There is so much more to impact than sales statistics, accreditation and chart positions. I see all these figures flying around in multiple threads everyday by depressive stans trying to prove something, and it honestly becomes so overwhelming. It doesn't necessarily mean that one artist is better, or has had a greater influence than another. It is all about how the public feel towards that person and how they react to not only their music, but their performances, interviews and their life at the forefront of popular culture. It's all about connection. Who does the public relate to the most? That's what can determine impact.
The public doesn't need to relate to someone for that person to have impact.
Rihanna musically. Rihanna is the artist you will HEAR - her songs are played all over the world, you can't escape them!
Lady Gaga has had a bigger cultural impact. She is the artist who has had a bigger impact in fashion too.
Trust me - I have spent the last two years travelling the world so I would know!
Katy Perry has made no impact whatsoever so she is last.
This too. Cultural impact is more significant imo though, and I think that Katy has made an impact, just a small one compared to Rihanna and Lady Gaga.
If you are talking about overall impact,Lady Gaga takes the cake (cake cake no pun). But musically or radio-wise at least, she is facing a tough competition with Rihanna. Here in the Philippines, local radios overplay the **** out of Rihanna's songs. But then again, Rihanna has yet to come here whereas Katy and Gaga already did, with KP twice.
Gaga has clearly had a bigger impact on the world.
Rihanna is known for her music, and there isn't really much else you can say about her other than she's a musician. But Gaga could be considered a Musician, artist, fashion icon, LGBT Spokesperson, etc. Rihanna has made some big accomplishments in the music industry, no denying that, but Gaga has had major accomplishments in AND out of music. Especially with the whole "Born This Way Foundation" thing.
As for Katy, I don't understand why she's even an option.
Rihanna can't be compared to her. And I don't Katy Perry has any impact, sorry. 
