The key point is this. You are all looking at this as an AI problem. This is not an AI problem. Identification of general sarcasm from a single tweet is impossible, but what the Secret Service would genuinely want is classification of threats from an user's tweet record and the people he associates with. Some general thoughts that would go towards a solution:
Keyword analysis of the person's tweet record would get you a lot of the way. You can infer the person's political alignment, degree of preparation for a threat, physical location and so on. If someone makes a bomb threat against a politician he is opposed to, and talks about fertiliser suppliers, and is living where the guy is due to speak, then that makes you more worried than someone whose next tweets are about the next episode of My Little Pony.
Don't detect sarcasm, detect reactions to sarcasm. If it's a joke, the person's twitter followers would likely react to it as a joke. 'Haha', retweets, and so on. Serious threats are not likely retweeted widely, and if they are replied to with statements/users that are also redflagged as per #1, you'd really get worried.
Use the broader tweet record. Tweets that have been said by millions of people should be given a reduced threat. Only way to be realistic in terms of investigative effort.
There aren't actually that many effective ways to murder a politician. That means looking for 'realistic' threats is fairly trivial through application of a whitelist.
Don't give a yes/no answer. I think an actual useful tool for an analyst would be something that doesn't say 'this is sarcastic', but gives an useful user interface that gives relevant past and previous tweet excerpts, and a button to pass this on for deeper analysis. A time saving tool.
Comparatively little attention is paid, however, to the deflation of the great depression in the early 30's...
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