How this calculation works
Count vote orders in which candidate A is ahead at every nonempty prefix.
Count = C(a+b,a) × (a−b)/(a+b) for a>bA worked example
Five votes versus three give 56 possible orders, of which 14 keep A strictly ahead.
Good to know
A tied prefix is excluded. Votes within each candidate group are indistinguishable.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count vote orders in which candidate A is ahead at every nonempty prefix.
The primary result is labeled “Valid counting orders”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A tied prefix is excluded. Votes within each candidate group are indistinguishable.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Five votes versus three give 56 possible orders, of which 14 keep A strictly ahead.
Which rule does this calculator apply?
Count = C(a+b,a) × (a−b)/(a+b) for a>b