Only a handful of Australia's top CEOs are on Twitter. They probably have more important things to do like, you know, manage thousands of people and make billions of dollars. 
But among those that are on the social media site, something weird is happening. They are attracting lots of dubious followers. 
Take ANZ boss Mike Smith. The head of what is now the smallest member of Australia's big four banks (it's still worth $78 billion) created quite a stir when he joined the service in   April. It's a good way to communicate with customers, and to articulate ANZ's admirable stance on various issues. 
#genderequality is more than just workplace diversity. It's about ensuring women have the same opportunities as men http://t.co/omkqdMXwOM
??? Mike Smith (@MikeSmith_ANZ)     July 29, 2015
Smith has only tweeted 21 times, but has swiftly amassed a 17,000-plus strong following. 
  Maybe there's heightened interest on Twitter at the moment about Australia's red hot housing market? (That's actually quite plausible). Perhaps people are getting excited about the latest Basel III capital requirement rules for banks? (I doubt it).
Whatever the case, it appears a lot of Smith's followers are, at the very least, questionable. 
According to TwitterAudit, a service that attempts to monitor this, just 37 per cent - or about 6000 - of Smith's Twitter followers are real. Another Twitter service, Status People, puts that number even lower, at 17 per cent.   
This is not to say Smith has been buying fake followers. And an ANZ spokesperson denies that flat out. "I can absolutely confirm that we have not been buying fake followers for Mike!" he tells Fairfax Media. "Numbers of followers is not a measure we target - and certainly there is no point to having fake or bot followers."
Almost all famous people on Twitter attract fake followers. (Last week it emerged that Hillary Clinton has more than 1 million of them, for example). 
Yet the percentage seems quite high. And Smith isn't the only one in this awkward position.
There's Telstra boss Andy Penn, who has been an enthusiastic user of Twitter since taking that job in   May (he even broadcast the company's annual results on Periscope, Twitter's video streaming app). TwitterAudit finds that again, just 37 per cent of Penn's followers are real. Status People puts the number of real followers at 17 per cent. (Curiously, these are the exact same percentages as for Smith).  
A Telstra spokesperson also denies there's any corporate shenanigans behind the telco CEO's massive social media follower numbers. "We haven't bought followers. There would be zero value for us buying followers for an executive account on Twitter."
By way of contrast, Richard Goyder, the head of Wesfarmers (the conglomerate that owns supermarket giant Coles), has around 2300 followers on Twitter, far fewer than his counterparts. But at least they're mostly real, 82 per cent of them, according to TwitterAudit. 
To put things in perspective, use the the undisputed king of CEO Twitter, Rupert Murdoch. The octogenarian media mogul just gets it. 
Just for the record, SkyNewsAust is totally independent of News Corp.
??? Rupert Murdoch (@rupertmurdoch)     August 29, 2015
And as a result, a clear majority of his 600,000-plus followers -  62 per cent - are legit, according to Twitter Audit. ( For what its worth, Twitter audit says 93 per cent of my relatively small following is real.)
So what is going on?
Twitter does not comment on third-party applications. But there might be an issue with TwitterAudit's methodology. It's understood that TwitterAudit counts any account with an "egg" profile picture (the default blank profile pic) or that has not tweeted before as "fake". Since it's well established that only 40 per cent of Twitter accounts actually tweet (lots of people use Twitter just to read stuff) this could be an issue.
Also, Penn and Smith are both members of Twitter's suggested user list of Australian business leaders (while Goyder isn't). One theory is that many new users who have signed up for the service but not yet added a profile picture or published their own tweets have followed both CEOs. So there's that.
Perhaps there really is nothing untoward about the large number of questionable accounts that following Australia's top CEOs.
But regardless, this little episode does seem to be yet another illustration of some of the issues plaguing Twitter. 
Twitter gets a lot of attention in the media. This week alone it has featured in strongly worded editorials and suffered criticism from politicians ("east coast Twitterati") for having too much influence on society. But it actually remains quite a niche service, and as a business, Twitter Inc. is really struggling.
The company is in the process of searching for a new CEO, and its stock price has been in the gutter because Wall Street thinks its user base is too small and not growing quickly enough. It only has about 316 million active users compared to Facebook's 1.5 billion.  
Lots of people try Twitter and then quit because it's too confusing. So ultimately, inactive followers and fake accounts remain a much bigger problem for Twitter than for Australia's CEOs.