The Condorcet jury theorem and extension of the franchise with rationally ignorant voters

The Condorcet Jury Theorem (CJT), which provides a justification for democracy, is based on voters who are imperfectly informed insofar as they know the correct policy with a probability of less than one but greater than one-half. We reassess the consequences of the CJT for democracy when extension of the franchise adds equal numbers of non-distinguishable informed and uninformed voters to the collective decision making group. Uninformed voters vote correctly with probability one-half. We show that adding equal numbers of informed and uninformed voters maintains the CJT conclusion that enlarging the group of decision makers increases the likelihood of a correct collective decision.