Put 1 cup of mayo in a large bowl. Put the vinegar, salt, sugar, pickling spice in a small saucepan. Bring to a boil while stirring to dissolve the sugar and salt, remove from heat and let steep for 5 minutes.
Strain into the mayo and place the coleslaw dressing in refrigerator to cool.
Quarter the cabbage and remove the core and any wilted leaves. Slice the cabbage as thinly as you can. Cut through the shreds 4 or 5 times so that the cabbage is in somewhat bite-size pieces. Grate the carrots.
Toss the cabbage, carrots, raisins, and celery seed in the coleslaw dressing until everything is well coated and mixed.