The white slips of paper symbolize equality among the villagers; all are susceptible to the dire fate of the lottery winner. Even when Tessie protests her husband Bill's drawing of the marked slip, one of the villagers reminds her "All of us took the same chance." Just as the black box portends death, the slips found inside represent the inescapable quality of death; none may escape, regardless of status or virtue.
The three legged stool supports the ominous black box and easily represents the tradition of the lottery. The narrator observes that the "villagers kept their distance, leaving a space between themselves and the stool." While the villagers acknowledge the presence of the stool, none feel inclined to move closer; their fear distances them from the stool and the tradition of the lottery. Even so, the stool still remains as it supports the dreaded black box; in this way, the reader can understand the conflict of the villagers keeping a tradition that nobody supports or enjoys versus their collective fear of removing it all together.
The stones symbolize death, but also the villagers' unanimous support of the lottery tradition. Even as Tessie protests the drawing, the villagers collect their stones and move in to throw them. In many ways, throwing the stones equates to the villagers casting their ballot in favor of the continued use of the lottery. In the hands of both the old and the very young, the reader can determine that the lottery will continue to be an accepted tradition by future generations.
In "The Lottery" the black box itself is a symbol. When the unnamed narrator mentions the box. No one in the town remembers the original box, so the current box they are using, which is also old and warn, is a replacement box.
The original paraphernalia for the lottery had been lost long ago, and the black box now resting on the stool had been put into use even before Old Man Warner, the oldest man in town, was born. Mr. Summers spoke frequently to the villagers about making a new box, but no one liked to upset even as much tradition as was represented by the black box.
This old box represents the tradition of the lottery itself. No one really knows how the lottery began, but they keep following through with it, because it is what has always been done.
Also, the lottery itself is a symbol. It symbolizes the harsh traditions of our society, many of which we carry out daily without knowing why. People go through the rites the way most people wash their hands. They do not know why they do what they do, yet they continue with the ceremony that results in the death of a friend and neighbor.