The stories are very similar in terms of the drawing of names.  In The Lottery they draw lots to see who will be punished where as The Hunger Games has the reaping.  The hopelessness of the sitution for the chosen person(s) and the reaction of the townspeople to the process is also similar.  There is a deep sense of depression in both stories.  The townspeople disagree with the process but they seem to be beaten down.  They feel there is nothing they can do but go along with the whole thing.  The short story The Ones Who Walked Away from Omelas also follows this theme.

Jackson's "The Lottery" is a great parallel text for The Hunger Games.  In "The Lottery," the townspeople really seem to embrace the tradition, even though they fear the black box and what it represents.  Even if you look at Tessie's protests in the end, she protests how the drawing took place, but she never actually criticizes the idea of the stoning.  She just wants a redrawing.  If she had her way, she would have probably happily stoned the other poor victim. 

Like post #5 suggests, the participants in the Hunger Games in the districts do so out of fear, but what about all of the people in the Capitol?  They, like the townspeople in "The Lottery," support the tradition of the Games and are so used to seeing it as entertainment that they don't even think about the inherent wrongness of it all.  Effie Trinket thinks eating with your fingers is "savage" but has no qualms about selecting two kids' names out of a lottery to die in publicized bloodsport.

Moral blindness is very evident in both texts. In Jackson's piece, the only reason the lottery continues is based upon tradition. (Even when one villager suggests they stop the lottery, others state that they can't...it is just what they do). As for the novel, the people of the districts do what they do out of fear. The Capitol controls everything. They know that if they fail to adhere to the rules of the Capitol they will suffer. Essentially, they are victims.

One difference exists between the two texts. In "The Lottery," the villagers choose as a whole to continue (seen by everyone stoning Tessie). In the novel, the people (other than the District One tributes) take part out of pure fear.

If you're talking about the mockingjay badge that Katniss wears, I think it could symbolize continued victimization. Nobody ever dared question the ongoing ritual of the Hunger Games, or even dared oppose them. Katniss started something when she volunteered to take her sister's place. When she left her home district to go to the capital, she was given the badge. After it was given to her, it seemed to become a catalyst for a seething rebelliousness amongst some of the districts, and Katniss became a symbol of future hope and freedom. She became the "girl on fire" that inspired an explosive chain of events.

You should read Catching Fire, the 2nd book in the trilogy. It's even better than Hunger Games.  

In both cases, there are these horrible things that are done largely because they are traditional.  The people who do the horrible things don't even think about what's going on.  They've become morally blind because they just trust tradition.