Let's say I make a website on carrot.com and use that domain as my primary domain. Then let's say I also buy carrot.co.uk and 301 redirect it to carrot.com. Now what will happen if some people links to carrot.co.uk? Will that link popularity just be wasted?
If you use permanent redirection (301) from carrot.co.uk to carrot.com, all the link pointed to carrot.co.uk will actually will be treated by SE's as pointed to carrot.com.