[EM] Manual Construction of Smith Set

[Richard, the VoteFair guy]

On 1/27/2022 2:30 AM, Kristofer Munsterhjelm wrote:
 > So I disagree. I don't think simplicity requires you to
 > throw away Smith compliance.

I agree.  Yet remember that my goal is to make it easy for voters to 
watch vote counting on a stage and understand what's going on.

Kristofer suggests River and some other mathematically good methods, but 
all of them require using the pairwise counts in ways that are not as 
easy to understand as asking "which number is bigger?, that's the winner 
in this pair."

Yes Copeland is simple, but ...

The popularity of IRV has shown that vote counting is easier to 
understand when candidates are eliminated one at a time.  Most watchers 
won't trust a process that ends so quickly, and fails to also 
(sequentially) reveal who was least popular, who was second-least 
popular, etc.

In a different message ... Kristofer Munsterhjelm wrote:
 > So "on stage", Smith//IRV may not be a good method. I don't
 > think that IRV itself would be a good method for on-stage
 > voting, but if you had to do it then I would imagine either
 > Benham (if you need strategy resistance) or BTR (otherwise)
 > would be better than Smith//IRV.

Actually one of the big selling points of IRV is it can be done on stage 
simply by piling ballots into stacks.  The stacks are named by 
candidate, and the ballot goes to the stack of that ballot's currently 
highest-ranked candidate.  The height of the stacks make some 
comparisons very clear.  When the heights are similar, simple counting 
can confirm which stack has fewer ballots.

Near the end of the process the tallest stack can be counted to see if 
it contains more than half the ballots.  For added clarity, the ballots 
in all the other stacks can be counted to show there are fewer ballots 
in all those other stacks.

With IRV it's even easier -- but not fairer -- (than other methods) 
because after each elimination the only ballot stack that needs to be 
re-allocated is the stack that supports the candidate just eliminated.

I'll repeat that I strongly dislike IRV!!!  So I'm not defending it!

I'm just trying to point to something better that also can be counted in 
a way where watchers can easily verify the (relative) fairness of each step.

When a method requires subtraction -- such as for calculating margins -- 
or sorting pairwise counts, the ease of understanding disappears.  (Yes 
subtracting can be done by hand on a white board, but following the 
subtraction process many times would make some watcher's head hurt. Yes 
a calculator is usually trustworthy, but a watcher doesn't want to watch 
lots of numbers being entered on the calculator and then transcribed 
onto signs, and then named, etc.  Yes sorting can be followed, but it's 
not easy to trust if the process also involves something else going on too.)

Yes, BTR-IRV does fit the requirement of being better, but IMO it's not 
good enough.  It elects the Condorcet winner, but in a way that would 
prompt lots of voters to ask "why are we protecting the Condorcet winner 
when it has the shortest stack of ballots?"

In contrast, it's usually easy to follow eliminations that are based on 
something that's easy to understand, such as eliminating a candidate who 
loses every one-on-one match against the remaining candidates.

I believe such methods exist.  They may not have established names. 
They must be easy for non-math-savvy watchers to follow.  Yes they won't 
have superb mathematical characteristics.  But IRV too easily yields 
flawed results, so getting better results shouldn't be difficult to 
achieve, even with the can-be-followed-on-stage constraint.

Richard Fobes
The VoteFair guy


On 1/27/2022 2:30 AM, Kristofer Munsterhjelm wrote:
> On 26.01.2022 20:30, Richard, the VoteFair guy wrote:
>> My conclusion is that ALWAYS eliminating EVERY non-Smith-set candidate
>> is too difficult to do as a visible process on an auditorium stage.  As
>> Kristofer says:
>>
>> On 1/16/2022 10:31 AM, Kristofer Munsterhjelm wrote:
>>> But you still need to decide when to stop, which can be pretty
>>> difficult. At first it'd seem to be obvious: if the bottom-most
>>> candidate beats anyone else pairwise, he'd be in the Smith set, no?
>>> But that doesn't quite work. Consider something like this: ...
>>
>> It's much easier, and almost as "good," to eliminate pairwise losing
>> candidates as they occur during elimination rounds.
>>
>> As a reminder, a "pairwise losing candidate" is the candidate who would
>> lose every one-on-one match against each and every remaining
>> (not-yet-eliminated) candidate.
>>
>> That would eliminate MOST, but not all, non-Smith-set candidates in MOST
>> cases.
>>
>> Thanks to those who helped get us close to a process that could be
>> understood by an audience of typical voters.
>
> The problem is, of course, that there's not always a Condorcet loser.
> And so you may eliminate a Smith set member because the method's
> fallback metric fails to exclude them from elimination.
>
> Meanwhile, both the "move to the right of the line" and the sorting
> proposals will succeed in identifying the Smith set. And they're both
> simple, IMHO, so I would disagree with your conclusion.
>
> If you need only a single winner, there are plenty of alternatives that
> pass Smith. Copeland elimination seamlessly handles the pairwise loser
> elimination step, because a Condorcet loser is also a Copeland loser;
> and since Smith set members have above average Copeland score whenever
> non-Smith members exist, you'll eliminate every non-Smith member before
> you eliminate every Smith member. It shouldn't be too difficult to
> phrase, either: instead of "eliminate the candidate who loses every
> pairwise contests", it's "eliminate the candidate who loses the most
> pairwise contests".
>
> Or Forest's sequential pairwise elimination, which in a sense mimics
> legislative procedure and so should also be pretty easy to explain.
> First set up an ordering, then go up it and say "does the next proposal
> beat my current proposal? If so, switch it out, otherwise keep my
> current proposal".
>
> Or even BTR. If your elimination procedure, instead of saying "eliminate
> the worst by some measure X" says "eliminate the candidate of the second
> worst and worst who beats the other one pairwise". This also passes Smith.
>
> So I disagree. I don't think simplicity requires you to throw away Smith
> compliance.
>
> -km
>