What voting schemes are more effective at eliciting correct forecasts from small teams?

Consider the following voting schemes:

  • Plurality
  • Cumulative voting
  • Approval voting
  • Plurality with elimination
  • Borda Count
  • Successive elimination

Now suppose

  • 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!

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