One of the issues that I see in search results is the way they are ordered sequentially on search engine webpages : would it be based on true relevance, or on bribery, results are shown as an ordered list. Incidentally, some results are harder to access than others, because they are buried in deep pages, or very low on an infinite scroll, which raises the incentive for bribery.
I remember the age of non numeric libraries. When I was a kid, if we wanted to find a book at the library, we had to browse an index of authors names in a wooden box, small sheets of cardboard in alphabetical order. You could see the whole box in front of you : each sheet had an equal chance to be found, the same ease of access.
This is also true for entries in a paper dictionnary, chapters in a book, phone numbers in a directory.
One of the the differences between a real world paper library and a network such as internet , or potentially Safenet, is that the first is finite, while the other is not.
An interface design difficulty arises, because you can’t possibly show the whole “wood box”, or the whole entries, so you need to present a selection, which , ultimately, led to bribery based systems.
One solution would be categorizing:
In the paper library there were several wood boxes, one for novels, one for science, one for poetry, etc …
This permitted simplifying the search by raising relevancy without cutting equality of access.
An ideal search engine could be organised the same way : you would for instance browse for : litterature → novels → 19th century → german … or sports → biking → gear → online shop → uk → accepts safecoins …
I think we should dig that way for a search system that offers both high relevancy and equality of access.
Maybe take inspiration from gopher’s arborecence ( not defunct yet 
)
One of the challenges will be finding an UI design that prevents any incentive for bribing.
Categories and non linear display can be paths of research.
On another aspect, I think it would be fundamental to have some sort of proof of search algorythm integrity :
When you browse results , a checksum or similar non trickable flag should tell the user that the results displayed were processed by code that is known and verifiable. A bit like self authentication : in Safe if you can read the contents in clear, it mathematically means you are the one with the correct credentials.
A decent Safe search engine app should provide such a level of certainty : if you can read the results, then you mathematically know how they were processed.
Just my thoughts, design ideas. I am not in position for coding such a complex system, but would love to see it happen.
Maybe @Shane ? do you copy ?