Bertrand Ballot Prefix Paths
Count vote paths that stay ahead and see how a strict boundary changes the result.
Free theory articleCount vote paths that stay ahead and see how a strict boundary changes the result.
Concept & interpretation
The Bertrand Ballot Problem considers an election between two candidates, A and B. If candidate A receives a votes and candidate B receives b votes (with a > b), we are interested in the probability that candidate A stays strictly ahead of candidate B throughout the counting process.
Experiment
You can interactively explore the ballot paths in the Bertrand Ballot Prefix Paths module.
- Set the A votes control to 3.
- Set the B votes control to 1.
- Set the Rule control to "Strict".
- Observe that the Valid paths output displays 2, the All orderings is 4, and the Probability is 0.5.
- Change the Rule control to "Weak" and notice the difference in valid conditions.