Skis are basically unstable.  There is no righting moment on a ski shape once it starts to heel, so it will capsize without a live paddler once it tips fractionally to one side or the other.  A bit like a bicycle really.  That is why tippiness has to be a subjective measurement and depends a lot on the shape of he paddler.

An interesting study in physics , hopefully it wouldn't be construed as a solid basis for chosing a ski. Way to many variables in body shape and CG.If there is a new ski paddler looking for a ski this might serve as a distraction from their need to actually paddle those skis they are interested in. If you were to buy the ski soley based on the results of the hypothetical tippometer you would probably get some very real lessons in applied physics.  Sandy

Can someone explain the concepts of 'primary' and 'secondary' stability? How does this translate into what the paddler experiences on the water? Is it better to have more primary or more secondary stability, or is that paddler dependant? Does anyone have examples of which boats display more/less characteristics of each?

A boat that has a perfectly circular cross-section can have good primary stability, but poor secondary stability.  This is because the centre of bouyancy doesn't move when the boat rolls.  An example might be a sprint kayak (near circular cross-sections), or a rowing shell.

A cross-section that is more oval or tending towards rectangular can have the same primary stability as above, but much better secondary stability because the centre of bouyancy will shift as the boat rolls.  Most surf-ski's have a flat spot on the hull that creates more secondary stability.  So this is something visual to look out for when comparing boats.  Having said that, its virtually impossible to assess a boats stability by just looking at it.  There are one or two other variables that come into the stability physics that require accurate measurement.  So you should always paddle the boat, before passing judgement.

On a slight different note, if a circular cross-section is unstable why use it?  Well, it minimises the wetted surface area which means more speed.  This is not always the case, but as a general rule of thumb holds true.  Stability versus Speed is basically the bottom line.  Of course, everyone wants the fastest boat with stability.  This is not impossible, but not easy either.  Also, the human element makes it a classic design problem where there is more than one possible outcome, depending upon the strengths and weakenesses of the paddler.  Yes, it can get a bit technical, but fascinating also.  The current generation in surf-skis are seriously pushing the envelope in this department.