Thanks for letting me know about the New Yorker article.  That does make a difference.

Just read this interesting article about Yelp on SearchEngineWatch.

http://searchenginewatch.com/article/2364585/Court-Rules-Yelp-May-Demand-Money-for-Adding-and-Removing-Reviews

I can't believe that this would be considered a permitted form of "hard bargaining".

But, hard bargaining or not this is something that a "good business" would not do.

This question was about one of my personal rants.  I couldn't help myself. 

Visitors often copy and paste my content and post it elsewhere...

Congratulations!   You must have great content!

... but they don't link to me.

Those weasels!

This happens with my content a lot.  It makes me mad.

How does Google treat this duplicated content?

They claim that they know where the content originated, but they are either overestimatin' their abilities or just lyin' about them.   Some people will argue in Google's favor but they don't know what they are talkin' about.  (If you are one of these people, I'll not argue with you, you can keep belivin' it.  I know I am right.)

What is the best way to handle it? File DCMA claims or ask them for a link?

These weasels probably don't have public whois and no contact info on their website.  If they do have contact info on their website it is probably phony.

If you can send them a message (and a human reads it) the message will probably be ignored, maybe even laughed at.  If you get a reply it will probably be the verbal equivalent of being flipped off.  Some people just don't understand copyright.  Some people understand copyright or are located where they can abuse the copyright of people in your country.  They have built a business out of stealing your content and mine.  They often have thousands of websites with your content and mine. They are making tons of munny.

If you file a DCMA, you better have absolute knowledge that the content truly belongs to you and that they are not displaying it under a valid "fair use", because they can sue you if you play this the wrong way.

The remaining people who steal your content, just don't know that they are stealing.  They think that anything on the web is fair game.  A lot of the stolen content is on legit websites.  They hired an SEO who hired someone else, in a country where copyright is not thought about, and they grabbed your content, slapped it on somebody's website and said that they wrote it just for the client.

Good luck.  Be careful.  Find a way to keep the blood pressure down.  Buy a punchin' bag.    My experience is, chasing weasels only gets you tired, most of them are only out after dark and you will never find them.

So, you can see that I think that this is harmful and it is really hard to do anything about it.

ADDED:  Got so busy in my rant I forgot to answer....

How does this affect ranking?

If you have a healthy, vigorous site, having a few pieces of stolen content on other websites will probably not hurt you if they are weak websites.  However, it can tank your rankings if the content is on strong websites - stronger than yours.  Also, it can kill your rankings if it is on lots of weak websites.

Examples:

I was selling some products that were made in China.  My content got grabbed by hundreds of Chinese websites publishing in English.  My rankings tanked.  Tanked.  The result was that I gave thousands of dollars worth of outdoor gear to Goodwill.

I had several articles about commodities (like what is traded on exchanges).  They ranked in the top three of google for searches on those commodities.  Tens of thousands (I am not joking) of spam commodities websites grabbed my articles or pieces of my articles and republished them.  My articles disappeared from google even though I had held those great rankings for a couple of years and they were on PR6 pages.  Fortunately, they have recently returned to good rankings and I am making money from them again but lost great revenue for a couple of years.

I agree.  If the author was a talented writer then you will lose the benefit of their authority if you change the attribution to "nobody".  If the writer continues to produce good work in the future then you will benefit from the growth of their authority over time.

Google says that someday they will start ranking the works of authoritative writers higher in search.

I have been writing as part of my profession for about 40 years.  The first works that I produced still have my name on them.  My past employers have not scrubbed my name from my work.

Today, with authorship in Google, your employees might get very angry they see you scrub authorship when someone leaves.  If they did good work for you they will want to carry that with them.  So, if you want to get the best possible work out of your authors they best not see you scrubbing credit for their work.

Keep in mind that a powerful author leaving your biz and going to your competitor will help your competitor as well.... but at the same time the work that they do for your competitor will also be helping you.  Nothing like having a competitor paying for some authority that flows through to your website.