[EM] Quick and Clean Burial Resistant Smith

[Kristofer Munsterhjelm]

On 08.01.2022 02:42, Richard, the VoteFair guy wrote:
> On 1/7/2022 4:27 PM, Forest Simmons wrote:
>> Actually, neither RP nor Schulze has better Condorcet efficiency than
>> Smith//TopTwoRunOff, which is the simple method you should be aiming for.
> 
> To anyone, I have some questions (that might also be in the minds of a
> few lurkers).
> 
> How are the "top two" candidates determined according to the
> Smith//TopTwoRunoff method?
> 
> Or, where is Smith//TopTwoRunoff described? (I didn't find it in
> Electowiki.)

I'm not Forest, but I think it would go like this:

- First determine the Smith set. If there's a CW, you're done.
- Otherwise eliminate everybody who's not in the Smith set.
- Count the number of first preferences after elimination.
- Let X be the first preference winner, and Y the runner-up.
- Of the two, elect the candidate who beats the other pairwise.

Smith,TTR is slightly easier and gives you summability at the cost of
ISDA. However, it would probably produce worse results (e.g. consider if
the Smith set all have plurality count zero, being hidden behind
polarizing candidates who are not in the Smith set).

> Since the topic is simplicity, how can ballots be hand counted to
> determine the Smith set?

I would imagine you could do it like this: First find the candidate who
beats the most other candidates pairwise. Choose one at random if
there's a tie. Then repeatedly add someone who beats anyone in the
current set until no such candidate exists. What you end up with is the
Smith set.

It's perhaps a bit labor intensive, though. You'd most likely need to
calculate the Condorcet matrix.

> Yes I know that pairwise counting can be done by having each person at a
> table keep track of only one pair of candidates -- as each ballot is
> passed from person to person.  But how can those pairwise vote counts be
> simply(!) converted into the Smith set -- for any set of ballots?
> 
> As a related question, how does "//" differ from "/"?  In other words,
> is Smith/TopTwoRunoff different from Smith//TopTwoRunoff, and if so, how?

There's to my knowledge no difference, it's just a matter of notation.

-km