[EM] Possible Condorcet-composite method DMTBR disproof

Kevin Venzke stepjak at yahoo.fr
Thu Mar 24 17:15:24 PDT 2022

Hi Kristofer,

Le jeudi 24 mars 2022, 18:03:03 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
> I may have a disproof showing that if X is DMTBR, then Condorcet//X and
> Smith,X are not necessarily so. But this is a pretty strong claim, so
> I'd like to check with the list first.
> For the (somewhat inelegant) election:
> 14: L>C>R>X>Y>Z
> 10: R>C>L>Y>Z>X
> 7: C>L>R>X>Z>Y
> 15: Y>Z>X>L>C>R
> 15: Z>C>R>L>Y>X
> 7: Z>X>C>R>L>Y
> 22: Y>X>R>C>L>Z
> can anyone check if:
>     - the innermost DMT set is {L, C, R},
>     - the IRV winner is L,
>     - the Condorcet winner is C,
>     - and if the bloc of 14 voters votes L>X>C>R>Y>Z instead, then the
> Smith set contains every candidate?

Those all look correct to me, although I'm not sure if "innermost DMT set" is
always a clear term. You might have more than one I think, where neither is a
subset of the other. I am no expert on the concept though...


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