Page 24 - Towards Trustworthy Elections New Directions in Electronic Voting by Ed Gerck (auth.), David Chaum, Markus Jakobsson, Ronald L. Rivest, Peter Y. A. Ryan, Josh Benaloh, Miroslaw Kutylowski, Ben Adida ( (z-lib.org (1)

E. Gerck
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To increase reliability in spite of interference, Information Theory introduces
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the idea of using different channels of information as intentional redundancy.
More channels, more redundancy, less interference.
It is clear from the foregoing, thus, that by sending information from A to B
in a properly redundant form, the probability of accuracy and reliability errors
can be reduced —which can be theoretically and experimentally verified. For
example, by sending to B two different messages created from the same final
ballot screen that the voter saw and confirmed: (1) a printout and (2) an elec-
tronic record. With more properly redundant channels (e.g., a copy of the screen
memory), the probability of errors could be made even smaller.
One could expect, however, that to make the probability of errors approach
zero, redundancy must increase indefinitely, and the rate of transmission there-
fore would approach zero. This is by no means true, as shown by the Tenth
Theorem (in current wording) [9, 11]: With the addition of a correction channel
equal to or exceeding in capacity the amount of noise in the original channel, it
is possible to so encode the correction data sent over this channel that all but
an arbitrarily small fraction of the errors contributing to the noise are corrected.
This is not possible if the capacity of the correction channel is less than the
noise.
By direct application of the Tenth Theorem, we state below the condition to
make the probability of errors approach zero.

Error-Free Condition: There exists an optimal design that can reduce election
outcome errors (interference) to a value as close to zero as desired, which we call
error-free. The existence condition is given by

C ≥ E
where C is the capacity of the correction channels and E is the capacity of the
error channels.
Referring to the Intuition discussion in Section 5, not only can we now quantify
what we mean by enough,as C ≥ E, but we can also specify in terms of inner
metrics the expected risk value for each error channel and for the voting process
as a whole.
The optimal design is used in our framework to reduce both physical inter-
ference (provably) and conceptual interference within all three boundaries (see
boundary definitions in Section 6). In physical terms within the first two bound-
aries, a conforming voting means implements the optimal design to provably
increase accuracy and reliability in a communication process that includes the
ballot as seen and cast by a voter (the starting point A), the ballot box as a

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Redundancy is the variety in a channel that exceeds the amount of information actu-
ally transmitted. English writing is estimated to be 50% redundant, which accounts
for our ability to detect and compensate for typing errors; fr xmpl, ndrstndng txt
even without vowels. In the process of communication, redundancy is essential to
combat interference, to assure reliability and to keep a communication process in
operation in spite of interference [9, 11].