The search engine will determine which results are most relevant (by using a complex algorithm based on how important it thinks the pages are). Everybody using this search engine will see the same results.
The things you want to see might not be the same as the things others want to see. However, you are more likely to want to see things that people "compatible with you" liked. If A likes B and B likes C, and B also likes D, then chances are that A will like D.
You could filter the results of your search (from the search engine) through a personal search filter. This would reorder your searches depending on
1) Things you have liked before
2) Things that people compatible with you have liked before.
When you visit a web page, you record whether you found it valuable. This updates your personal search filter and how compatible you are with other people. If you liked page A and B didn't like page A, you will not value the opinion that B liked page C. However if B liked A, you would be compatible with B and their opinion would affect your search filter.
This can be seen below:
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