morenoingrato said:

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You probably could've linked the article that used this image, as you clearly (as the URL indicates) have it from 538: https://fivethirtyeight.com/features/what-we-know-about-tulsi-gabbards-base/
I have an addendum to the conclusion Geoffrey Skelley has: "On the other hand, garnering approval from conservative media isn’t likely to improve her poor favorability among Democrats or attract the support she needs to win the primary, no matter how loyal her base is."
I don't think winning the primary is her major concern (and I expect her to fold shortly before Iowa to endorse Bernie Sanders). But the debates give many candidates a national voice, which they can use to push their topic. And Gabbard has such a topic, so I think that is her major concern, to educate more people about the ongoing endless wars.
Oh, and yes, I don't think it is bad Gabbard speaks to conservative media. Bernie Sanders was criticized beforehand as he agreed to a town hall on Fox News, but the actual town hall was inspiring and showed even among the viewers of Fox News are many people wishing for a better solution, which Sanders might present. Antagonizing Trumps base will not bring them to vote differently, on the contrary, if you affront Trumps voter base it is more likely they will vote for him again next year. If you on the other hand present a better solution, that might drain support for Trump.
Also an interesting note: Clinton and some others float the idea Gabbard will run as a third-party-candidate and as a spoiler to the democratic candidate. But if her support among previous Trump-voters is so big, she might be more a spoiler to Trump would she run as Independent (which she denied).
As a side note, Kim Iversen has detailed her support for Tulsi Gabbard:
https://www.youtube.com/watch?v=K4yxzkiLefg
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