Can we make a voting system where it is cryptographically hard to find a dictator As Wikipedia says, Arrow's impossibility theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

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*If every voter prefers alternative X over alternative Y, then the
group prefers X over Y.


*If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain
unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).


*There is no "dictator": no single voter possesses the power to always determine the group's preference.
Let's say we decide that we really want a ranked-choice voting system, and that we prioritize the first two criteria over the third. But we also have some additional criteria which may or may not be realizable with a ranked-choice voting system:

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*We don't want someone to be a statically appointed dictator. That is, which voter is the dictator in a particular vote should be determined by voter preferences, AKA how voters voted in that vote itself. Ideally the dictator could be any of the voters depending upon which preferences voters have.

*It should be hard, that is, cryptographically hard, to determine which voter is the dictator without knowing what some given fraction, say 50% for example, of the votes are.

*As a strengthening of the previous criterion, we don't want someone who knows what less than the given fraction of the votes are to be able to narrow down who the dictator is to some given fraction of the voting population. Again, we could use 50% as an a example.

Is it known whether it possible to create a ranked choice voting system that meets these criteria? If so, is it possible or not?
 A: After reading some of the literature mentioned in the comments, I am convinced that my original question was flawed. Specifically, I accept that there is no way to meet the first two fairness criteria without having a dictator that is completely determined by the voting system, independently of the votes cast.
I think the closest thing to what I had in mind, while being actually possible, would be to randomize what the voting system is itself, after the votes are counted, through cryptographically secure means. Since all voting systems meeting the first two criteria have system-determined dictators, all such systems would either not meet those two criteria, or be equivalent to randomly picking one of some non-empty subset of voters to be the dictator.
I am less certain about this, but I think that if any non-empty subset other than the entire voting population is chosen via looking at what they voted, then that would violate, the second fairness criteria, which is known as independence of irrelevant alternatives, hereafter IIA.
For example, choosing one of voters that had the most common top preference is equivalent to first-past-the-post voting which is known to violate IIA.
Similarly, choosing to remove from the random dictator pool the voters who voted the least common way, (leaving them all there in the unanimous case,) would violate IIA since adding alternatives can push voters in and out of that pool, therefore affecting the outcome under some randomizations.
