"The Lottery" and "The Possibility of Evil" are alike in that they show the evil that lurks behind the placid, seemingly kind-hearted, and ordinary life of a small town.

They are different in that in "The Lottery," the evil is institutionalized in a twisted superstition the whole village participates in, whereas in "The Possibility of Evil," the evils lurks in the heart of one individual.

In "The Lottery," an annual lottery chooses one villager to be stoned to death under the belief it will ensure a good harvest. The seemingly gentle villagers in their house dresses, aprons, and work clothes chat kindly to each other about mundane things and even act supportive of each other, only to turn into barbaric murderers once a victim is selected. A tradition they know is wrong but can't seem to shed literally destroys lives in the village.

In "The Possibility of Evil," Miss Strangeworth seems like a kindhearted, ordinary person, but underneath that facade lurks a twisted individual who sends poison pen letters meant to destroy her neighbor's lives. Evil lives in her town just as it does in the village in "The Lottery," but in this case, it is localized in one person.

Both of Shirley Jackson's stories, "The Lottery" and "The Possibility of Evil" are about the drawbacks and disadvantages of small-town life. People in small towns are friendly. They all know each other. But this can be a disadvantage. They all have a peculiar small-town mentality. They know who goes to church and who doesn't, and they know which churches people go to. They are all very much class-conscious. They can all turn against one of their fellow citizens for a variety of reasons. If, for example, a man is a heavy drinker, or gets arrested, or beats his wife, everybody in town will know about it. Some people can't stand small-town life with its gossip, its prying, its pettiness, its peer pressure, and its self-appointed aristocrats and tyrants like Miss Strangeworth in "The Possibility of Evil." It is not pleasant for most of us to have everybody knowing everything about our personal affairs. But that is inescapable in really small towns, such as Shirley Jackson depicts in both "The Lottery" and "The Possibility of Evil." In "The Lottery," the total population is right around three hundred. We get the impression that the town in "The Possibility of Evil" is just about the same. She is really putting small towns under her microscope.

Shirley Jackson lived in San Francisco, a big, cosmopolitan, notoriously tolerant city. This is a clue that she preferred the anonymity of a big city to the enforced intimacy of a small town. Her two stories can be read as a critique of small-town people and small-town life. People in small towns all over America are becoming more sophisticated, and perhaps more liberal and more tolerant, in recent times because of the influence of television, movies, and computers, among other factors. There is probably no longer such a feeling of coziness and claustrophobia that made so many young Americans want to get way out of their hometowns as soon as they were old enough to escape to one of the major cities.

The anxieties of all of us, our worries, vexations, bothers, troubles, fears, exertions, and so on, are really concerned with someone else’s opinion....For the most part, our envy and hatred also spring from the same root.

Now it is obvious that our happiness, resting as it does mainly on peace of mind and contentment, could scarcely be better promoted than by limiting and moderating these motives to reasonable proportions that would possibly be a fiftieth of what they are at present, and thus by extracting from our flesh this thorn that is always causing us pain. Yet this is very difficult, for we are concerned with a natural and innate perversity. Tacitus says: “The thirst for fame is the last thing of all to be laid aside by wise men.” The only way to be rid of this universal folly is clearly to recognize it as such and for this purpose to realize how utterly false, perverse, erroneous, and absurd most of the opinions usually are in men’s minds, which are, therefore, in themselves not worth considering.

-Arthur Schopenhauer

Identify significant differences between "The Lottery" and "The Possibility of Evil." 

In both stories, someone is attempting to hold on to a past that feel somehow better, perhaps more innocent or more traditional; however, in "The Possibility of Evil," it is Miss Strangeworth, and in "The Lottery," it is the town itself. At seventy-one years of age, Miss Strangeworth seems like a bit of a remnant, insisting that the grocer remember when she buys tea, tending to the roses that her grandmother planted generations ago, and living as though "the town belonged to her" because of how long her family has lived there:

The town where she lived had to be kept clean and sweet, but people everyone were lustful and evil and degraded, and needed to be watched; the world was so large, and there was only one Strangeworth left in it.

To say that the town must be "kept" clean and sweet implies that it used to be those things and that Miss Strangeworth feels some responsibility to maintain it in the face of what she sees as impending change. She believes, in fact, that it is actually her job to do so, because she is the last of her family line. Nevermind that she lies and causes pain to others, she feels that the ends justify the means: maintaining tradition and innocence.

In "The Lottery," on the other hand, the town itself—rather than one individual—has taken a similar position. Despite there being talk in other towns about doing away with the lottery "no one [in this town] liked to upset even as much tradition as was represented by the black box," which they use to conduct the drawing. Mr. Summers, who runs the lottery, always talks about building a new box since the current one grows "shabbier each year" and is "splintered badly along one side." People here are, in fact, so desirous of maintaining tradition that they aren't even willing to consider replacing the box, let alone reconsidering the justice of the lottery itself. Old Man Warner says,

Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work any more, live that way for a while [....]. There's always been a lottery [...].

Again, an older person takes issue with the perceived values of the younger, and Old Man Warner seems to speak for the town (whose residents won't even seriously consider using a new box that isn't broken down). In this story, then, it is the town holding on to the past and the individual— Tessie Hutchinson—being punished for it; in the first story, it is one individual holding on to the past and the town being punished for it.

Identify significant differences between "The Lottery" and "The Possibility of Evil." 

The original question had to be edited down.  One particular difference between both stories is that the role of the community is portrayed differently.  In "The Lottery," the community is shown to be a force of terror.  The community is responsible for the perpetration of evil, in this case with Tessie.  The community's tradition of stoning an individual is reflective of this terror.  The agent of action in such destruction is the community.

In "The Possibility of Evil," it is the individual that is responsible for social destruction.  Miss Strangeworth is a "one woman wrecking crew" of the social fabric.  In a way, she terrorizes the community.  No one else can do what she does.  The community is one in which individuals are on their own, except for Miss Strangeworth's intrusiveness.  In this narrative, the individual, not the community, is responsible for the terror in the community.  Both works detail how the destruction of the social fabric is a part of the small town experience.  Yet, in each, the agents of action for this destruction differs.