I have before now written round how I consider that outbound links on a page can boost its power on the search engines. I observed the effects that outbound links had on a low ranking web site in contrast to another that I run, without the outbound links, but with enormous amounts of SEO work and a respectable page rank, not merely on the home page but additionally on the inner pages.
So, what grounds may there be for the search engines to boost your position just because you point to another page, probably on your own website, with the search terms in the anchor text?
It appears extreme, but it is a inference that I have come back to several times looking at a number of sites covering different niches in excess of a couple of years. It does seem to work.
Looking at search engines, they live by providing their visitors quality results. You find the results you would like on a search engine and so use it repeatedly. They have to provide quality answer.
Say then, you are searching for "Acme Widgets". You want to understand how to make one and search "how to make an Acme widget". What results might the search engines show you?
What the search engine does not know is what level you are concerned in the information at. Are you wishing to make one for yourself, or do you want to determine how they are made because you are interested in the method. The results have to cover this answer for all people.
It is the same with numerous searches. If you search for 'search engine optimise a site', do you want a step by step set of results, or someone that could tell you what is desirable and do it for you?
In both of these cases, if you are sent to a page that gives you the high level evaluation, probably a video of the manufacture or an SEO experts page, then the basic level query is answered. If that website then links to the full details, say the step by step advice, then you could dig deeper to find a fuller answer.
It has been accepted previously that search engines like to send traffic to a page with the high level answer from where they can then dig deeper to a more complete answer. So, why do the search engines recognize that your page could provide the additional particulars?
Well, the page itself must have an evaluation of the search terms and there must be a link to extra information. If this link carries the search terms on a page about those search terms, then it is potential that the target page provides further details about the subject.
And that is what makes me think that an outbound link on a site page might hold some weight at least with the search engines. Probably not a lot, but enough to tip the balance. Whether the link need to be on another site or whether it could safely be the same web site, I am still working out!