Cook sweet potatoes in a large pot of boiling salted water until halfway cooked, (a knife inserted into center will encounter resistance), about 5 minutes. Drain and cool. (This step can be done 1 day ahead if sweet potatoes are kept covered and refrigerated.)
Combine cider, sugar, butter, nutmeg, and allspice in a large non-stick skillet over medium-high heat. Bring to a boil, stirring often.
Add potatoes and reduce heat so liquid is simmering. Cook 5 minutes, stirring occasionally.
Add cranberries and continue cooking until liquid is reduced to a syrupy glaze and potatoes are tender, about 10 minutes. If the glaze becomes very thick before potatoes become tender, thin with a small amount of cider.
When potatoes are tender, transfer to a serving bowl with a slotted spoon. Season to taste with salt and pepper.
Pour remaining glaze over sweet potatoes and serve.