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"Okay, but then you're imposing an additional constraint over and above the control scheme -- in this case, the mechanic of moving a playable character over 3 positions."

I used 3 positions as an example from the aforementioned games, in contrast to how the other scheme in question does not move the character in such a way. I wasn't implying you must use 3 positions... although in my experience 2 characters/3 positions is challenging to  work with on its own!  

"But there shouldn't be any reason the up/down control couldn't move each character over, say, 4 positions, or 5, or 2. "

Agreed.

"In addition, as you pointed out, just because Lion and Mario Bros. happen to control "characters", doesn't mean the playable object under control by the control scheme couldn't be something else entirely different, like in your examples, a vehicle or a door. "

Agreed, as long as those two "characters" are independently moving on screen.

"Which also means, even the implementation of the up/down control as moving something "up" or "down" is only one possible mechanic. It could just as easily be used to accelerate and brake, open or close, jump or crouch. "

As long as we don't  discard the two independent "characters" I am in agreement, and I'll explain further why below.

"So, by logical extension, having two characters, one for each up/down controller, is just one possible implementation of the control  scheme, but not the only one.  As I pointed out, Egg and Manhole (just to name two) use the same control scheme to control only one playable character on the screen." 

So here's my explanation: 

I don't think one can separate the scheme from the gameplay when talking about design... meaning the 2 independent rocker D-pads (UP/DOWN) were always linked to two independent characters in the G&W games., while the 4-POSITION buttons were linked to one character.  In conceiving of the jam, I wanted to try working under one specific constraints to see what we might create. So I listed the two control schemes we are discussing (among others) as separate and said we would choose one to work with, along with examples to see beforehand. Technically, in terms of hardware, you are right... these are four inputs. But In designing the jam, I connected the scheme with the gameplay, and in this case, two independent "characters" are always used. 

"Of course, as the host, it's your prerogative to add limitations to the game design on top of the control scheme,"

So I'm not adding limitations here, I'm adhering to what was described previously in the jam description. These two schemes relate to different approaches to gameplay design in the two independently moving characters on screen. 

"but I think allowing participants to work within the constraint of the chosen control scheme (and the other limitations of the Game & Watch technology), without imposing limitations on the game design, is likely to produce far more interesting and innovative games." 

I think I'm being unfairly judged here! Please take my words to heart.

There is always a balance between limitations and freedom in creativity and there are alot of possibilities to mine in just one of the schemes as I described them in the original jam description.  It's really a challenge, though, because we are used to being given more possibilities than we will ever use. In this jam, I wanted to push us the other direction. 

"In fact, I would argue, it was this approach to game design by Gunpei and his team that was able to produce such a wide variety of games in the Game & Watch series, rather than just variations on a theme, even though many of the games share the same control scheme." 

There was a wide variety in the G&W series, and I think it's up for discussion which of these were really great or not... is this based on sales? How fun is Ball today? Was trying to replicate console games a good idea, as in the Legend of Zelda? Which are your favourite games, and why? But I'll leave that for a different thread.