Hi Deb,
For anyone interested here is the thread I started on participating triplicity rulers some time back.
http://skyscript.co.uk/forums/viewtopic.php?t=2395
From my reading of her reply Lee Lehman was not suggesting a one size fits all approach to triplicity rulers. In particular she suggested that she had found using a simple day/night ruler for horary and electional work more effective in practical terms. However, she seemed open to using participating rulers in natal work. Her argument being that horary fitted better to a simple set of outcomes while natal charts allowed far more scope for free will and potentiality where participating rulers could be expressed.
To follow a two ruler approach to triplicity in natal work, like the early modern English astrologers, would effectively rule out the whole tradition of Dorothean triplicity rulerships dating from the earliest hellenistic astrology and carried on through the Persian, Jewish, Arab and Latin medieval astrologers like Bonatti. Rather than being an obscure peripheral technique many Arab and medieval astrologers used triplicity rulers as a key technique for identifying the destiny of an individual throughout life. A representative example of this approach being Abu 'Ali Al-Khayat's - 'The Judgement of Nativities'.
As Tom suggests there would be other issues such as the status of planets when considering the almutens, transits or the peregrine nature of planets. For example, Ibn Ezra provides delineation of the houses based on the different triplicity rulers.
I cannot do better than quote a comment from Astrojin in the previous thread:
In Bonatti's (see Liber Astronomiae) and Ibnn Ezra's (see The Book of Wisdom) both use Dorotehan trip rulers. This is because, in their scheme of interpreting houses, each trip ruler of each house gives different meaning or governership of the house e.g. 7th house may govern your spouse, associates and conflicts but using the trip rulers; the in-sect trip ruler of the 7th may govern your spouse, the out-of-sect trip ruler of the 7th governs your conflicts and the participating trip ruler of the 7th governs your associates. This cannot be done if we drop the participating rulership of trip rulers. Some astrologers may argue that we don't have to stick with Dorothean's as long as we have all three trip rulers for each element (which still means we cannot discard the participating trip rulers).
So I cannot completely agree with you when you state:
...there is little evidence of the participating ruler actually being used - except for the kind of 'Dorothean' technique that breaks periods into three and uses one ruler for each period.
First of all that is quite an enormous exception. Certainly in natal work the evidence seems quite strong they were using participating rulers. Of course traditional astrology texts can be frustrating in the lack of worked examples they provide. Are you thinking about this lack of participating rulers in terms of horary particularly or are you making a generalised point here?
One piece of research that seems worth exploring is looking for references to planets being peregrine when they one would not expect this using participating rulers. Thus despite their otherwise debilitated essential dignity Saturn in Aries , Mars in Taurus, Jupiter in Gemini and Moon in Scorpio would never be peregrine under the Dorothean triplicity system.
In the case of Ptolemy's system , I accept the ambiguity of the application of the third participating ruler makes Lilly's two triplicity ruler aproach a pragmatic interpretation. Still , what we call often call 'Ptolemy's' table of essential dignities is surely 'Lilly's' table in terms of only representing two triplicity rulers?
Finally, you state:
When it comes to triplicities, there only is the 3-ruler scheme, the differences are mainly about minor discrepancies within this scheme, and the emphasis we place upon it.
True but in practical terms this does lead to a myriad of ways to work with them. For example:
Three Triplicity Rulers operating
( Day ruler indicated first, night ruler second and participating ruler in brackets)
a) Dorotheus of Sidon's system of Triplicity rulers:
Fire: Sun/Jupiter/ (Saturn)
Earth: Venus/Moon/ (Mars)
Air: Saturn/ Mercury/ (Jupiter)
Water: Venus/Mars/ (Moon)
b) Ptolemy's system of Triplicity rulers:
Fire: Sun/ Jupiter/ (Mars)
Earth: Venus/ Moon/ (Saturn)
Air: Saturn/ Mercury/ (Jupiter)
Water: Venus/Moon/ (Mars)
c) Morin's suggested Triplicity system
Fire: Sun /Mars (Jupiter)
Earth: Mercury/ Saturn (Venus)
Air: Saturn /Venus (Mercury)
Water: Jupiter/ Moon (Mars)
Two ruler approaches ( Participating ruler omitted)
a) Lilly's system of Triplicity Rulers:
Fire: Sun /Jupiter
Earth: Venus/Moon
Air : Saturn/Mercury
Water: Mars /Mars
b) Lee Lehman's simplified version of Dorothean Triplicities
Fire: Sun/Jupiter
Earth: Venus/Moon
Air: Saturn/Mercury
Water: Venus/Mars
That is not counting the other variations other traditional astrologers may have cooked up. You will find a few creative suggestions on the link to the previous thread!
For now, I find Lee Lehman's suggestion very helpful. Thus I use only the night/day Dorothean rulers for horary but bring in participating rulers for natal charts.
In horary terms I suppose the differences are not that dramatic between the Ptolemy/Lilly approach and the Dorothean triplicity system being restricted to the day ruler of the water triplicity being Mars or Venus.
As so often Morin is 'out there' with a very idiosyncratic approach. I do not think his triplicity system has ever been popular with other astrologers.