Dice Binning Calculator for Post-Election Audits

Joseph Lorenzo Hall (joehall@berkeley.edu), UC Berkeley School of Information

To increase the transparency of the 1% manual tally process, a few California counties have begun to use 10-sided dice to produce publicly-verifiable random numbers (See Cordero, Wagner and Dill 2006). Unfortunately, using 10-sided dice to 1) select from only a few precincts or 2) to select from many precincts can require a lot of re-rolling of the dice. To increase the efficiency of the process, Cordero et al. suggest "binning" the dice rolls so that each precinct has a range of corresponding values, of equal width, that allow a higher percentage of dice rolls to "hit". This calculator implements this idea. It can also output the binning data in a form that is easily pasteable into a spreadsheet. Please click here for source code and licensing information.

Settings

Results

Range is 100. (This is the quantity of random numbers 2 dice can produce.)
Rounded interval is 7. (This is the number of random numbers per bin.)
Interval modulus is 9 (9% of rolls). (This is the number of random numbers that will require a re-roll.)

Paste these bins into a spreadsheet

Roll 00-06, pick precinct 1
Roll 07-13, pick precinct 2
Roll 14-20, pick precinct 3
Roll 21-27, pick precinct 4
Roll 28-34, pick precinct 5
Roll 35-41, pick precinct 6
Roll 42-48, pick precinct 7
Roll 49-55, pick precinct 8
Roll 56-62, pick precinct 9
Roll 63-69, pick precinct 10
Roll 70-76, pick precinct 11
Roll 77-83, pick precinct 12
Roll 84-90, pick precinct 13
Roll 91-99, reroll dice

Source Code, Licensing, Version, Etc.

The source code to this script is available here, licensed under the BSD license (see source for license text).

This is version 1.2 of dicebins.php (as of 2009-04-09 19:36:24 PDT).