What do you think is the reasoning behind Haymitch's unified front stategy for Peeta and Katniss? What are the effects of the strategy, and why does it work?

The most direct aim of Haymitch's strategy is to create a narrative in the Games that will attract sponsors and hence help Katniss and Peeta in the arena. Haymitch likely gets the idea when he realizes Peeta is in love with Katniss, and knows that their "love story" will make them popular. But the effects of the strategy are more wide-reaching. Katniss, so conflicted by her commitment to stoicism and her class resentments, might have had more trouble trusting Peeta if she hadn't had the excuse that it was all part of the show. By using this defense, she is able to delude herself that she isn't actually falling for Peeta, even though it's clear to the reader that she has feelings for him. Finally, the strategy has a touch of rebellion to it. The whole concept of the Hunger Games is to keep people separate from one another, to discourage rebellion. But this plan actually suggests community, and that manifests in Katniss's suicide ploy at the end of the Games. She uses the love narrative to protect herself once they return to the world, but the rebellious sense of community has already been suggested.