Analemma_'s comment made it sound like some broad and well-studied thing. All I've seen is mention of a single city. This is not remotely enough to support the claim.
My claim was based on skimming an article that said fares ranged from about 10 to 50% of funding and I speculated that most probably tended toward 10% since most are small, and small ones depend on federal funding, special purpose taxes (Georgia has a lot of SPLOST[0] projects), and partnerships.
Smaller systems suffer from low ridership and might see more benefit from dropping fares. A full bus and an empty bus cost about as much to run, but a system of full buses is easier to bolster and improve because more people will support it.
And I don't see why this would be connected to behavior on buses and trains. Where is this research? At least for Seattle since everyone wants to focus on it for some reason. News articles for a single city are not research.
I'm just stating that was the reason given by Metro and was the public perception at the time. I was among the public affected by it, and my anecdotal experience is that problems on the routes starting in Seattle and ending in the suburbs were fewer after the free fare zone was eliminated. It certainly doesn't consitute reasarch.
I seemed to remember reading something similar about Austin's buses when they went fare-free in the 80s. I found this linked in the Austin CapMetro wiki page: http://www.nctr.usf.edu/pdf/473-132.pdf
This reminds me of MetaFilter, where a one-time $5 payment is required to post. Just this small speedbump seems to do a pretty good job of keeping opportunistic trolls and vandals off the site. "Free" is too often an invitation to abuse.