Punchscan - Tabulation Procedure

Tabulation Procedure

As an example, consider a two candidate election between Coke and Pepsi, as illustrated in the preceding diagram. The order of the letters beside the candidates' names could be A and then B, or B and then A. We will call this ordering, and let =0 for the former ordering and =1 for the latter. Therefore,

: order of symbols beside candidate list,

.

Likewise we can generalize for other parts of a ballot:

: order of symbols through the holes,

.

: which hole is marked,

.

: result of the ballot,

.

Note that the order of the candidates' names are fixed across all ballots. The result of a ballot can be calculated directly as,

(Equation 1)

However when one layer of the ballot is shredded, either or is destroyed. Therefore there is insufficient information to calculate from the receipt (which is scanned). In order to calculate the election results, an electronic database is used.

Before the election, the database is created with a series of columns as such. Each row in the database represents a ballot, and the order that the ballots are stored in the database is shuffled (using a cryptographic key that each candidate can contribute to). The first column, has the shuffled order of the serial numbers. contains a pseudorandom bitstream generated from the key, and it will act as a stream cipher. will store an intermediate result. contains a bit such that:

The result of each ballot will be stored in a separate column, where the order of the ballots will be reshuffled again. Thus contains the row number in the column where the result will be placed.

After the election is run and the values have been scanned in, is calculated as:

And the result is calculated as,

This is equivalent to equation 1,

The result column is published and given the ballots have been shuffled (twice), the order of the results column does not indicate which result is from which ballot number. Thus the election authority cannot trace votes to serial numbers.