Does Alexa Widget improve Alexa ranking?

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I am just trying this out as Alexa uses a weird method to calculate a homepage ranking by traffic and page views, but only a small portion of internet user uses Alexa toolbar (I think). Therefore, people are arguing that it is inaccurate, nevertheless, it is one of the method to compare the ranking of a website from another, something like Google Pagerank and Technorati Ranking by backlinks

I am too lazy to install Alexa Toolbar just to add up to my homepage ranking, so I am trying out the widget. Get your Alexa Ranking Widget, and for wordpress and blogspot user, you just have to copy the code and past them in the place you would like it to appear.