[EM] Manual Construction of Smith Set

[Kristofer Munsterhjelm]

On 27.01.2022 21:12, Richard, the VoteFair guy wrote:
> 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.

Then why not use Copeland *elimination*? It smoothly generalizes the
idea of Condorcet loser elimination: the Condorcet loser is
automatically also the Copeland loser. It passes your "which number is
bigger" test (in this case, which Copeland number is smaller). And it
passes Smith.

As Forest mentioned, SPE is also pretty clear if you've been doing
parliamentary procedure. First set the agenda. Then go "proposal X vs
proposal X plus amendment Y; okay, the majority wants the former...
proposal X vs proposal X plus amendment Z..." and whatever is left
standing at the end wins.

Or minmax elimination: repeatedly eliminate the candidate who's got the
worst showing against someone else. If you can have a notion of "how
bad" and eliminate the most bad, as IRV does, then there are plenty of
ways to fill in that notion, that IMHO can be presented on stage.

I would, on a more general position, also disagree that elimination is
the simplest. Neither Range, Approval, nor Plurality uses elimination.
And one may say many things about their shortcomings, but "hard to
understand" isn't one of them.

> 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.

Oh, okay. I thought by "on stage", you meant where each candidate is
represented by a person, like in the Smith line example.

> 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.)

The right/left of the line process doesn't require subtraction. At any
step, you ask candidates who were just added to the Smith set, "would
you lose to any of the guys not yet on this side of the line in a
runoff? If so, who?".

Copeland elimination doesn't use subtraction either, unless you count
"is X greater than Y" as subtraction as it's the same thing as "is X-Y >
0". If so, then IPE loses too because you need to answer "does X beat Y
pairwise" to determine who the pairwise loser is.

And River doesn't need subtraction unless you use margins. All that's
required for either River or RP is to be able to sort contests in order
of their strength, i.e. a 60-40 contest beats a 51-49 contest. Then you
go down the list and admit information about the final order ("A must
come before B"), skipping contradictions, until you have a full order.
River and RP differ on what exactly a contradiction is. (Using wv
amounts to throwing out all pairwise contests where your candidate is a
loser.)

> 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.

I guess the trouble I'm having is that I don't understand what that
criterion implies, because as I've mentioned, there seem to me to be
plenty of methods that pass this criterion, but yet that you discard.
Like SPE or Copeland-elimination. Perhaps even the advanced methods (as
long as you don't use subtraction).

I guess in a broader sense, it all seems a little arbitrary. Addition is
fine, subtraction is not, Borda-elimination is okay until it's pointed
out that it *is* Borda-elimination. What's the pattern? Would, say, a
Condorcet method modeled around a single-elimination tournament be okay?
I have no idea.

-km