. to minimize 
"wasted votes". Votes are wasted in two ways: Undervotes, where you 
vote for someone who fails to win a seat, and Overvotes, where you 
vote for someone who gets more votes than they need to win a seat.

The STV procedure, invented by Thomas Hare and Carl George Andrae in 
the 1850's, goes like this:
(1) Count voters' first choices.
(2) Has any candidate reached the winning threshold?
	If not, eliminate last-place candidate and transfer ballots. 
Each ballot goes to the highest-ranked candidate that is still in the 
race. Go back to (2).
	If so, go to (3)
(3) Have all seats been filled?
	If not, distribute surplus ballots of all newly elected 
candidates. Recommendsd procedure that has become standard: calculate 
the fraction (Number of votes received above the winning threshold / 
total votes received), mark each ballot received by that winning 
candidate as now being worth (that fraction times its previous 
value), distribute each ballot to the highest-ranked candidate still 
in the race. Go back to (2).
	If so, you are finished.

So, Undervotes are dealt with in step (2), Overvotes in step (3). 
Each ballot does as much work as it can toward electing a candidate.
-- 
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John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.