Copyright ©2008 by Paul Niquette All rights reserved.
ballot box is quietly tumbling into obsolescence, displaced not
by the newest technologies in voting machines nor by the World Wide Web
but by the oldest of technologies: the mail-box. Some states have
already accomplished the improvement. By de-synchronizing the voting
process, voters don't have to wait in long lines. Then too, each
voter, ballpoint-in-hand, can take plenty of quality time to study ballots
and campaign literature -- and websites.
By mail-in ballot, members of the electorate can vote early -- weeks before traditional election campaigns are over. For candidates and campaigns, that creates yet another political segmentation. In addition to age, faith, gender, occupation, party, and schooling, a whole new demographic of early deciders must be targeted before any ballots get mailed out.
Long after election day, bags full of postmarked envelopes
come tumbling into county offices for county counters to count, resulting
Nail-Biter Ballots. Here are salients
of a real life drama as described in this puzzle.
Sophisticated solvers will do some parsing and likely
make six observations:
Thus, we can write…
(621,800 – bUNCOUNTED) * 0.6678 > 621,800 * 0.6667…which means that bUNCOUNTED = 0, 1, 2, … 1,023, the solution being...
Even if all 1,023 ballots were "no" votes, the tax measure would nevertheless receive 414,554 "yes" votes, just enough for passage.
Nota bene: This is not a statistical outcome tantamount to saying, "With ___% of ballots counted, we are confident in projecting that the measure will pass."uppose that we let fUNCOUNTED represents the fraction of the total ballots cast that are uncounted at the intermediate (11/25) stage. Evidently bUNCOUNTED= 621,800 * fUNCOUNTED. One can re-write the expressions developed above as follows:
(621,800 – 621,800 * fUNCOUNTED) * 0.6678 > 621,800 * 0.6667Thus, with 99.83017% of the ballots counted and 66.78% of those voting "yes," one can declare absolutely that the measure will pass, winning at least 2/3rds of the total vote.
Sophisticated solvers might create a model from this solution.
One simple way to do that is to use the expressions above as templates,
thereby 'generalizing' from the 'particular'...
...to produce graphs like this one.
A measure or a candidate requiring a 50% majority can be declared the winner with only 75% of the votes counted, provided that the tally is at least 65% favorable (green curve).