[EM] Help me understand some notation

[Daniel Carrera]

On Thu, Jan 20, 2022 at 1:44 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> In the case of a three candidate Smith set, the simplest way to get the
> Smih,X winner is to use X finish order as the (reverse) agenda for SPE
> (Sequential Pairwise Elimination): start at the least promising end of the
> agenda (i.e. the last candidate in the finish order) and make one pass of
> Bubble Sort. The candidate who ends up on top is the highest Smith
> candidate (provided cardinality(Smith)=3).
>
> The beauty of this is its seamless-ness ... no need to even construct or
> even mention Smith.
>


Ha! That's really neat. So that makes a family of methods with good
properties that are realistic options for real world elections. This family
is similar but simpler than BTR-IRV because they don't have the IRV vote
redistribution step. I scribbled a few diagrams and I can see how this will
always work for a 3-member Smith set, but not for larger ones. Still... it
should be really rare to see a real world election with cardinality(Smith)
> 3. And even in those cases, the methods are at least Smith efficient.

--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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