This was originally posted on Search Engine Roundtable and with authorship rights to Barry Schwartz.
Google’s John Mueller said on Twitter that Google ignores the rel=shortlink link attribute.
Th proposed usage of this is by adding rel=”shortlink” to a hyperlink, a page indicates that the hyperlink may be used for space constrained and/or manual entry (e.g. printed or spoken) applications and that the destination of that hyperlink carries the same meaning (even if formatting such as sort order and highlighting is lost). Typical use cases include pasting links into microblogging services such as Twitter and anywhere manual entry is required (e.g. printed or spoken URLs).
Either way, if you want Google to pass signals from your short URLs, make sure they 301 to the main URL.