DATE: | 9/14/94 | ||

TO: | Faculty Senate | ||

FROM: | Don Eidam | ||

RE: | Saving Time: A Proposed New Voting Algorithm |

Traditionally our first fall meeting has been devoted to elections, with nominations, ballots, counting of ballots, motions on how to conduct runoffs, runoff elections, ... Although the parallel processing and time pressure that ensues is not as chaotic as it appears, it almost invites errors and it normally consumes the entire meeting corpus with the "real" agenda business RTA'd.

In addition, our ad hoc runoff criteria are subject to the criticism that sometimes one's prior vote may have been "wasted". But note:

Since at least the time of Pliny the Younger, people have grappled with the dilemmas of voting algorithms. In 1952, economist Kenneth Arrow (Stanford, 1972 Nobelist) proved the Impossibility Theorem, that finding an absolutely fair and decisive voting system is impossible: "...I began to get the idea that maybe there was [a] theorem here, namely that there was no voting method that would satisfy all the conditions that I regarded as rational and reasonable...it actually turned out to be a matter of only a few days' work."(1)

Although this is the method used in most campus elections (e.g. those conducted by APSCUF-MU and the School Deans), our tradition is to elect by majority. In a plurality election with 20 candidates, one could be elected with <6% of the total number. Indeed, Roberts advocates a majority in most elections so that those selected are perceived as having the support of the body; and his

Alternate Algorithm 1 is thus apparently rejected.

Voters indicate on their ballots their first, second, third, ...choices. If there is no majority the candidate with the fewest votes is eliminated and the choices are renumbered accordingly (3). The ballots are counted again and the algorith continues recursively until a candidate receives a majority (

A soliciation for nominations will be mailed to you prior to the first day of the fall semester; you may then mail/phone/email nominees' names to the chairperson before the first Tuesday in September. A pre-printed blank ballot will be distributed to you at the beginning of the meeting with entries such as:

- ACAD. POL. COMM: NON-SCHOOL

- 1

- 2

- 3

- ...

Voter 1 | Voter 2 | Voter 3 | Voter 4 | Voter 5 | Voter 6 | Voter 7 | Voter 8 | |
---|---|---|---|---|---|---|---|---|

R 1 |
Newton | Newton | Newton | Euler | Euler | Archimedes | Archimedes | Guass |

A 2 |
Archimedes | Euler | Euler | Archimedes | Gauss | Euler | Gauss | Euler |

N 3 |
Euler | Archimedes | Gauss | Newton | Archimedes | Gauss | Euler | Newton |

K 4 |
Gauss | Gauss | Gauss | Newton | Newton | Newton | Archimedes |

No majority; Gauss is eliminated(4):

1 | Newton | Newton | Newton | Euler | Euler | Archimedes | Archimedes | Euler |

2 | Archimedes | Euler | Euler | Archimedes | Archimedes | Euler | Euler | Newton |

3 | Euler | Archimedes | Newton | Newton | Newton | Newton | Archimedes |

No majority; Archimedes is eliminated:

1 | Newton | Newton | Newton | Euler | Euler | Euler | Euler | Euler |

2 | Euler | Euler | Euler | Newton | Newton | Newton | Newton | Newton |

Majority; Euler is elected.

(1)COMAP staff,

(2)See XXXIV-XXXVII, Jones'

(3)In practice, this simply involves redistributing the ballots in one pile onto the other piles.

(4)As two Senators have noted, this is called "Gaussian elimination".

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