Consider the following voting schemes:
- Cumulative voting
- Approval voting
- Plurality with elimination
- Borda Count
- Successive elimination
- We have a team of 10 people
- We have a question with 3 outcomes A, B or C, and the correct outcome is B
- Team members can express likelihood of outcomes by order for example A>B>C.
- The 10 team members express their preferences as follows:
- 2 for B>A> C
- 2 for B>C>A
- 1 for A>B>C
- 2 for A>C>B
- 2 for C>B>A
- 1 for C>A>B
- We randomly select a leader among those 10 people (this is important for certain voting schemes)
- The team has to vote on a single outcome, A, B or C
Which voting schemes give the best outcome on average, where we perform repeated experiments to randomly select the team leader after performing a single assignment of forecasts to team members (it doesn’t matter what order, say 1-3 have A, 4-8 have B and 9-10 have C)?
This is a numerical thought experiment which I will do in Python. The hard part is coding the 6 voting rules and then the simulation is easy. TBA!