Please give a protocol to incrementally reveal information.
A politician wishes to make a yes/no announcement with out shocking the economy. They set a date 100 days in the future, and every day reveal more about the announcement so that at the end of the 100 days, there is no uncertainty about the announcement. What should the politician reveal each day?
An example of a (mediocre) protocol is to fill a urn with a ball with the true announcement and 99 randomly chosen announcements and each day the politician removes one of the randomly chosen announcements. This protocol is good because by inspecting the urn each day, the public's uncertainty either decreases or stays the same until at the end there is no uncertainty. However, this protocol is bad because it does not reduce the publics uncertainty by a consistent amount each day. The amount of information revealed is only consistent in expectation. For example if on the third to last day the remaining balls are all yes, then the public already knows the announcement. Further it can happen that the last two balls are yes and no. This means that there was no reduction in uncertainty from the beginning.
Thinking of the announcement as communicating 1 bit on a channel, an optimal protocol is a series of communications that so that after the t of n incremental communication, exactly t/n bits have been communicated. Does such a protocol exist? And if so, what is a straight forward implementation such a protocol?