[EM] Test elections

[Kristofer Munsterhjelm]

On 11/29/21 11:38 PM, Richard Lung wrote:
> 
> 
> Hello Kristofer and All,
> 
> 
> Can't at present find reply I did make to your test elections.
> 
>  From memory, the nominal winner was B followed by C. But the real 
> winner was A because A had almost a quota -- to half a vote -- that was 
> not a statistically significant shortfall.

Thank you for running one of the test elections through FAB. For the 
benefit of the list, I'll repeat the election here :-)

  752: A>B>C
1750: A>C>B
1752: B>C>A
    1: C>A>B
  750: C>B>A

With this test election, the outcome is A>B>C for every positional 
system with alpha < 0.49 (where Plurality has alpha=0 and Antiplurality 
is alpha=1), B>A>C for Borda, and C>B>A for every positional system with 
alpha > 0.501.

I was trying to find out if single-winner FAB could be modeled as a 
positional system elimination method (the way IRV is 
Plurality-elimination). If it is, it's Coombs, because if the winner is 
B, and C is second place, that means A must've been eliminated first.

The test is rather crude, though, so if you have more time later I can 
try more refined tests. The second test election may also provide some 
information.

I agree that three-candidate single-winner elections are not very good 
demonstrators of a voting method that's intended to be multiwinner - but 
the elections' simplicity also makes it easier to try experiments like 
these.

-km