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In both stories they had volunteered someone in tribute. In the Hunger Games Katniss volunteered for her sister. In the Lottery Tessie asked for her kids to participate in the drawing when their family got picked so it would be a lesser chance of her being called.

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Everyone including the children were to participate in the drawing for both stories.

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In both stories the people were very nervous to be drawn and when they got drawn they put up a fight.

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Each story had very similar rituals, they both gathered the townspeople and drew someone's name.