Pare, dice potatoes and cook in boiling water until very tender. Drain, saving liquid. Reserve 1 cup for softening yeast. Mash potatoes thoroughly and return to liquid. Cool to lukewarm.
Soften yeast in reserved lukewarm potato water and add to potatoes with remaining ingredients. Beat well. Cover and let stand at room temperature 24 hours. Pour into sterilized jar. Cover and store in cool, dark place.
Use 1 cup of the mixture to replace 1 yeast cake in recipes. Fresh starter should be prepared at least every 2 weeks, using 1 cup of the old or a fresh cake of yeast.