Lingering Doubts

[Lord Edric Baratheon]

Lately I've been thinking about how many people seem to think the purple wedding plotting is quite ridiculous, having petyr and olenna scheming, and the necklace changing hands many times, only to have olenna deliver the poison herself (apparently). So clearly littlefinger is a creeper and he was totally in on this plot, as was olenna redwyne somehow. There is something going on with house tyrell definitely, maybe not as with house martell (dornish masterplan hype!), but they're players in the game that's for sure, either that or they're patsies for littlefinger. Anyway, it does seem that there is something missing in this plot, did littlefinger and olenna set out to kill a king on their own?? doesn't seem likely.

My lingering doubt is : Was Tywin in on this plan? I've always thought it very likely that he is.