Broad search simply for the definition
Here's another approach. To make sure my research isn't tainted by cherrypicking, I typed a neutral term into google: "Definition Beat Generation". Here are the defnitions that I found going through four google pages, only excluding repition and irrelevant sites. These are hardly formal sources, but the purpose of this exercise is to show that confusion about this term and how it is to be used is a genuine issue. Simply saying the one definition is the "majority" without putting effort into supporting the claim is not a valid way to prove a point.

Sources that place subculture/generation first and group of writers second:
http://www.macmillandictionary.com/dictionary/british/the-Beat-Generation

http://encarta.msn.com/dictionary_1861685998/Beat_Generation.html

Sources that place group of writers first, subculture/generation second, and also mention "artists":
http://www.thefreedictionary.com/Beat+Generation

http://www.directhit.com/ansres/Beat-Generation-Definition.html

Sources that only mention the group of writers, not the subculture/generation:
http://encyclopedia2.thefreedictionary.com/beat+generation

Sources that only mention the group of writers, not the subculture/generation, but also mention "artists":
http://www.answers.com/topic/beat-generation

Sources that only mention the subculture/generation, not the group of writers:
http://wordnetweb.princeton.edu/perl/webwn?s=beat%20generation

http://www.audioenglish.net/dictionary/beat_generation.htm

http://dictionary.cambridge.org/dictionary/british/the-beat-generation

http://www.bluesforpeace.com/beat.htm

http://www.mnemonicdictionary.com/word/beat

[If this method genuinely points to a "majority" opinion, then clearly this would be it]

Iffy:
http://www.gradesaver.com/dharma-bums/study-guide/section8/

http://www.oxfordadvancedlearnersdictionary.com/dictionary/beat-generation

Now for serious sources I encountered when typing the same term into Google Book search: 
Lawlor here identifies the exact problem I identified as being the major problem with this page. A page like this which strives for accuracy should acknowledge that there is no set definition (no "majority", no consus) on how the term should be used:

"Several key questions are central to the study of the Beat Generation. The first is whether a Beat Generation actually exists. If the Beat Generation consists of Kerouac, Ginsberg, Burroughs, and a few others, then the Beat Generation does not exist because a generation cannot be based on just a few people. On the other hand, if the Beat Generation includes dozens and dozens of artists, including not only writers but also dancers, painters, sculptors, musicians, then the Beat Generation does not exist because the concept is too loose, too vague."

William Lawlor. Beat culture: lifestyles, icons, and impact. ABC-CLIO, 2005 
ISBN 1851094008, 9781851094004. pg. 78.

For this one, there may be some confusion by what Kerouac means by “people who had been beaten down” since that could apply to either the small group or the broader subculture. However, Morgan provides the same definition I presented earlier in which Kerouac identifies it as “certain members of the generation that came of age after World War II who affected detachment,” etc. It’s conceivable that one might argue Kerouac meant his group of friends by “certain people, but from many other sources, he meant the broader subculture (open for debate, but let’s have that debate instead of blindly dismissing without evidence to support counterclaims). Here’s the quote from Morgan:

“Once the press began to identify those writers collectively as ‘the Beat Generation,’ some within the group began to struggle with a definition for the word beat. Since it was Jack Kerouac who had originally coined the phrase, he was asked repeatedly what he meant by it. Initially he said that the Beat Generation was composed of people who had been beaten down, worn out, and exhausted. As time passed, he refined his definition to emphasize the beatific, blessed, or sympathetic qualities of his generation.”

Bill Morgan, William Morgan. The Typewriter Is Holy: The Complete, Uncensored History of the Beat Generation. Simon and Schuster, 2010. ISBN 1416592423, 9781416592426. 

There's more, but I'm out of time.