Google will quickly correct this error and you'll find the traffic on that page drops to nothing. You may also find other duplicate pages on your site penalized in the same way. You may also find your site penalized by Google for essentially screen scraping sites and copying their content verbatim and in it's entirety.
I'd recommend you set up a robots.txt to block Google from indexing identical pages on your site. Copying content verbatim and republishing in it's entirety is not a good SEO strategy unless you have thousands of throw-away domains and wear a black hat.
Sorry about the negative message, I'm sure this was very exciting for you guys but I don't think it's sustainable.
Perhaps an alternative is to have your users highlight the paragraph or snippet on each page they found interesting and archive that instead. Then publish those snippets on your site. Generally I've found republishing paragraph size chunks of text is OK with Google and will net you decent SEO traffic. It worked for my job search engine when we republished job descriptions and limited them to the first 400 chars. You can also mash the paragraphs up into pages with multiple chunks of text that e.g. show all chunks of text a particular user found interesting or a set of users or by date or location. That will give you the best of both worlds - lots of content to SEO and no dup content penalty.
Best of luck!!