AAPT Election votes
(for elections of Board members and Officers)
First, a reminder of what the economist Kenneth Arrow has proved quite rigorously – Arrow’s Paradox. With respect to voting procedures, it says (in effect) that for EVERY voting system where there are three or more alternatives there is at least one set of circumstances such that in those circumstances the system produces paradoxical results (and/or violates obvious criteria of fairness). Moreover, different procedures have different virtues not directly connected to fairness of the election results. (E.g., raised-hands in a public assembly is more efficient than paper ballots; paper ballots are useful when the privacy of a voter’s ballot may be important.)
In our situation there are three factors which make balloting in the “traditional” sense impossible – or at least impractical. (1) Election must be by a majority of votes cast. (2) There are usually in the neighborhood of 10-15 nominees for five positions. (3) Balloting is conducted by U.S. Postal service or a single electronic ballot. So, the use of an Instant Runoff Voting (IRV) procedure is suggested, whereby each voter’s preferences among nominees for runoff purposes are coded into the initial ballot, and those preferences can be accessed in an automatic runoff procedure when no nominee has attained the requisite minimum of votes for election. [More information about IRV is available through a number of web-sites: e.g., www.instantrunoff.com/irv/html. Or www.chrisgates.net/irv (an interactive animation!) ]
What follows is a detailed account of how the procedures proposed actually count the votes. (These procedures are borrowed from California State University, Los Angeles.)
Single Transferable Vote (“Instant Run-Off”) – a la CSULA
Each voter ranks as many (or as few) of the candidates on the ballot as he or she wishes, in his or her order of preference – 1, 2, 3, …
Tallying the ballots:
- A ‘majority quota’ is established – half the total number of (valid) ballots plus 1.
- An initial tabulation is performed in this manner: the ballots are apportioned into ‘stacks’ – each stack containing the ballots which mark a given candidate as number 1 choice. The ballots in each stack are counted. If a candidate’s stack contains enough ballots to equal or exceed the majority quota, that candidate is declared elected. (With the quota as a simple majority and each voter voting only one 1st choice, there can be at most one such winner.)
- What happens next depends upon whether a candidate is declared elected.
(a) Suppose there is a winner. [If the balloting is only to fill one position, that has now been effected.] Now all the ballots in the winner’s stack are reapportioned among the other stacks on the basis of each ballot’s next preference (e.g., after an initial winner is declared, those ballots are apportioned one by one among the other candidates as dictated by each ballot’s number 2 preference). Ballots which list no next preference are set aside, and play no further role in the tally. The stacks are counted again. If any candidate’s stack now equals or exceeds the majority quota, that candidate is declared elected. We now “loop” back to 3(a) – and the procedure is repeated with the ballots in this second winner’s stack apportioned among remaining stacks according to each ballots next preference. And so on.
(b) Suppose, on the other hand – as presumably happens sooner or later – no candidate’s stack contains enough votes to equal the majority quota. The candidate’s stack with the fewest ballots is cannibalized – that candidate is no longer in the running and the ballots in the stack are apportioned among the remaining stacks according to each ballot’s next preference – and ballots with no next preference are set aside. (If there is a tie for smallest stack, the winner (loser?) is determined by lot.) The stacks are counted again. Now we “loop” back to 3(a) again – if there is a winner, the winner’s stack is reapportioned for another loop; if there is no winner, the smallest stack is cannibalized and stacks are counted again.
- Eventually, there are no more stacks of ballots to count, and the tally is over. Order of finish is given (from the top down) by the order in which winners are declared – and (from the bottom up) by the order in which losers are eliminated.
