You can steep the juice in advance; add the ginger beer and rum just before serving so the punch will be fizzy. Ginger beer, which actually contains no alcohol, tastes like a spicy ginger ale.
Combine first 5 ingredients in a large Dutch oven; bring to a boil. Remove from heat; let stand 30 minutes.
Strain cranberry mixture through a fine sieve into a bowl; discard solids. Chill thoroughly. Stir in rum and ginger beer just before serving.
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