Speculation as to who could inherit and/or assume the position Madonna had as the definitive global superstar has been a process as long as Madge's career. It takes more than singing to be on terms pop culture critics have deemed "legendary" or "iconic". It takes someone who tried their hands at acting, fashion design/branding, etc. at some point in their career.
As to who could be the next Madonna, let's look at assumed contemporary acts who have been speculated by others but stand no chance.
The next Madonna will not be Miley Cyrus. Don't let the live mashup of "Don't Tell Me" and "We Can't Stop" on MTV fool you. Don't believe she's the next Madonna just because she's using the shock value part of sexuality just like Madge (But instead of either Erotica or Hard Candy, Cyrus created her own level of repelling sexual shock value called Bangerz.) "But neither of them are regarded as good singers!" That's like saying McDonald's isn't what a diet should be based on. Even with less than stellar reviews of her live singing, Madge has been able to sing [her best singing having been "Like a Prayer"].
Cyrus on the other hand...no. Just no. Recent "album success" be damned, we can eliminate Cyrus for her terrible singing and for the fact that she recently started experimenting with her image. Madge was doing that in-between songs since her debut album.
Musically in album releases, discounting all Hannah Montana affiliated and the EP The Time of Our Lives she is technically on her 3rd proper [non-EP length] album. Not enough of an extensive portfolio to really give credit to any Madge sequel labeling.
Also eliminated early on, Katy Perry. Like her other predecessor, she suffers mainly by not being able to sing even on a decent level. What has her a notch above Cyrus (But not by much) are fluke singles that can actually provide some level of audible enjoyment ["Hot 'N Cold" and "Firework"]. Whenever experimenting with image, Perry found and stuck with "Candy Coated Pop-tart" for Teenage Dream; then she tried being a "Candy Coated...'edgy for her' pop-tart" on her recent album Prism.
Image wise alone, Perry cannot be the next Madonna. As opposed to switching up her look from "Candy Coated" to say "40s Noir Glamour", Perry's image is nowhere near flexible as Madonna's. Madge went from "virgin" to "sexual" to "brunette" to "erotic" to "geisha" and Jesus knows what else.
Musically, Perry just added a 3rd album to her name. As with Cyrus, Perry's discography remains sorely underdeveloped to really gauge if she could even be considered as the next Madonna [cover of V Magazine with Madge be damned.]
Interestingly, Britney Spears is not the next Madonna either; even with the fact all 8 of her albums have peaked in the Top 5 of the Billboard 200 [6 of them going to #1]. Spears has gotten plenty of next Madge level criticism for perceived lack of singing ability. Acting isn't a strong suit of any of the names mentioned or yet to be mentioned, especially with Britney ("But Britney knew to quit acting. She can't possibly be the next Madonna!" All T, All Shade...I agree.)
Yet there is something Spears has done that disqualifies her from assuming Madge's former position as Global Superstar of the World...accepting a residency/doing the Vegas thing as Celine Dion, Cher, Toni Braxton and so many other performers have done. Performing in Las Vegas while a guaranteed paying gig...let's face it...is saying "Let me warm up for about 3-5 'Farewell Tours' around the world."
Madonna won't retire willingly or accept any Vegas residency not so long as delusion sets its course...err she draws breath and does her best to put forth new material.
With them out of the way, here are the three names to consider when speculating who the next Madonna could be: Lady Gaga, Rihanna and Beyoncé. When talking about contemporary acts whose divisive perceived singing abilities, horrible acting and fashion ventures for better or worse rivals that of "her Madgesty", these three have the field beat. However, there are certain areas where one has the others beat in terms of discography, filmography and overall selling points.
Yet the strengths in certain areas are clear enough to differentiate 3rd, 2nd and 1st...
3rd place is Rihanna. She has enough of the discography in terms of quantity that can be measured in this; and of the three candidates, has the most albums to her name. All 7 of Rihanna's albums have ended up in the Top 10 of the Billboard 200:
- Unapologetic at #1
- Good Girl Gone Bad at #2
- Loud at #3
- Talk That Talk at #3
- Rated R at #4
- A Girl Like Me at #5
- Music of the Sun at #10
Considering this is up against Madge's discography, with Like a Virgin, True Blue, Like a Prayer, Music, American Life [amazingly], Confessions on a Dance Floor, Hard Candy and MDNA having gone #1 and Rihanna's first #1 having taken 7 albums to do...she doesn't have the commercial pull even Madonna has. Image wise, while versatile, just revolves around sex; even with the different hairstyles and level of clothing being questionable, it is not enough.
Madge has experimented with being deep on an album twice. The first time was the Grammy winning Ray of Light which came with the image of "attempted spiritual depth/bohemian one with the Earth". Even in the 80s Madge experimented with androgyny in the video for "Express Yourself". Rihanna has yet to do anything that qualifies as daring in that regard.
Her acting was met with negative reviews just like Madonna. However, "Riri" was really in the 2012 movie Battleship and that movie was derided by anybody that even heard of the movie. Filmography isn't there yet.
With Gaga and Beyoncé left, it's difficult on the surface to tell who the next Madge is. With ARTPOP, Gaga just added a 3rd album to her name. In terms of quantitative discography, Gaga isn't quite there yet, but she's been around since 2008-2009. Beyoncé hasn't switched up her image that much if at all [save for a pixie haircut that mysteriously got the hair length that appeared in "XO"] and has really gone from blonde to brunette in around 2006, back to being blonde. That being said, there is a slight favor for one more so than the other and it isn't who people think...
2nd place is Lady Gaga. "WHAT?!" I know, but I will explain that later. Let's get this out of the way now. There are a LOT of similarities between Mother Monster and "Her Madgesty":
BOTH have worn some crazy outfits in the name of artistic expression, sexual liberation/"Girl Power" trope, shock value and fashion [most often all at once] Madonna's most daring outfit? The "Cone Bra". Gaga's most daring outfit? The Meat Dress (There was a lot to consider when picking the most batshit outfit from either one).
BOTH have been read for filth in terms of acting and have Razzie Award nominations to their names. (But Gaga only having one nomination for Machete Kills and Madge...still trying to act.)
The key in Gaga getting second place in this is the fact that she has really done one major movie role and it wasn't a female lead. That and it is way too obvious to declare Gaga the next Madonna ("Because Gaga can sing. You can say it." That's actually the next point.) if we are looking at singing.
To be the next Madonna, the artist in question has to be divisive as all hell when it comes to perceived singing ability. Gaga's flack is poured upon through antics and fashion choices; not singing and that is the difference. Any of the previous candidates can be lambasted for their antics but Gaga's singing ability isn't as divisive as the number one candidate and woman I'm declaring the next Madonna...
1st place and the Next Madonna...Beyoncé. Yes, she doesn't switch up her image every other day. However, there are these things that are eerily similar to the career of Madonna...
BOTH owe a muffin basket the size of Earth to the trope of "Girl Power". Beyoncé's "Girl Power" was est. with the Destiny's Child song "Independent Women" and was mainstreamed with the Beyoncé snippet turned song "***Flawless" when a key portion of a TEDTalk with Chimamanda Ngozi Adichie was discovered to have been inserted into the song.
Madge has used the "sexual liberation" version of "Girl Power" since Like a Virgin onward.
BOTH had their first single be a bust and not chart on the Hot 100. Beyoncé's first solo single, "Work it Out" from the Austin Powers: Goldmember failed to chart on the Hot 100 [around the time Kelly Rowland found #1 success with "Dilemma" ft. Nelly].
Madge's first single "Everybody" failed to chart on the Hot 100 [but began the backup plan of the century; finding success on the Dance charts].
BOTH aren't regarded as actress dujours, but have been in a critically favored movie where the cast ended up elevating their acting profile. Beyoncé has the movie adaptation of the Broadway musical Dreamgirls as a plus in her acting anthology...even if Jennifer Hudson went on to win the Oscar.
Madge has A League of Their Own as possibly the only plus in her acting career without singing (Or playing Eva Peron)...even if she was easily outshined by co-stars Tom Hanks and Geena Davis.
Finally, BOTH have the most polarizing perceived singing ability of any current female music act. Beyoncé and Madonna even have been blasted for relying on choreography and image to make up for their "questionable" singing ability.
The key difference is Beyoncé's live shows. Just like "Her Madgesty", there is a ton of visual spectacle at a Beyoncé concert [especially with husband Jay-Z currently with the On the Run tour]. However, live singing of Mrs. Knowles-Carter has been met with better fanfare than Madonna.
Oh and for posterity, both have had a string of 5 number 1 albums in the 2000s...
- Dangerously in Love #1 [2003; debut]
- B'Day #1 
- I Am...Sasha Fierce #1 
- 4 #1 
- Beyoncé #1 
- Music #1 [2000; 8th album]
- American Life #1 [2003; same year as Beyoncé's debut]
- Confessions on a Dance Floor #1 
- Hard Candy #1 
- MDNA #1 
With everything accounted for...
Beyoncé is The Next Madonna.