Google page rank and Alexa rank are couple of those factors which decide the popularity of blogs on Paper. Alexa seems to be undergoing lots of changes (Improvements) and recently Alexa got new design and because of this people who were using old Alexa widget are not working perfectly.
Alexa service offers a widget for Bloggers which they can embed on their blog. Personally, I have seen lots improvement in my Alexa ranking after putting Alexa widget on my blog. This actually helps Alexa to keep exact count of visitors on your blog. If you have not added Alexa widget, I would suggest you to add it on your blog.
Getting back to the topic, Alexa added a new way to add widget on your blog. Alexa added a new section for Site owners which can be used to verify the ownership and add and edit details about your site. This is very useful, if you have a good alexa ranking site, you can add detailed detail about your site and make your site Alexa profile look more professional.
You can grab ad codes for Alexa widget on your blog by going to this link. Click on Alexa site widgets, add your site link and grab the code to be embedded on your blog. You have different widget options and sizes for widget.
When you update the info, you need to provide email address which include your domain address. If you have not created your domain Email address, read: How to create domain email address.
That;s it, not watch your Alexa ranking improving every day.