User:Psephomancy/Voting for voting systems

by Tyler Borgard, June 26, 2017

A group of 31 people are trying to figure out what ranked voting system they should use. Six different voting systems are suggested:

• Plurality
• Anti-plurality (whoever has the least number of last place votes wins)
• Top 2 Runoff
• Instant Runoff
• Borda Count
• Copeland (the winner is whoever has the most paired wins minus paired losses; this is perhaps the simplest Condorcet method out there)

They decide to hold an election with ranked ballots, and here are the ballots cast:

4 ballots: Plurality > Borda > Anti-plurality > Top 2 Runoff > Instant Runoff > Copeland
3 ballots: Plurality > Borda > Anti-plurality > Top 2 Runoff > Copeland > Instant Runoff
1 ballot: Plurality > Borda > Copeland > Top 2 Runoff > Instant Runoff > Anti-plurality
5 ballots: Plurality > Copeland > Borda > Anti-plurality > Instant Runoff > Top 2 Runoff
2 ballots: Plurality > Top 2 Runoff > Anti-plurality > Copeland > Instant Runoff > Borda
6 ballots: Top 2 Runoff > Copeland > Instant Runoff > Borda > Anti-plurality > Plurality
4 ballots: Copeland > Instant Runoff > Borda > Anti-plurality > Top 2 Runoff > Plurality
3 ballots: Instant Runoff > Borda > Anti-plurality > Copeland > Top 2 Runoff > Plurality
2 ballots: Borda > Instant Runoff > Anti-plurality > Copeland > Top 2 Runoff > Plurality
1 ballot: Anti-plurality > Instant Runoff > Copeland > Borda > Top 2 Runoff > Plurality

In order to get a fair result, the people decide to figure out the election winner using each of the 6 systems they voted on. But when they do this, they notice something interesting. Plurality wins under the plurality method. Anti-plurality wins under the anti-plurality method. Top 2 Runoff wins under the Top 2 Runoff method. In fact, every single voting system wins the election under itself!

Frustrated, the 31 people decide to abandon ranked ballots altogether and switch to range voting. Then they live happily ever after. The End.