Why are the votes encoded as 1 and 0 for two candidates?

Conditions

• Exactly two candidates are considered.
• Each candidate receives one ballot value.
• The intended vote is for exactly one candidate.

Reasoning, step by step

1. Reduce the election to two candidates, represented physically by two pens.
2. Encode the preference numerically: write 1 for the candidate supported and 0 for the candidate not supported.
3. Use this binary encoding to turn the election into a pair of numeric ballot entries.
4. Allow the system to mathematically verify that exactly one candidate is chosen.

Example

The speaker says the election has two candidates, represented by the pens, and that he wants to vote for the pen on the right. He writes a one and a zero to represent his vote for the two candidate pens.

Common misconceptions

• Assuming the values are arbitrary: The values 1 and 0 specifically represent support and non-support, enabling the sum-to-one validity check.

Watch the explanation

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