[EM] Method Definition Considerations

[Kristofer Munsterhjelm]

On 05.06.2022 03:14, Forest Simmons wrote:

> That question will never arise in connection with IRV. 
> 
> Why not? 
> 
> Because (1) the standard definition of IRV is entirely operational:
> step1, step 2, etc. Furthermore (2) it is modeled on a well known
> run-off process.
> 
> My main point is that we need to keep this handicap in mind when
> broaching any method for public consumption.
> 
> People expect an election method to consist of elimination steps
> described in the language of vote transfers, in order to transparently
> preserve the "one person, one vote" dictum.
> 
> Most people would not say that an election method "has" a counting
> procedure ... rather they would consider the election method to "be"  a
> counting procedure.
> 
> To them, two different counting procedures are two different election
> methods, never mind the possibility that they could be equivalent
> methods derived from a common characterization.
> 
> We ignore these considerations at our own peril!

Getting myself back on topic (ahem):

I agree. There's a related problem, that the operational procedure might
seem completely alien. Consider, for instance, my fpA-sum fpC, which can
be described operationally as:

"A candidate beats another pairwise if more voters prefer the first
candidate to the second, than the second to the first.

For each candidate, count the number of other candidates he beats
pairwise. If there exists one candidate who beats every other candidate
pairwise, elect him.

Otherwise, let each candidate's score be the number of first preferences
he has obtained, minus the sum of the number of first preferences
obtained by candidates who beat him pairwise. Elect the candidate with
the highest score."

(For simplicity, I've omitted descriptions of how you determine what
candidates are beaten pairwise by what other candidates. I also use sum
fpC instead of max fpC simply because it's easier to explain.)

Now suppose this is operational enough. The procedure itself looks
arbitrary if you're focused only on the counting. Why is it A's first
preferences minus the sum of candidates pairwise beating A? Why not some
other preference? Why not A's first preferences plus the sum of counts
of everybody A beats?

The reason it's like that is, of course, that this particular choice
makes fpA - sum fpC pass DMTCBR. But you can't easily explain that in an
operational manner.

The mathematically derived methods are procedurally ugly but
mathematically neat. IRV (and Plurality, Approval, Range, etc.) has it
the other way around.

So, are there any advanced Condorcet methods with understandable
procedural rules? I would perhaps say Ranked Pairs and Benham. The
former has the logic of "consider the landslides before you consider the
close races", and the latter could be understood as a patch on IRV to
not fail Burlington scenarios.

In the graded domain, perhaps MJ? It's the tiebreakers that get you, though.

(If you're exceptionally good at popularizing science, *maybe* Schulze.
The beatpath heuristic is more mathematical, the Schwartz set more
procedural. But I doubt it.)

-km