The IDF, for one, utilized a series of deception maneuvers to conceal the operation's genesis from Hezbollah. The IDF, as well as other Israeli governmental organs, is also on Twitter and Youtube. It's not clear at the moment whether this will be of any utility to them in terms of persuasion, but it does allow them to reach a wider audience and potential rapid-response to negative news.
The IDF's influence is also directed almost wholly at a external audience. Although one could say that the operation itself is a form of influence designed to undermine Hamas and convince the population to punish it, this has historically been a poor means of influencing people. If you drop a bomb on someone they tend to support your adversary even more. The IDF did text-message Gazans to leave, but hasn't really gone far in trying to persuade them that it is not targeting them or that Hamas does not serve their interests.Hamas itself is grandstanding to both the Palestinian population and the Arab world and setting itself up as a champion of the Arab people under attack. It has largely succeeded in influencing news coverage, as a stream of images of of civilians crawling from rubble is all one sees of the conflict on network news. That being said, it's unclear how useful external sympathy will be to them, as while outside actors have issued perfunctory protests, there is almost an air of indifference to the present conflict. The support that really matters for Hezbollah is the interplay between Palestinian loyalties, strategic choices, and aims, as well as that of the Arab world in itself.
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