Fair voting procedure when there are many issues When several people have to decide about a single yes/no issue*, the natural decision rule to use is the majority rule. 

But when there are many issues to decide upon, the majority rule is "unfair" in the following sense: it is possible that the majority's opinion will be accepted on all topics and the minority's opinion will not be accepted on any topic. As an extreme example, it is possible that 51% of the population will decide about 100% of the issues.

I am looking for a decision rule which prevents this unfairness.

Formally, define a "uniform group" as a group of people who always vote in the same way. Define the "acceptance rate" of a uniform group as the percentage of issues on which the opinion of the uniform group got accepted. 

Define a "fair decision rule" as a rule for which, for every uniform group containing X percent of the population, the acceptance rate tends to X when the number of issues tends to infinity.

MY QUESTION IS: Does there exist a fair division rule as defined above?

(* I restrict the question to yes/no issues, since when the issues are not binary the problems are much more complicated).
That's interesting: the flavor of the frequentist approach to probability used for a socio-political fairness criterion: if my measure as a population group is $0&lt;p&lt;1$, and known, then my opinion should be accepted by the whole at the same measure, as number of issues goes to infinity. In other words, current observed acceptance rate should be a consistent estimator of theoretical acceptance rate, and equal to my measure.  

Then it is very easy to create such a decision rule, while saving public money: no need to hold one referendum after another, just construct a die, with as many sides as there are "uniform groups", with the die's weight distributed in such a way that the side representing uniform group $i$ will have probability of turning up equal to $p_i$. It won't be difficult to construct, and publicly and objectively test it for the desired properties.

Then, wherever an issue comes up for voting, just roll the die. And ok, spend some money for a suitable public ceremony.

Whenever there is a census, the relative size of each uniform group can be re-measured and a new die can be constructed.

Why do I have the feeling though that no uniform group is likely to ever accept such a scheme?

(This of course puts aside the importance of each issue, in general, for each uniform group, etc, but I took that from the OP which concentrates on number of issues, irrespective of what the issues are about, and to whom they matter and how much they matter, and how do we measure that etc).